Cricketr analyzes Ind-Aus faceoff in WTC 2023!!

“The unexamined life is not worth living.” – Socrates

“There is no easy way from the earth to the stars.” – Seneca

“If you want to go fast, go alone. If you want to go far, go together.” – African Proverb

1. Introduction

In this post, I put my R package cricketr to analyze the Indian and Australia World Test Championship (WTC) final squad ahead of the World Test Championship 2023.My R package cricketr had its birth on Jul 4, 2015. Cricketr uses data from Cricinfo.

Indian squad

Rohit Sharma (Captain), Shubman Gill, Cheteshwar Pujara, Virat Kohli, Ajinkya Rahane, Ravindra Jadeja, Shardul Thakur, Mohd. Shami, Mohd. Siraj, Ishan Kishan (wk).

According to me, Ishan Kishan has more experience than KS Bharat, though Rishabh Pant would have been the ideal wicket keeper/left-handed batsman. I think Shardul Thakur would be handful in the English conditions. For a spinner it either Ashwin or Jadeja. Maybe the balance shifts in favor of Jadeja

Australian squad

Pat Cummins (capt), Alex Carey (wk), Cameron Green, Josh Hazlewood, Usman Khawaja, Marnus Labuschagne, Nathan Lyon, Todd Murphy, Steven Smith (vice-capt), Mitchell Starc, David Warner.

Not sure if Scott Boland would fill in, instead of Todd Murphy 1

Let me give you a lay-of-the-land (post) below

The post below is organized into the following parts

Analysis of Indian WTC batsmen from Jan 2016 – May 2023
Analysis of Indian WTC batsmen against Australia from Jan 2016 -May 2023
Analysis of Australian WTC batsmen from Jan 2016 – May 2023
Analysis of Australian WTC batsmen against India from Jan 2016 -May 2023
Analysis of Indian WTC bowlers from Jan 2016 – May 2023
Analysis of Indian WTC bowlers against Australia from Jan 2016 -May 2023
Analysis of Australian WTC bowlers from Jan 2016 – May 2023
Analysis of Australian WTC bowlers gainst India from Jan 2016 -May 2023
Team analysis of India and Australia

All the above analysis use data from ESPN Statsguru and use my R pakage cricketr

The data for the different players have been obtained using calls such as the ones below.

# Get Shubman Gill's batting data
#shubman <-getPlayerData(1070173,dir=".",file="shubman.csv",type="batting",homeOrAway=c(1,2), result=c(1,2,4))
#shubmansp <- getPlayerDataSp(1070173,tdir=".",tfile="shubmansp.csv",ttype="batting")

#Get Shubman Gill's data from Jan 2016 - May 2023
#df <-getPlayerDataHA(1070173,tfile="shubman1.csv",type="batting", matchType="Test")
#df1=getPlayerDataOppnHA(infile="shubman1.csv",outfile="shubmanTestAus.csv",startDate="2016-01-01",endDate="2023-05-01")

#Get Shubman Gills data from Jan 2016 - May 2023, against Australia
#df <-getPlayerDataHA(1070173,tfile="shubman1.csv",type="batting", matchType="Test")
#df1=getPlayerDataOppnHA(infile="shubman1.csv",outfile="shubmanTestAus.csv",opposition="Australia",startDate="2016-01-01",endDate="2023-05-01")

Note: To get data for bowlers we need to use the corresponding profile no and use type =‘bowling’. Details in my posts below

To do similar analysis please go through the following posts

Note 1: I will not be analysing each and every chart as the charts are quite self-explanatory

Note 2: I have had to tile charts together otherwise this will become a very, very long post. You are free to use my R package cricketr and check out for yourself ##3. Analysis of India WTC batsmen from Jan 2016 – May 2023

Findings

Kohli has the best average of 48+. India has won when Rohit and Rahane played well
Kohli’s tops the list in cumulative average runs, followed by Pujara and Rohit is 3rd. Gill is on the upswing.
Against Australia Pujara has the best cumulative average runs record followed by Rahane, with Gill in hot pursuit. In the strike rate department Gill tops followed by Rohit and Rahane
Since 2016 Smith, Labuschagne has an average of 53+ since 2016!! Warner & Khwaja are at ~46
Australia has won matches when Smith, Warner and Khwaja have played well.
Labuschagne, Smith and C Green have good records against India. Indian bowlers will need to contain them
Ashwin has the highest wickets followed by Jadeja against all teams. Ashwin’s performance has dropped over the years, while Siraj has been becoming better
Jadeja has the best economy rate followed by Ashwin
Against Australia specifically Jadeja has the best record followed by Ashwin. Jadeja has the best economy against Australia, followed by Siraj, then Ashwin
Cummins, Starc and Lyons are the best performers for Australia. Hazzlewood, Cummins have the best economy against all opposition
Against India Lyon, Cummins and Hazzlewood have performed well
Hazzlewood, Lyon have a good economy rate against India
Against Australia India has won 17 times, lost 60 and drawn 22 in Australia. At home India won 42, tied 2, lost 28 and drawn 24
At the Oval where the World Test Championship is going to be held India has won 4, lost 10 and drawn 10.

Note 3: You can also read this post at Rpubs at ind-aus-WTC !! The formatting will be nicer!

Note 4: You can download this post as PDF to read at your leisure ind-aus-WTC.pdf

2. Install the cricketr package

if (!require("cricketr")){
    install.packages("cricketr",lib = "c:/test")
}
library(cricketr)

3a. Basic analysis

The analyses below include – Runs frequency plot – Mean strike rate – Run Ranges

Kohli’s strike rate increases with increasing runs, while Gill’s seems to drop. So it is with Pujara & Rahane

par(mfrow=c(3,3))
par(mar=c(4,4,2,2))
batsmanRunsFreqPerf("kohliTest.csv","Kohli")
batsmanMeanStrikeRate("kohliTest.csv","Kohli")
batsmanRunsRanges("kohliTest.csv","Kohli")

batsmanRunsFreqPerf("rohitTest.csv","Rohit")
batsmanMeanStrikeRate("rohitTest.csv","Rohit")
batsmanRunsRanges("rohitTest.csv","Rohit")

batsmanRunsFreqPerf("shubmanTest.csv","S Gill")
batsmanMeanStrikeRate("shubmanTest.csv","S Gill")
batsmanRunsRanges("shubmanTest.csv","S Gill")

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))
batsmanRunsFreqPerf("rahaneTest.csv","Rahane")
batsmanMeanStrikeRate("rahaneTest.csv","Rahane")
batsmanRunsRanges("rahaneTest.csv","Rahane")

batsmanRunsFreqPerf("pujaraTest.csv","Pujara")
batsmanMeanStrikeRate("pujaraTest.csv","Pujara")
batsmanRunsRanges("pujaraTest.csv","Pujara")

3b. More analyses

Kohli hits roughly 5 4s in his 50 versus Gill,Pujara who is able to smash 6 4s.

par(mfrow=c(3,3))
par(mar=c(4,4,2,2))

batsman4s("kohliTest.csv","Kohli")
batsman6s("kohliTest.csv","Kohli")
batsmanMeanStrikeRate("kohliTest.csv","Kohli")

batsman4s("rohitTest.csv","Rohit")
batsman6s("rohitTest.csv","Rohit")
batsmanMeanStrikeRate("rohitTest.csv","Rohit")

batsman4s("shubmanTest.csv","S Gill")
batsman6s("shubmanTest.csv","S Gill")
batsmanMeanStrikeRate("shubmanTest.csv","S Gill")

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

batsman4s("rahaneTest.csv","Rahane")
batsman6s("rahaneTest.csv","Rahane")
batsmanMeanStrikeRate("rahane.csv","Rahane")

batsman4s("pujaraTest.csv","Pujara")
batsman6s("pujaraTest.csv","Pujara")
batsmanMeanStrikeRate("pujaraTest.csv","Pujara")

3c.Boxplot histogram plot

This plot shows a combined boxplot of the Runs ranges and a histog2ram of the Runs Frequency Kohli’s average is 48, while Rohit,Pujara is 40 with Rahane and Gill around 33.

batsmanPerfBoxHist("kohliTest.csv","Kohli")

batsmanPerfBoxHist("rohitTest.csv","Rohit")

batsmanPerfBoxHist("shubmanTest.csv","S Gill")

batsmanPerfBoxHist("rahaneTest.csv","Rahane")

batsmanPerfBoxHist("pujaraTest.csv","Pujara")

3d. Contribution to won and lost matches

For the functions below you will have to use the getPlayerDataSp() function. When Rohit Sharma and Pujara have played well India have tended to win more often

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanContributionWonLost("kohlisp.csv","Kohli")
batsmanContributionWonLost("rohitsp.csv","Rohit")
batsmanContributionWonLost("rahanesp.csv","Rahane")
batsmanContributionWonLost("pujarasp.csv","Pujara")

3e. Performance at home and overseas

This function also requires the use of getPlayerDataSp() as shown above. This can only be used for Test matches

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanPerfHomeAway("kohlisp.csv","Kohli")
batsmanPerfHomeAway("rohitsp.csv","Rohit")
batsmanPerfHomeAway("rahanesp.csv","Rahane")
batsmanPerfHomeAway("pujarasp.csv","Pujara")

3f. Batsman average at different venues

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("kohliTest.csv","Kohli")
batsmanAvgRunsGround("rohitTest.csv","Rohit")
batsmanAvgRunsGround("rahaneTest.csv","Rahane")
batsmanAvgRunsGround("pujaraTest.csv","Pujara")

3g. Batsman average against different opposition

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsOpposition("kohliTest.csv","Kohli")
batsmanAvgRunsOpposition("rohitTest.csv","Rohit")
batsmanAvgRunsOpposition("rahaneTest.csv","Rahane")
batsmanAvgRunsOpposition("pujaraTest.csv","Pujara")

3h. Runs Likelihood of batsman

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanRunsLikelihood("kohli.csv","Kohli")

## Summary of  Kohli 's runs scoring likelihood
## **************************************************
## 
## There is a 52.91 % likelihood that Kohli  will make  12 Runs in  26 balls over 35  Minutes 
## There is a 30.81 % likelihood that Kohli  will make  52 Runs in  100 balls over  139  Minutes 
## There is a 16.28 % likelihood that Kohli  will make  142 Runs in  237 balls over 335  Minutes

batsmanRunsLikelihood("rohit.csv","Rohit")

## Summary of  Rohit 's runs scoring likelihood
## **************************************************
## 
## There is a 43.24 % likelihood that Rohit  will make  10 Runs in  21 balls over 32  Minutes 
## There is a 45.95 % likelihood that Rohit  will make  46 Runs in  85 balls over  124  Minutes 
## There is a 10.81 % likelihood that Rohit  will make  110 Runs in  199 balls over 282  Minutes

batsmanRunsLikelihood("rahane.csv","Rahane")

## Summary of  Rahane 's runs scoring likelihood
## **************************************************
## 
## There is a 7.75 % likelihood that Rahane  will make  124 Runs in  224 balls over 318  Minutes 
## There is a 62.02 % likelihood that Rahane  will make  12 Runs in  26 balls over  37  Minutes 
## There is a 30.23 % likelihood that Rahane  will make  55 Runs in  113 balls over 162  Minutes

batsmanRunsLikelihood("pujara.csv","Pujara")

## Summary of  Pujara 's runs scoring likelihood
## **************************************************
## 
## There is a 60.49 % likelihood that Pujara  will make  15 Runs in  38 balls over 55  Minutes 
## There is a 31.48 % likelihood that Pujara  will make  62 Runs in  142 balls over  204  Minutes 
## There is a 8.02 % likelihood that Pujara  will make  153 Runs in  319 balls over 445  Minutes

3h1. Moving average of batsman

Kohli’s moving average in tests seem to havw dropped after a peak in 2017, 2018. So it is with Rahane

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanMovingAverage("kohli.csv","Kohli")
batsmanMovingAverage("rohit.csv","Rohit")
batsmanMovingAverage("rahane.csv","Rahane")
batsmanMovingAverage("pujara.csv","Pujara")

3i. Cumulative Average runs of batsman in career

Kohli’s cumulative average averages to ~48. Shubman Gill’s cumulative average is on the rise.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanCumulativeAverageRuns("kohliTest.csv","Kohli")

batsmanCumulativeAverageRuns("rohitTest.csv","Rohit")

batsmanCumulativeAverageRuns("rahaneTest.csv","Rahane")

batsmanCumulativeAverageRuns("pujaraTest.csv","Pujara")

batsmanCumulativeAverageRuns("shubmanTest.csv","S Gill")

3j Cumulative Average strike rate of batsman in career

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanCumulativeStrikeRate("kohliTest.csv","Kohli")

batsmanCumulativeStrikeRate("rohitTest.csv","Rohit")

batsmanCumulativeStrikeRate("rahaneTest.csv","Rahane")

batsmanCumulativeStrikeRate("pujaraTest.csv","Pujara")

batsmanCumulativeStrikeRate("shubmanTest.csv","S Gill")

3k. Future Runs forecast

Here are plots that forecast how the batsman will perform in future. In this case 90% of the career runs trend is uses as the training set. the remaining 10% is the test set.

A Holt-Winters forecating model is used to forecast future performance based on the 90% training set. The forecated runs trend is plotted. The test set is also plotted to see how close the forecast and the actual matches

Take a look at the runs forecasted for the batsman below.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanPerfForecast("kohli.csv","Kohli")
batsmanPerfForecast("rohit.csv","Rohit")
batsmanPerfForecast("rahane.csv","Rahane")
batsmanPerfForecast("pujara.csv","Pujara")

3l. Relative Mean Strike Rate plot

The plot below compares the Mean Strike Rate of the batsman for each of the runs ranges of 10 and plots them. The plot indicate the following

frames <- list("kohliTest.csv","rohitTest.csv","pujaraTest.csv","rahaneTest.csv","shubmanTest.csv")
names <- list("Kohli","Rohit","Pujara","Rahane","S Gill")
relativeBatsmanSR(frames,names)

3m. Relative Runs Frequency plot

The plot below gives the relative Runs Frequency Percetages for each 10 run bucket. The plot below show

frames <- list("kohliTest.csv","rohitTest.csv","pujaraTest.csv","rahaneTest.csv","shubmanTest.csv")
names <- list("Kohli","Rohit","Pujara","Rahane","S Gill")
relativeRunsFreqPerf(frames,names)

3n. Relative cumulative average runs in career

Kohli’s tops the list, followed by Pujara and Rohit is 3rd. Gill is on the upswing. Hope he performs well.

frames <- list("kohliTest.csv","rohitTest.csv","pujaraTest.csv","rahaneTest.csv","shubmanTest.csv")
names <- list("Kohli","Rohit","Pujara","Rahane","S Gill")
relativeBatsmanCumulativeAvgRuns(frames,names)

3o. Relative cumulative average strike rate in career

ROhit has the best strike rate followed by Kohli, with Shubman Gill ctaching up fast

frames <- list("kohliTest.csv","rohitTest.csv","pujaraTest.csv","rahaneTest.csv","shubmanTest.csv")
names <- list("Kohli","Rohit","Pujara","Rahane","S Gill")
relativeBatsmanCumulativeStrikeRate(frames,names)

3p. Check Batsman In-Form or Out-of-Form

The below computation uses Null Hypothesis testing and p-value to determine if the batsman is in-form or out-of-form. For this 90% of the career runs is chosen as the population and the mean computed. The last 10% is chosen to be the sample set and the sample Mean and the sample Standard Deviation are caculated.

The Null Hypothesis (H0) assumes that the batsman continues to stay in-form where the sample mean is within 95% confidence interval of population mean The Alternative (Ha) assumes that the batsman is out of form the sample mean is beyond the 95% confidence interval of the population mean.

A significance value of 0.05 is chosen and p-value us computed If p-value >= .05 – Batsman In-Form If p-value < 0.05 – Batsman Out-of-Form

Note Ideally the p-value should be done for a population that follows the Normal Distribution. But the runs population is usually left skewed. So some correction may be needed. I will revisit this later

This is done for the Top 4 batsman

checkBatsmanInForm("kohli.csv","Kohli")

## [1] "**************************** Form status of Kohli ****************************\n\n Population size: 154  Mean of population: 47.03 \n Sample size: 18  Mean of sample: 32.22 SD of sample: 42.45 \n\n Null hypothesis H0 : Kohli 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : Kohli 's sample average is below the 95% confidence interval of population average\n\n Kohli 's Form Status: In-Form because the p value: 0.078058  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("rohit.csv","Rohit")

## [1] "**************************** Form status of Rohit ****************************\n\n Population size: 66  Mean of population: 37.03 \n Sample size: 8  Mean of sample: 37.88 SD of sample: 35.38 \n\n Null hypothesis H0 : Rohit 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : Rohit 's sample average is below the 95% confidence interval of population average\n\n Rohit 's Form Status: In-Form because the p value: 0.526254  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("rahane.csv","Rahane")

## [1] "**************************** Form status of Rahane ****************************\n\n Population size: 116  Mean of population: 34.78 \n Sample size: 13  Mean of sample: 21.38 SD of sample: 21.96 \n\n Null hypothesis H0 : Rahane 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : Rahane 's sample average is below the 95% confidence interval of population average\n\n Rahane 's Form Status: Out-of-Form because the p value: 0.023244  is less than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("pujara.csv","Pujara")

## [1] "**************************** Form status of Pujara ****************************\n\n Population size: 145  Mean of population: 41.93 \n Sample size: 17  Mean of sample: 33.24 SD of sample: 31.74 \n\n Null hypothesis H0 : Pujara 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : Pujara 's sample average is below the 95% confidence interval of population average\n\n Pujara 's Form Status: In-Form because the p value: 0.137319  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("shubman.csv","S Gill")

## [1] "**************************** Form status of S Gill ****************************\n\n Population size: 23  Mean of population: 30.43 \n Sample size: 3  Mean of sample: 51.33 SD of sample: 66.88 \n\n Null hypothesis H0 : S Gill 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : S Gill 's sample average is below the 95% confidence interval of population average\n\n S Gill 's Form Status: In-Form because the p value: 0.687033  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

3q. Predicting Runs given Balls Faced and Minutes at Crease

A multi-variate regression plane is fitted between Runs and Balls faced +Minutes at crease.

BF <- seq( 10, 400,length=15)
Mins <- seq(30,600,length=15)
newDF <- data.frame(BF,Mins)
kohli1 <- batsmanRunsPredict("kohli.csv","Kohli",newdataframe=newDF)
rohit1 <- batsmanRunsPredict("rohit.csv","Rohit",newdataframe=newDF)
pujara1 <- batsmanRunsPredict("pujara.csv","Pujara",newdataframe=newDF)
rahane1 <- batsmanRunsPredict("rahane.csv","Rahane",newdataframe=newDF)
sgill1 <- batsmanRunsPredict("shubman.csv","S Gill",newdataframe=newDF)

batsmen <-cbind(round(kohli1$Runs),round(rohit1$Runs),round(pujara1$Runs),round(rahane1$Runs),round(sgill1$Runs))
colnames(batsmen) <- c("Kohli","Rohit","Pujara","Rahane","S Gill")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns

##    BallsFaced MinsAtCrease Kohli Rohit Pujara Rahane S Gill
## 1          10           30     6     3      3      2      7
## 2          38           71    24    19     16     17     24
## 3          66          111    41    35     29     31     40
## 4          94          152    58    51     42     45     56
## 5         121          193    76    66     55     59     73
## 6         149          234    93    82     68     74     89
## 7         177          274   110    98     80     88    106
## 8         205          315   128   114     93    102    122
## 9         233          356   145   129    106    116    139
## 10        261          396   163   145    119    130    155
## 11        289          437   180   161    132    145    171
## 12        316          478   197   177    144    159    188
## 13        344          519   215   192    157    173    204
## 14        372          559   232   208    170    187    221
## 15        400          600   249   224    183    202    237

4. Analysis of India WTC batsmen from Jan 2016 – May 2023 against Australia

4a. Relative cumulative average

Against Australia specifically between 2016 – 2023, Pujara has the best record followed by Rahane, with Gill in hot pursuit. Kohli and Rohit trail behind

frames <- list("kohliTestAus.csv","rohitTestAus.csv","pujaraTestAus.csv","rahaneTestAus.csv","shubmanTestAus.csv")
names <- list("Kohli","Rohit","Pujara","Rahane","S Gill")
relativeBatsmanCumulativeAvgRuns(frames,names)

4b. Relative cumulative average strike rate in career

In the Strike Rate department Gill tops followed by Rohit and Rahane

frames <- list("kohliTestAus.csv","rohitTestAus.csv","pujaraTestAus.csv","rahaneTestAus.csv","shubmanTestAus.csv")
names <- list("Kohli","Rohit","Pujara","Rahane","S Gill")
relativeBatsmanCumulativeStrikeRate(frames,names)

5. Analysis of Australia WTC batsmen from Jan 2016 – May 2023

5a Basic analyses

par(mfrow=c(3,3))
par(mar=c(4,4,2,2))
batsmanRunsFreqPerf("stevesmithTest.csv","S Smith")
batsmanMeanStrikeRate("stevesmithTest.csv","S Smith")
batsmanRunsRanges("stevesmithTest.csv","S Smith")

batsmanRunsFreqPerf("warnerTest.csv","Warner")
batsmanMeanStrikeRate("warnerTest.csv","Warner")
batsmanRunsRanges("warnerTest.csv","Warner")

batsmanRunsFreqPerf("labuschagneTest.csv","M Labuschagne")
batsmanMeanStrikeRate("labuschagneTest.csv","M Labuschagne")
batsmanRunsRanges("labuschagneTest.csv","M Labuschagne")

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))
batsmanRunsFreqPerf("cgreenTest.csv","C Green")
batsmanMeanStrikeRate("cgreenTest.csv","C Green")
batsmanRunsRanges("cgreenTest.csv","C Green")

batsmanRunsFreqPerf("khwajaTest.csv","Khwaja")
batsmanMeanStrikeRate("khwajaTest.csv","Khwaja")
batsmanRunsRanges("khwajaTest.csv","Khwaja")

5b. More analyses

par(mfrow=c(3,3))
par(mar=c(4,4,2,2))
batsman4s("stevesmithTest.csv","S Smith")
batsman6s("stevesmithTest.csv","S Smith")
batsmanMeanStrikeRate("stevesmithTest.csv","S Smith")

batsman4s("warnerTest.csv","Warner")
batsman6s("warnerTest.csv","Warner")
batsmanMeanStrikeRate("warnerTest.csv","Warner")

batsman4s("labuschagneTest.csv","M Labuschagne")
batsman6s("labuschagneTest.csv","M Labuschagne")
batsmanMeanStrikeRate("labuschagneTest.csv","M Labuschagne")

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))
batsman4s("cgreenTest.csv","C Green")
batsman6s("cgreenTest.csv","C Green")
batsmanMeanStrikeRate("cgreenTest.csv","C Green")

batsman4s("khwajaTest.csv","Khwaja")
batsman6s("khwajaTest.csv","Khwaja")
batsmanMeanStrikeRate("khwajaTest.csv","Khwaja")

5c.Boxplot histogram plot

This plot shows a combined boxplot of the Runs ranges and a histog2ram of the Runs Frequency

Smith, Labuschagne has an average of 53+ since 2016!! Warner & Khwaja are at ~46

batsmanPerfBoxHist("stevesmithTest.csv","S Smith")

batsmanPerfBoxHist("warnerTest.csv","Warner")

batsmanPerfBoxHist("labuschagneTest.csv","M Labuschagne")

batsmanPerfBoxHist("cgreenTest.csv","C Green")

batsmanPerfBoxHist("khwajaTest.csv","Khwaja")

5d. Contribution to won and lost matches

For the 2 functions below you will have to use the getPlayerDataSp() function. Australia has won matches when Smith, Warner and Khwaja have played well.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanContributionWonLost("stevesmithsp.csv","S Smith")
batsmanContributionWonLost("warnersp.csv","Warner")
batsmanContributionWonLost("labuschagnesp.csv","M Labuschagne")
batsmanContributionWonLost("cgreensp.csv","C Green")

batsmanContributionWonLost("khwajasp.csv","Khwaja")

5e. Performance at home and overseas

This function also requires the use of getPlayerDataSp() as shown above. This can only be used for Test matches

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanPerfHomeAway("stevesmithsp.csv","S Smith")
batsmanPerfHomeAway("warnersp.csv","Warner")
batsmanPerfHomeAway("labuschagnesp.csv","M Labuschagne")
batsmanPerfHomeAway("cgreensp.csv","C Green")

batsmanPerfHomeAway("khwajasp.csv","Khwaja")

5f. Batsman average at different venues

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanAvgRunsGround("stevesmithTest.csv","S Smith")
batsmanAvgRunsGround("warnerTest.csv","Warner")
batsmanAvgRunsGround("labuschagneTest.csv","M Labuschagne")
batsmanAvgRunsGround("cgreenTest.csv","C Green")

batsmanAvgRunsGround("khwajaTest.csv","Khwaja")

5g. Batsman average against different opposition

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanAvgRunsOpposition("stevesmithTest.csv","S Smith")
batsmanAvgRunsOpposition("warnerTest.csv","Warner")
batsmanAvgRunsOpposition("labuschagneTest.csv","M Labuschagne")
batsmanAvgRunsOpposition("khwajaTest.csv","Khwaja")

5h. Runs Likelihood of batsman

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanRunsLikelihood("stevesmithTest.csv","S Smith")

## Summary of  S Smith 's runs scoring likelihood
## **************************************************
## 
## There is a 58.76 % likelihood that S Smith  will make  21 Runs in  38 balls over 56  Minutes 
## There is a 24.74 % likelihood that S Smith  will make  70 Runs in  148 balls over  210  Minutes 
## There is a 16.49 % likelihood that S Smith  will make  148 Runs in  268 balls over 398  Minutes

batsmanRunsLikelihood("warnerTest.csv","Warner")

## Summary of  Warner 's runs scoring likelihood
## **************************************************
## 
## There is a 7.22 % likelihood that Warner  will make  155 Runs in  253 balls over 372  Minutes 
## There is a 62.89 % likelihood that Warner  will make  14 Runs in  21 balls over  32  Minutes 
## There is a 29.9 % likelihood that Warner  will make  65 Runs in  94 balls over 135  Minutes

batsmanRunsLikelihood("labuschagneTest.csv","M Labuschagne")

## Summary of  M Labuschagne 's runs scoring likelihood
## **************************************************
## 
## There is a 32.76 % likelihood that M Labuschagne  will make  74 Runs in  144 balls over 206  Minutes 
## There is a 55.17 % likelihood that M Labuschagne  will make  22 Runs in  37 balls over  54  Minutes 
## There is a 12.07 % likelihood that M Labuschagne  will make  168 Runs in  297 balls over 420  Minutes

batsmanRunsLikelihood("khwajaTest.csv","Khwaja")

## Summary of  Khwaja 's runs scoring likelihood
## **************************************************
## 
## There is a 64.94 % likelihood that Khwaja  will make  14 Runs in  29 balls over 42  Minutes 
## There is a 27.27 % likelihood that Khwaja  will make  79 Runs in  148 balls over  210  Minutes 
## There is a 7.79 % likelihood that Khwaja  will make  165 Runs in  351 balls over 515  Minutes

5i. Moving average of batsman

Smith and Warner’s moving average has been on a downward trend lately. Khwaja is playing well

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanMovingAverage("stevesmith.csv","S Smith")
batsmanMovingAverage("warner.csv","Warner")
batsmanMovingAverage("labuschagne.csv","M Labuschagne")
batsmanMovingAverage("khwaja.csv","Khwaja")

5j. Cumulative Average runs of batsman in career

Labuschagne, SMith and Warner havwe very good cumulative average

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanCumulativeAverageRuns("stevesmithTest.csv","S Smith")

batsmanCumulativeAverageRuns("warnerTest.csv","Warner")

batsmanCumulativeAverageRuns("labuschagneTest.csv","M Labuschagne")

batsmanCumulativeAverageRuns("khwajaTest.csv","Khwaja")

5k. Cumulative Average strike rate of batsman in career

Warner towers over the others in the cumulative strike rate, followed by Labuschagne and Smith

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanCumulativeStrikeRate("stevesmithTest.csv","S Smith")

batsmanCumulativeStrikeRate("warnerTest.csv","Warner")

batsmanCumulativeStrikeRate("labuschagneTest.csv","M Labuschagne")

batsmanCumulativeStrikeRate("khwajaTest.csv","Khwaja")

5l. Future Runs forecast

Here are plots that forecast how the batsman will perform in future. In this case 90% of the career runs trend is uses as the training set. the remaining 10% is the test set.

Take a look at the runs forecasted for the batsman below.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

batsmanPerfForecast("stevesmithTest.csv","S Smith")
batsmanPerfForecast("warnerTest.csv","Warner")
batsmanPerfForecast("labuschagneTest.csv","M Labuschagne")
batsmanPerfForecast("khwajaTest.csv","Khwaja")

5m. Relative Mean Strike Rate plot

The plot below compares the Mean Strike Rate of the batsman for each of the runs ranges of 10 and plots them. The plot indicate the following

frames <- list("stevesmithTest.csv","warnerTest.csv","khwajaTest.csv","labuschagneTest.csv","cgreenTest.csv")
names <- list("S Smith","Warner","Khwaja","Labuschagne","C Green")
relativeBatsmanSR(frames,names)

5n. Relative Runs Frequency plot

The plot below gives the relative Runs Frequency Percetages for each 10 run bucket. The plot below show

frames <- list("stevesmithTest.csv","warnerTest.csv","khwajaTest.csv","labuschagneTest.csv","cgreenTest.csv")
names <- list("S Smith","Warner","Khwaja","Labuschagne","C Green")
relativeRunsFreqPerf(frames,names)

5o. Relative cumulative average runs in career

frames <- list("stevesmithTest.csv","warnerTest.csv","khwajaTest.csv","labuschagneTest.csv","cgreenTest.csv")
names <- list("S Smith","Warner","Khwaja","Labuschagne","C Green")
relativeBatsmanCumulativeAvgRuns(frames,names)

5p. Relative cumulative average strike rate in career

frames <- list("stevesmithTest.csv","warnerTest.csv","khwajaTest.csv","labuschagneTest.csv","cgreenTest.csv")
names <- list("S Smith","Warner","Khwaja","Labuschagne","C Green")
relativeBatsmanCumulativeStrikeRate(frames,names)

5q. Check Batsman In-Form or Out-of-Form

A significance value of 0.05 is chosen and p-value us computed If p-value >= .05 – Batsman In-Form If p-value < 0.05 – Batsman Out-of-Form

This is done for the Top 4 batsman

checkBatsmanInForm("stevesmith.csv","S Smith")

## [1] "**************************** Form status of S Smith ****************************\n\n Population size: 144  Mean of population: 53.76 \n Sample size: 17  Mean of sample: 45.65 SD of sample: 56.4 \n\n Null hypothesis H0 : S Smith 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : S Smith 's sample average is below the 95% confidence interval of population average\n\n S Smith 's Form Status: In-Form because the p value: 0.280533  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("warner.csv","Warner")

## [1] "**************************** Form status of Warner ****************************\n\n Population size: 164  Mean of population: 45.2 \n Sample size: 19  Mean of sample: 26.63 SD of sample: 44.62 \n\n Null hypothesis H0 : Warner 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : Warner 's sample average is below the 95% confidence interval of population average\n\n Warner 's Form Status: Out-of-Form because the p value: 0.042744  is less than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("labuschagne.csv","M Labuschagne")

## [1] "**************************** Form status of M Labuschagne ****************************\n\n Population size: 52  Mean of population: 59.56 \n Sample size: 6  Mean of sample: 29.67 SD of sample: 19.96 \n\n Null hypothesis H0 : M Labuschagne 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : M Labuschagne 's sample average is below the 95% confidence interval of population average\n\n M Labuschagne 's Form Status: Out-of-Form because the p value: 0.005239  is less than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBatsmanInForm("khwaja.csv","Khwaja")

## [1] "**************************** Form status of Khwaja ****************************\n\n Population size: 89  Mean of population: 41.62 \n Sample size: 10  Mean of sample: 53.1 SD of sample: 76.34 \n\n Null hypothesis H0 : Khwaja 's sample average is within 95% confidence interval of population average\n Alternative hypothesis Ha : Khwaja 's sample average is below the 95% confidence interval of population average\n\n Khwaja 's Form Status: In-Form because the p value: 0.677691  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

5r. Predicting Runs given Balls Faced and Minutes at Crease

A multi-variate regression plane is fitted between Runs and Balls faced +Minutes at crease.

BF <- seq( 10, 400,length=15)
Mins <- seq(30,600,length=15)
newDF <- data.frame(BF,Mins)
ssmith1 <- batsmanRunsPredict("stevesmith.csv","S Smith",newdataframe=newDF)

warner1 <- batsmanRunsPredict("warner.csv","Warner",newdataframe=newDF)

khwaja1 <- batsmanRunsPredict("khwaja.csv","Khwaja",newdataframe=newDF)
labuschagne1 <- batsmanRunsPredict("labuschagne.csv","Labuschagne",newdataframe=newDF)

cgreen1 <- batsmanRunsPredict("cgreen.csv","C Green",newdataframe=newDF)

batsmen <-cbind(round(ssmith1$Runs),round(warner1$Runs),round(khwaja1$Runs),round(labuschagne1$Runs),round(cgreen1$Runs))
colnames(batsmen) <- c("S Smith","Warner","Khwaja","Labuschagne","C Green")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns

##    BallsFaced MinsAtCrease S Smith Warner Khwaja Labuschagne C Green
## 1          10           30       7     10     10           9      13
## 2          38           71      23     30     24          24      29
## 3          66          111      38     50     38          40      44
## 4          94          152      53     70     53          55      60
## 5         121          193      69     90     67          70      75
## 6         149          234      84    110     81          85      91
## 7         177          274     100    130     95         100     106
## 8         205          315     115    150    109         116     122
## 9         233          356     130    170    123         131     137
## 10        261          396     146    190    137         146     153
## 11        289          437     161    210    151         161     168
## 12        316          478     177    230    165         176     184
## 13        344          519     192    250    179         192     199
## 14        372          559     207    270    193         207     215
## 15        400          600     223    290    207         222     230

6. Analysis of Australia WTC batsmen from Jan 2016 – May 2023 against India

6a. Relative cumulative average runs in career

Labuschagne, Smith and C Green have good records against India

frames <- list("stevesmithTestInd.csv","warnerTestInd.csv","khwajaTestInd.csv","labuschagneTestInd.csv","cgreenTestInd.csv")
names <- list("S Smith","Warner","Khwaja","Labuschagne","C Green")
relativeBatsmanCumulativeAvgRuns(frames,names)

6b. Relative cumulative average strike rate in career

Warner, Labuschagne and Smith have a good strike rate against India

frames <- list("stevesmithTestInd.csv","warnerTestInd.csv","khwajaTestInd.csv","labuschagneTestInd.csv","cgreenTestInd.csv")
names <- list("S Smith","Warner","Khwaja","Labuschagne","C Green")
relativeBatsmanCumulativeStrikeRate(frames,names)

7. Analysis of India WTC bowlers from Jan 2016 – May 2023

7a Wickets frequency chart

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))
bowlerWktsFreqPercent("shamiTest.csv","Shami")
bowlerWktsFreqPercent("sirajTest.csv","Siraj")
bowlerWktsFreqPercent("ashwinTest.csv","Ashwin")
bowlerWktsFreqPercent("jadejaTest.csv","Jadeja")
bowlerWktsFreqPercent("shardulTest.csv","Shardul")

7b Wickets Runs chart

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerWktsRunsPlot("shamiTest.csv","Shami")
bowlerWktsRunsPlot("sirajTest.csv","Siraj")
bowlerWktsRunsPlot("ashwinTest.csv","Ashwin")
bowlerWktsRunsPlot("jadejaTest.csv","Jadeja")
bowlerWktsRunsPlot("shardulTest.csv","Shardul")

7c. Average wickets at different venues

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerAvgWktsGround("shamiTest.csv","Shami")
bowlerAvgWktsGround("sirajTest.csv","Siraj")
bowlerAvgWktsGround("ashwinTest.csv","Ashwin")
bowlerAvgWktsGround("jadejaTest.csv","Jadeja")
bowlerAvgWktsGround("shardulTest.csv","Shardul")

7d Average wickets against different opposition

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerAvgWktsOpposition("shamiTest.csv","Shami")
bowlerAvgWktsOpposition("sirajTest.csv","Siraj")
bowlerAvgWktsOpposition("ashwinTest.csv","Ashwin")
bowlerAvgWktsOpposition("jadejaTest.csv","Jadeja")
bowlerAvgWktsOpposition("shardulTest.csv","Shardul")

7e Cumulative average wickets taken

Ashwin’s performance has dropped over the years, while Siraj has been becoming better

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

bowlerCumulativeAvgWickets("shamiTest.csv","Shami")

bowlerCumulativeAvgWickets("sirajTest.csv","Siraj")

bowlerCumulativeAvgWickets("ashwinTest.csv","Ashwin")

bowlerCumulativeAvgWickets("jadejaTest.csv","Jadeja")

bowlerCumulativeAvgWickets("shardulTest.csv","Shardul")

7g Cumulative average economy rate

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerCumulativeAvgEconRate("shamiTest.csv","Shami")

bowlerCumulativeAvgEconRate("sirajTest.csv","Siraj")

bowlerCumulativeAvgEconRate("ashwinTest.csv","Ashwin")

bowlerCumulativeAvgEconRate("jadejaTest.csv","Jadeja")

bowlerCumulativeAvgEconRate("shardulTest.csv","Shardul")

7h Wicket forecast

Here are plots that forecast how the bowler will perform in future. In this case 90% of the career wickets trend is used as the training set. the remaining 10% is the test set.

A Holt-Winters forecasting model is used to forecast future performance based on the 90% training set. The forecasted wickets trend is plotted. The test set is also plotted to see how close the forecast and the actual matches

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerPerfForecast("shamiTest.csv","Shami")
#bowlerPerfForecast("sirajTest.csv","Siraj")
bowlerPerfForecast("ashwinTest.csv","Ashwin")
bowlerPerfForecast("jadejaTest.csv","Jadeja")
bowlerPerfForecast("shardulTest.csv","Shardul")

7i Relative Wickets Frequency Percentage

frames <- list("shamiTest.csv","sirajTest.csv","ashwinTest.csv","jadejaTest.csv","shardulTest.csv")
names <- list("Shami","Siraj","Ashwin","Jadeja","Shardul")
relativeBowlingPerf(frames,names)

7j Relative Economy Rate against wickets taken

frames <- list("shamiTest.csv","sirajTest.csv","ashwinTest.csv","jadejaTest.csv","shardulTest.csv")
names <- list("Shami","Siraj","Ashwin","Jadeja","Shardul")
relativeBowlingER(frames,names)

7k Relative cumulative average wickets of bowlers in career

Ashwin has the highest wickets followed by Jadeja against all teams

frames <- list("shamiTest.csv","sirajTest.csv","ashwinTest.csv","jadejaTest.csv","shardulTest.csv")
names <- list("Shami","Siraj","Ashwin","Jadeja","Shardul")
relativeBowlerCumulativeAvgWickets(frames,names)

7l Relative cumulative average economy rate of bowlers

Jadeja has the best economy rate followed by Ashwin

frames <- list("shamiTest.csv","sirajTest.csv","ashwinTest.csv","jadejaTest.csv","shardulTest.csv")
names <- list("Shami","Siraj","Ashwin","Jadeja","Shardul")
relativeBowlerCumulativeAvgEconRate(frames,names)

7m Check for bowler in-form/out-of-form

The below computation uses Null Hypothesis testing and p-value to determine if the bowler is in-form or out-of-form. For this 90% of the career wickets is chosen as the population and the mean computed. The last 10% is chosen to be the sample set and the sample Mean and the sample Standard Deviation are caculated.

The Null Hypothesis (H0) assumes that the bowler continues to stay in-form where the sample mean is within 95% confidence interval of population mean The Alternative (Ha) assumes that the bowler is out of form the sample mean is beyond the 95% confidence interval of the population mean.

A significance value of 0.05 is chosen and p-value us computed If p-value >= .05 – Batsman In-Form If p-value < 0.05 – Batsman Out-of-Form

Note: The check for the form status of the bowlers indicate

checkBowlerInForm("shami.csv","Shami")

## [1] "**************************** Form status of Shami ****************************\n\n Population size: 106  Mean of population: 1.93 \n Sample size: 12  Mean of sample: 1.33 SD of sample: 1.23 \n\n Null hypothesis H0 : Shami 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Shami 's sample average is below the 95% confidence\n        interval of population average\n\n Shami 's Form Status: In-Form because the p value: 0.058427  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("siraj.csv","Siraj")

## [1] "**************************** Form status of Siraj ****************************\n\n Population size: 29  Mean of population: 1.59 \n Sample size: 4  Mean of sample: 0.25 SD of sample: 0.5 \n\n Null hypothesis H0 : Siraj 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Siraj 's sample average is below the 95% confidence\n        interval of population average\n\n Siraj 's Form Status: Out-of-Form because the p value: 0.002923  is less than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("ashwin.csv","Ashwin")

## [1] "**************************** Form status of Ashwin ****************************\n\n Population size: 154  Mean of population: 2.77 \n Sample size: 18  Mean of sample: 2.44 SD of sample: 1.76 \n\n Null hypothesis H0 : Ashwin 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Ashwin 's sample average is below the 95% confidence\n        interval of population average\n\n Ashwin 's Form Status: In-Form because the p value: 0.218345  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("jadeja.csv","Jadeja")

## [1] "**************************** Form status of Jadeja ****************************\n\n Population size: 108  Mean of population: 2.22 \n Sample size: 12  Mean of sample: 1.92 SD of sample: 2.35 \n\n Null hypothesis H0 : Jadeja 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Jadeja 's sample average is below the 95% confidence\n        interval of population average\n\n Jadeja 's Form Status: In-Form because the p value: 0.333095  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("shardul.csv","Shardul")

## [1] "**************************** Form status of Shardul ****************************\n\n Population size: 13  Mean of population: 2 \n Sample size: 2  Mean of sample: 0.5 SD of sample: 0.71 \n\n Null hypothesis H0 : Shardul 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Shardul 's sample average is below the 95% confidence\n        interval of population average\n\n Shardul 's Form Status: Out-of-Form because the p value: 0.04807  is less than alpha=  0.05 \n *******************************************************************************************\n\n"

8. Analysis of India WTC bowlers from Jan 2016 – May 2023 against Australia

8a Relative cumulative average wickets of bowlers in career

Against Australia specifically Jadeja has the best record followed by Ashwin

frames <- list("shamiTestAus.csv","sirajTestAus.csv","ashwinTestAus.csv","jadejaTestAus.csv","shardulTestAus.csv")
names <- list("Shami","Siraj","Ashwin","Jadeja","Shardul")
relativeBowlerCumulativeAvgWickets(frames,names)

8b Relative cumulative average economy rate of bowlers

Jadeja has the best economy followed by Siraj, then Ashwin

frames <- list("shamiTestAus.csv","sirajTestAus.csv","ashwinTestAus.csv","jadejaTestAus.csv","shardulTestAus.csv")
names <- list("Shami","Siraj","Ashwin","Jadeja","Shardul")
relativeBowlerCumulativeAvgEconRate(frames,names)

8. Analysis of India WTC bowlers from Jan 2016 – May 2023

8a. Wickets frequency chart

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))
bowlerWktsFreqPercent("cumminsTest.csv","Cummins")
bowlerWktsFreqPercent("starcTest.csv","Starc")
bowlerWktsFreqPercent("hazzlewoodTest.csv","Hazzlewood")
bowlerWktsFreqPercent("todd.csv","Todd")
bowlerWktsFreqPercent("lyonTest.csv","N Lyon")

8b. Wickets frequency chart

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerWktsRunsPlot("cumminsTest.csv","Cummins")
bowlerWktsRunsPlot("starcTest.csv","Starc")
bowlerWktsRunsPlot("hazzlewoodTest.csv","Hazzlewood")
bowlerWktsRunsPlot("todd.csv","Todd")
bowlerWktsRunsPlot("lyonTest.csv","N Lyon")

8c. Average wickets at different venues

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerAvgWktsGround("cumminsTest.csv","Cummins")
bowlerAvgWktsGround("starcTest.csv","Starc")
bowlerAvgWktsGround("hazzlewoodTest.csv","Hazzlewood")
bowlerAvgWktsGround("todd.csv","Todd")
bowlerAvgWktsGround("lyonTest.csv","N Lyon")

8d Average wickets against different opposition

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerAvgWktsOpposition("cumminsTest.csv","Cummins")
bowlerAvgWktsOpposition("starcTest.csv","Starc")
bowlerAvgWktsOpposition("hazzlewoodTest.csv","Hazzlewood")
bowlerAvgWktsOpposition("todd.csv","Todd")
bowlerAvgWktsOpposition("lyonTest.csv","N Lyon")

8e Cumulative average wickets taken

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))

bowlerCumulativeAvgWickets("cumminsTest.csv","Cummins")

bowlerCumulativeAvgWickets("starcTest.csv","Starc")

bowlerCumulativeAvgWickets("hazzlewoodTest.csv","Hazzlewood")

bowlerCumulativeAvgWickets("todd.csv","Todd")

bowlerCumulativeAvgWickets("lyonTest.csv","N Lyon")

8g Cumulative average economy rate

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerCumulativeAvgEconRate("cumminsTest.csv","Cummins")

bowlerCumulativeAvgEconRate("starcTest.csv","Starc")

bowlerCumulativeAvgEconRate("hazzlewoodTest.csv","Hazzlewood")

bowlerCumulativeAvgEconRate("todd.csv","Todd")

bowlerCumulativeAvgEconRate("lyonTest.csv","N Lyon")

8f. Future Wickets forecast

Here are plots that forecast how the bowler will perform in future. In this case 90% of the career wickets trend is used as the training set. the remaining 10% is the test set.

A Holt-Winters forecasting model is used to forecast future performance based on the 90% training set. The forecated wickets trend is plotted. The test set is also plotted to see how close the forecast and the actual matches

par(mfrow=c(2,3))
par(mar=c(4,4,2,2))

bowlerPerfForecast("cumminsTest.csv","Cummins")
bowlerPerfForecast("starcTest.csv","Starc")
bowlerPerfForecast("hazzlewoodTest.csv","Hazzlewood")
bowlerPerfForecast("lyonTest.csv","N Lyon")

8i. Relative Wickets Frequency Percentage

frames <- list("cumminsTest.csv","starcTest.csv","hazzlewoodTest.csv","todd.csv","lyonTest.csv")
names <- list("Cummins","Starc","Hazzlewood","Todd","N Lyon")
relativeBowlingPerf(frames,names)

8j Relative Economy Rate against wickets taken

frames <- list("cumminsTest.csv","starcTest.csv","hazzlewoodTest.csv","todd.csv","lyonTest.csv")
names <- list("Cummins","Starc","Hazzlewood","Todd","N Lyon")
relativeBowlingER(frames,names)

8k Relative cumulative average wickets of bowlers in career

Cummins, Starc and Lyons are the best performers

frames <- list("cumminsTest.csv","starcTest.csv","hazzlewoodTest.csv","todd.csv","lyonTest.csv")
names <- list("Cummins","Starc","Hazzlewood","Todd","N Lyon")
relativeBowlerCumulativeAvgWickets(frames,names)

8l Relative cumulative average economy rate of bowlers

Hazzlewood, Cummins have the best economy against all oppostion

frames <- list("cumminsTest.csv","starcTest.csv","hazzlewoodTest.csv","todd.csv","lyonTest.csv")
names <- list("Cummins","Starc","Hazzlewood","Todd","N Lyon")
relativeBowlerCumulativeAvgEconRate(frames,names)

8o Check for bowler in-form/out-of-form

A significance value of 0.05 is chosen and p-value us computed If p-value >= .05 – Batsman In-Form If p-value < 0.05 – Batsman Out-of-Form

Note: The check for the form status of the bowlers indicate

checkBowlerInForm("cummins.csv","Cummins")

## [1] "**************************** Form status of Cummins ****************************\n\n Population size: 81  Mean of population: 2.46 \n Sample size: 9  Mean of sample: 2 SD of sample: 1.5 \n\n Null hypothesis H0 : Cummins 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Cummins 's sample average is below the 95% confidence\n        interval of population average\n\n Cummins 's Form Status: In-Form because the p value: 0.190785  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("starc.csv","Starc")

## [1] "**************************** Form status of Starc ****************************\n\n Population size: 126  Mean of population: 2.18 \n Sample size: 15  Mean of sample: 1.67 SD of sample: 1.18 \n\n Null hypothesis H0 : Starc 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Starc 's sample average is below the 95% confidence\n        interval of population average\n\n Starc 's Form Status: In-Form because the p value: 0.057433  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("hazzlewood.csv","Hazzlewood")

## [1] "**************************** Form status of Hazzlewood ****************************\n\n Population size: 99  Mean of population: 2.04 \n Sample size: 12  Mean of sample: 1.67 SD of sample: 1.5 \n\n Null hypothesis H0 : Hazzlewood 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : Hazzlewood 's sample average is below the 95% confidence\n        interval of population average\n\n Hazzlewood 's Form Status: In-Form because the p value: 0.204787  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

checkBowlerInForm("lyon.csv","N Lyon")

## [1] "**************************** Form status of N Lyon ****************************\n\n Population size: 193  Mean of population: 2.08 \n Sample size: 22  Mean of sample: 2.95 SD of sample: 1.96 \n\n Null hypothesis H0 : N Lyon 's sample average is within 95% confidence interval \n        of population average\n Alternative hypothesis Ha : N Lyon 's sample average is below the 95% confidence\n        interval of population average\n\n N Lyon 's Form Status: In-Form because the p value: 0.975407  is greater than alpha=  0.05 \n *******************************************************************************************\n\n"

9. Analysis of Australia WTC bowlers from Jan 2016 – May 2023 against India

9a Relative cumulative average wickets of bowlers in career

Against India Lyon, Cummins and Hazzlewood have performed well

frames <- list("cumminsTestInd.csv","starcTestInd.csv","hazzlewoodTestInd.csv","lyonTestInd.csv")
names <- list("Cummins","Starc","Hazzlewood","N Lyon")
relativeBowlerCumulativeAvgWickets(frames,names)

9b Relative cumulative average economy rate of bowlers

Hazzlewood, Lyon have a good economy rate against India

frames <- list("cumminsTestInd.csv","starcTestInd.csv","hazzlewoodTestInd.csv","lyonTestInd.csv")
names <- list("Cummins","Starc","Hazzlewood","N Lyon")
relativeBowlerCumulativeAvgEconRate(frames,names)

10 Analysis of teams – India, Australia

#The data for India & Australia teams were obtained with the following calls

#indiaTest <-getTeamDataHomeAway(dir=".",teamView="bat",matchType="Test",file="indiaTest.csv",save=TRUE,teamName="India")
#australiaTest <- getTeamDataHomeAway(matchType="Test",file="australiaTest.csv",save=TRUE,teamName="Australia")

10a. Win-loss of India against all oppositions in Test cricket

Against Australia India has won 17 times, lost 60 and drawn 22 in Australia. At home India won 42, tied 2, lost 28 and drawn 24

teamWinLossStatusVsOpposition("indiaTest.csv",teamName="India",opposition=c("all"),homeOrAway=c("all"),matchType="Test",plot=TRUE)

10b. Win-loss of Australia against all oppositions in Test cricket

teamWinLossStatusVsOpposition("australiaTest.csv",teamName="Australia",opposition=c("all"),homeOrAway=c("all"),matchType="Test",plot=TRUE)

10c. Win-loss of India against Australia in Test cricket

Against Australia India has won 17 times, lost 60 and drawn 22 in Australia. At home India won 42, tied 2, lost 28 and drawn 24

teamWinLossStatusVsOpposition("indiaTest.csv",teamName="India",opposition=c("Australia"),homeOrAway=c("all"),matchType="Test",plot=TRUE)

10d. Win-loss of India at all away venues

At the Oval where WTC is going to be held India has won 4, lost 10 and drawn 10.

teamWinLossStatusAtGrounds("indiaTest.csv",teamName="India",opposition=c("all"),homeOrAway=c("away"),matchType="Test",plot=TRUE)

10d. Timeline of win-loss of India against Australia in Test cricket

plotTimelineofWinsLosses("indiaTest.csv",team="India",opposition=c("Australia"),
                         homeOrAway=c("away","neutral"), startDate="2016-01-01",endDate="2023-05-01")

11. Conclusion

The above analysis performs various analysis of India and Australia in home and away matches. While we know the performance of the player at India or Australia, we cannot judge how the match will progress in the neutral, swinging conditions of the Oval. Let us hope for a good match!

Feel free to try out your own analysis with cricketr. Have fun with cricketr!!

Also see

To see all posts click Index of posts

IPL 2023:GooglyPlusPlus now with by AI/ML models, near real-time analytics!

It is carnival time again as IPL 2023 is underway!! The new GooglyPlusPlus now includes AI/ML models for computing ball-by-ball Win Probability of matches and each individual player’s Win Probability Contribution (WPC). GooglyPlusPlus uses 2 ML models

Deep Learning (Tensorflow) – accuracy : 0.8584
Logistic Regression (glmnet-tidymodels) : 0.728

Besides, as before, GooglyPlusPlus will also include the usual near real-time analytics with the Shiny app being automatically updated with the previous day’s match data.

Note: The Win Probability Computation can also be done on a live feed of streaming data. Since, I don’t have access to live feeds, the app will show how Win Probability changed during the course of completed matches. For more details on Win Probability and Win Probability Contribution see my posts

GooglyPlusPlus has been also updated with all the latest T20 league’s match data. It includes data from BBL 2022, NTB 2022, CPL 2022, PSL 2023, ICC T20 2022 and now IPL 2023.

GooglyPlusPlus has the following functionality

Batsman tab: For detailed analysis of batsmen
Bowler tab: For detailed analysis of bowlers
Match tab: Analysis of individual matches, plot of Runs vs SR, Wickets vs ER in power play, middle and death overs, Win Probability Analysis of teams and Win Probability Contribution of players
Head-to-head tab: Detailed analysis of team-vs-team batting/bowling scorecard, batting, bowling performances, performances in power play, middle and death overs
Team performance tab: Analysis of team-vs-all other teams with batting /bowling scorecard, batting, bowling performances, performances in power play, middle and death overs
Optimisation tab: Allows one to pit batsmen vs bowlers and vice-versa. This tab also uses integer programming to optimise batting and bowling lineup
Batting analysis tab: Ranks batsmen using Runs or SR. Also plots performances of batsmen in power play, middle and death overs and plots them in a 4×4 grid
Bowling analysis tab: Ranks bowlers based on Wickets or ER. Also plots performances of bowlers in power play, middle and death overs and plots them in a 4×4 grid

Also note all these tabs and features are available for all T20 formats namely IPL, Intl. T20 (men, women), BBL, NTB, PSL, CPL, SSM.

Important note: It is possible, that at times, the Win Probability (Deep Learning) for some recent IPL matches will give an error. This is because I need to rebuild the models on a daily basis as the matches use player embeddings and there are new players. While I will definitely rebuild the models on weekends and whenever I find time, you may have to bear with this error occasionally.

Note: All charts are interactive, which means that you can hover, zoom-in, zoom-out, pan etc on the charts

The latest avatar of GooglyPlusPlus2023 is based on my R package yorkr with data from Cricsheet.

Check out the latest version of GooglyPlusPlus

Follow me on twitter for daily highlights @tvganesh_85

GooglyPlusPlus can analyse players, matches, teams, rank, compute win probability and much more.

Included below are some random analyses of IPL 2023 matches so far

A) Chennai Super Kings vs Gujarat Titans – 31 Mar 2023

GT won by 5 wickets ( 4 balls remaining)

a) Worm Wicket Chart

b) Ball-by-ball Win Probability (Logistic Regression) (side-by-side)

This model shows that CSK had the upper hand in the 2nd last over, before it changed to GT. More details on Win Probability and Win Probability Contribution in the posts given by the links above.

c) b) Ball-by-ball Win Probability (Logistic Regression) (overlapping)

Here the ball-by-ball win probability is overlapped. CSK and GT both had nearly the same probability of winning in the 2nd last over before GT edges CSK out

B) Punjab Kings vs Rajasthan Royals – 05 Apr 2023

This was a another closely fought match. PBKS won by 5 runs

a) Worm wicket chart

b) Batting partnerships

Shikhar Dhawan scored 86 runs

c) Ball-by-ball Win Probability using Deep Learning (overlapping)

PBKS was generally ahead in the win probability race

d) Batsman Win Probability Contribution

This plot shows how the different batsmen contributed to the Win Probability. We can see that Shikhar Dhawan has a highest win probability. He played a very sensible innings. Also it appears that there is no difference between Prabhsimran Singh and others, though he score 60 runs. This computation is based on when they come to bat and how the win probability changes when they get dismissed, as seen in the 2nd chart

C) Delhi Capitals vs Gujarat Titans – 4 Apr 2023

GT won by 6 wickets (11 balls remaining)

a) Worm wicket chart

b) Runs scored across 20 overs

c) Runs vs SR plot

d) Batting scorecard (Gujarat Titans)

e) Batsman Win Probability Contribution (Gujarat Titans)

Miller has a higher percentage in the Win Contribution than Sai Sudershan who held the innings together.Strange are the ways of the ML models!!

D) Sunrisers Hyderabad vs Lucknow Supergiants ( 7 Apr 2023)

LSG won by 5 wickets (24 balls left). SRH were bamboozled by the pitch while LSG was able to cruise along

a) Worm wicket chart

b) Wickets vs ER plot

c) Wickets across 20 overs

d) Ball-by-ball win probability using Deep Learning (overlapping)

e) Bowler Win Probability Contribution (LSG)

Bishnoi has a higher win probability contribution than Krunal, though he just took 1 wicket to Krunal’s 3 wickets. This is based on how the Win Probability changed at that point in the game.

The above set of plots are just a random sample.

Note: There are 8 tabs each for 9 T20 leagues (BBL, CPL, T20 (men), T20 (women), IPL, PSL, NTB, SSM, WBB). So there are a lot more detailed charts/analses.

Do take GooglyPlusPlus for a test drive!!!

Follow me on twitter @tvganesh_85 for daily highlights of previous day matches

Take a look at some of my other posts

To see all posts click Index of posts

GooglyPlusPlus: Computing T20 player’s Win Probability Contribution

In this post, I compute each batsman’s or bowler’s Win Probability Contribution (WPC) in a T20 match. This metric captures by how much the player (batsman or bowler) changed/impacted the Win Probability of the T20 match. For this computation I use my machine learning models, I had created earlier, which predicts the ball-by-ball win probability as the T20 match progresses through the 2 innings of the match.

In the picture snippet below, you can see how the win probability changes ball-by-ball for each batsman for a T20 match between CSK vs LSG- 31 Mar 2022

In my previous posts I had created several Machine Learning models. In order to compute the player’s Win Probability contribution in this post, I have used the following ML models

Logistic Regression model – glmnet : accuracy – 0.728 and roc_auc – 0.81 – Boosting Win Probability accuracy with player embeddings
Deep Learning model – DL – accuracy – 0.8639 and roc_auc – 0.946 – GooglyPlusPlus: Win Probability using Deep Learning and player embeddings

The batsman’s or bowler’s win probability contribution changes ball-by=ball. The player’s contribution is calculated as the difference in win probability when the batsman faces the 1st ball in his innings and the last ball either when is out or the innings comes to an end. If the difference is +ve the the player has had a positive impact, and likewise for negative contribution. Similarly, for a bowler, it is the win probability when he/she comes into bowl till, the last delivery he/she bowls

Note: The Win Probability Contribution does not have any relation to the how much runs or at what strike rate the batsman scored the runs. Rather the model computes different win probability for each player, based on his/her embedding, the ball in the innings and six other feature vectors like runs, run rate, runsMomentum etc. These values change for every ball as seen in the table above. Also, this is not continuous. The 2 ML models determine the Win Probability for a specific player, ball and the context in the match.

This metric is similar to Win Probability Added (WPA) used in Sabermetrics for baseball. Here is the definition of WPA from Fangraphs “Win Probability Added (WPA) captures the change in Win Expectancy from one plate appearance to the next and credits or debits the player based on how much their action increased their team’s odds of winning.” This article in Fangraphs explains in detail how this computation is done.

In this post I have added 4 new function to my R package yorkr.

batsmanWinProbLR – batsman’s win probability contribution based on glmnet (Logistic Regression)
bowlerWinProbLR – bowler’s win probability contribution based on glmnet (Logistic Regression)
batsmanWinProbDL – batsman’s win probability contribution based on Deep Learning Model
bowlerWinProbDL – bowlerWinProbLR – bowler’s win probability contribution based on Deep Learning

Hence there are 4 additional features in GooglyPlusPlus based on the above 4 functions. In addition I have also updated

-winProbLR (overLap) function to include the names of batsman when they come to bat and when they get out or the innings comes to an end, based on Logistic Regression

-winProbDL(overLap) function to include the names of batsman when they come to bat and when they get out based on Deep Learning

Hence there are 6 new features in this version of GooglyPlusPlus.

Note: All these new 6 features are available for all 9 formats of T20 in GooglyPlusPlus namely

a) IPL b) BBL c) NTB d) PSL e) Intl, T20 (men) f) Intl. T20 (women) g) WBB h) CSL i) SSM

Check out the latest version of GooglyPlusPlus at gpp2023-2

Note: The data for GooglyPlusPlus comes from Cricsheet and the Shiny app is based on my R package yorkr

A) Chennai SuperKings vs Delhi Capitals – 04 Oct 2021

To understand Win Probability Contribution better let us look at Chennai Super Kings vs Delhi Capitals match on 04 Oct 2021

This was closely fought match with fortunes swinging wildly. If we take a look at the Worm wicket chart of this match

a) Worm Wicket chart – CSK vs DC – 04 Oct 2021

Delhi Capitals finally win the match

b) Win Probability Logistic Regression (side-by-side) – CSK vs DC – 4 Oct 2021

Plotting how win probability changes over the course of the match using Logistic Regression Model

In this match Delhi Capitals won. The batting scorecard of Delhi Capitals

c) Batting Scorecard of Delhi Capitals – CSK vs DC – 4 Oct 2021

d) Win Probability Logistic Regression (Overlapping) – CSK vs DC – 4 Oct 2021

The Win Probability LR (overlapping) shows the probability function of both teams superimposed over one another. The plot includes when a batsman came into to play and when he got out. This is for both teams. This looks a little noisy, but there is a way to selectively display the change in Win Probability for each team. This can be done , by clicking the 3 arrows (orange or blue) from top to bottom. First double-click the team CSK or DC, then click the next 2 items (blue,red or black,grey) Sorry the legends don’t match the colors! 😦

Below we can see how the win probability changed for Delhi Capitals during their innings, as batsmen came into to play. See below

e) Batsman Win Probability contribution:DC – CSK vs DC – 4 Oct 2021

Computing the individual batsman’s Win Contribution and plotting we have. Hetmeyer has a higher Win Probability contribution than Shikhar Dhawan depsite scoring fewer runs

f) Bowler’s Win Probability contribution :CSK – CSK vs DC – 4 Oct 2021

We can also check the Win Probability of the bowlers. So for e.g the CSK bowlers and which bowlers had the most impact. Moeen Ali has the least impact in this match

B) Intl. T20 (men) Australia vs India – 25 Sep 2022

a) Worm wicket chart – Australia vs India – 25 Sep 2022

This was another close match in which India won with the penultimate ball

b) Win Probability based on Deep Learning model (side-by-side) – Australia vs India – 25 Sep 2022

c) Win Probability based on Deep Learning model (overlapping) – Australia vs India – 25 Sep 2022

The plot below shows how the Win Probability of the teams varied across the 20 overs. The 2 Win Probability distributions are superimposed over each other

d) Batsman Win Probability Contribution : India – Australia vs India – 25 Sep 2022

Selectively choosing the India Win Probability plot by double-clicking legend ‘India’ on the right , followed by single click of black, grey legend we have

We see that Kohli, Suryakumar Yadav have good contribution to the Win Probability

e) Plotting the Runs vs Strike Rate:India – Australia vs India – 25 Sep 2022

f) Batsman’s Win Probability Contribution- Australia vs India – 25 Sep 2022

Finally plotting the Batsman’s Win Probability Contribution

Interestingly, Kohli has a greater Win Probability Contribution than SKY, though SKY scored more runs at a better strike rate. As mentioned above, the Win Probability is context dependent and also depends on past performances of the player (batsman, bowler)

Finally let us look at

C) India vs England Intll T20 Women (11 July 2021)

a) Worm wicket chart – India vs England Intl. T20 Women (11 July 2021)

India won this T20 match by 8 runs

b) Win Probability using the Logistic Regression Model – India vs England Intl. T20 Women (11 July 2021)

c) Win Probability with the DL model – India vs England Intl. T20 Women (11 July 2021)

d) Bowler Win Probability Contribution with the LR model – India vs England Intl. T20 Women (11 July 2021)

e) Bowler Win Contribution with the DL model – India vs England Intl. T20 Women (11 July 2021)

Go ahead and try out the latest version of GooglyPlusPlus

Also see my other posts

To see all posts click Index of posts

T20 Win Probability using CTGANs, synthetic data

This should be my last post on computing T20 Win Probability. In this post I compute Win Probability using Augmented Data with the help of Conditional Tabular Generative Adversarial Networks (CTGANs).

A.Introduction

I started the computation of T20 match Win Probability in my earlier post

a) ‘Computing Win-Probability of T20 matches‘ where I used

vanilla Logistic Regression to get an accuracy of 0.67,
Random Forest with Tidy models gave me an accuracy of 0.737
Deep Learning with Keras also with 0.73.

This was done without player embeddings

b) Next I used player embeddings for batsmen and bowlers in my post Boosting Win Probability accuracy with player embeddings , and my accuracies improved significantly

glmnet : accuracy – 0.728 and roc_auc – 0.81
random forest : accuracy – 0.927 and roc_auc – 0.98
mlp-dnn :accuracy – 0.762 and roc_auc – 0.854

c) Third I tried using Deep Learning with Keras using player embeddings

DL network gave an accuracy of 0.8639

This was lightweight and could be easily deployed in my Shiny GooglyPlusPlus app as opposed to the Tidymodel’s Random Forest, which was bulky and slow.

d) Finally I decided to try and improve the accuracy of my Deep Learning Model using Synthetic data. Towards this end, my explorations led me to Conditional Tabular Generative Adversarial Networks (CTGANs). CTGAN are GAN networks that can be used with Tabular data as GAN models are not useful with tabular data. However, the best performance I got for

DL Keras Model + Synthetic data : accuracy =0.77

The poorer accuracy was because CTGAN requires enormous computing power (GPUs) and RAM. The free version of Colab, Kaggle kept crashing when I tried with even 0.1 % of my 1.2 million dataset size. Finally, I tried with just 0.05% and was able to generate synthetic data. Most likely, it is the small sample size and the smaller number of epochs could be the reason for the poor result. In any case, it was worth trying and this approach would possibly work with sufficient computing resources.

B.Generative Adversarial Networks (GANs)

Generative Adversarial Networks (GANs) was the brain child of Ian Goodfellow who demonstrated it in 2014. GANs are capable of generating synthetic text, tables, images, videos using available data. In Adversarial nets framework, the generative model is pitted against an adversary: a
discriminative model that learns to determine whether a sample is from the model distribution or the
data distribution.

GANs have 2 Deep Neural Networks , the Generator and Discriminator which compete against other

The Generator (Counterfeiter) takes random noise as input and generates fake images, tables, text. The generator learns to generate plausible data. The generated instances become negative training examples for the discriminator.
The Discriminator (Police) which tries to distinguish between the real and fake images, text. The discriminator learns to distinguish the generator’s fake data from real data. The discriminator penalises the generator for producing implausible results.

A pictorial representation of the GAN model can be shown below

Theoretically best performance of GANs are supposed to happen when the network reaches the ‘Nash equilibrium‘, i.e. when the Generator produces near fake images and the Discriminator’s loss is f ~0.5 i.e. the discriminator is unable to distinguish between real and fake images.

Note: Though I have mentioned T20 data in the above GAN model, the T20 tabular data is actually used in CTGAN which is slightly different from the above. See Reference 2) below.

C. Conditional Tabular Generative Adversial Networks (CTGANs)

“Modeling the probability distribution of rows in tabular data and generating realistic synthetic data is a non-trivial task. Tabular data usually contains a mix of discrete and continuous columns. Continuous columns may have multiple modes whereas discrete columns are sometimes imbalanced making the modeling difficult.” CTGANs handle these challenges.

I came upon CTGAN after spending some time exploring GANs via blogs, videos etc. For building the model I use real T20 match data. However, CTGAN requires immense raw computing power and a lot of RAM. My initial attempts on Colab, my Mac (12 core, 32GB RAM), took forever before eventually crashing, I switched to Kaggle and used GPUs. Still I was only able to use only a miniscule part of my T20 dataset. My match data has 1.2 million rows, hoanything > 0.05% resulted in Kaggle crashing. Since I was able to use only a fraction, I executed the CTGAN model over several iterations, each iteration with a random 0.05% sample of the dataset. At the end of each iterations I also generate synthetic dataset. Over 12 iterations, I generate close 360K of ‘synthetic‘ T20 match data.

I then augment the 1.2 million rows of ‘real‘ T20 match data with the generated ‘synthetic T20 match data to run my Deep Learning model

D. Executing the CTGAN model

a. Read the real T20 match data

!pip install ctgan
import pandas as pd
import ctgan
from ctgan import CTGAN
from numpy.random import seed

# Read the T20 match data
df = pd.read_csv('/kaggle/input/cricket1/t20.csv')

# Randomly sample 0.05% of the dataset. Note larger datasets cause the algo to crash
train_dataset = df.sample(frac=0.05)

# Print the real T20 match data
print(train_dataset.head(10))
print(train_dataset.shape)

             batsmanIdx  bowlerIdx  ballNum  ballsRemaining  runs   runRate  \
363695         3333        432      134             119   153  1.285714   
1082839        3881       1180      218              30    93  3.100000   
595799         2366        683      187              65   120  1.846154   
737614         4490       1381      148              87   144  1.655172   
410202          934       1003       19             106    35  1.842105   
525627          921       1711      251               1     8  8.000000   
657669         4718       1602      130             115   145  1.260870   
666461         4309       1989       44              87    38  0.863636   
651229         3336        754       30              92    36  1.200000   
709892         3048        421       97              28   119  1.226804   

            numWickets  runsMomentum  perfIndex  isWinner  
363695            0      0.092437  18.333333         1  
1082839           5      0.200000   4.736842         0  
595799            4      0.107692   9.566667         0  
737614            1      0.114943   9.130435         1  
410202            0      0.103774  20.263158         0  
525627            8      3.000000   3.837209         0  
657669            0      0.095652  19.555556         0  
666461            0      0.126437   9.500000         0  
651229            0      0.119565  13.200000         0  
709892            3      0.285714   9.814433         1  
(59956, 10)

b. Run CTGAN model on the real T20 data

import pandas as pd
import ctgan
from ctgan import CTGAN
from numpy.random import seed
from pickle import TRUE

df = pd.read_csv('/kaggle/input/cricket1/t20.csv')

#Specify the categorical features. batsmanIdx & bowlerIdx are player embeddings
categorical_features = ['batsmanIdx','bowlerIdx']

# Create a empty dataframe for synthetic data
df1 = pd.DataFrame()

# Loop for 12 iterations. Minimize generator & discriminator loss
for i in range(12):
    print(i)
    train_dataset = df.sample(frac=0.05)
    seed(33)

    ctgan = CTGAN(epochs=20,verbose=True,generator_lr=.001,discriminator_lr=.001,batch_size=1000)
    ctgan.fit(train_dataset, categorical_features)

    # Generate synthetic data
    samples = ctgan.sample(30000)

   # Concatenate the synthetic data after each iteration
    df1 = pd.concat([df1,samples])
    print(samples.head())
    print(df1.shape)

# Output the synthetic data to file
df1.to_csv("output1.csv",index=False)

0
Epoch 1, Loss G:  8.3825,Loss D: -0.6159
Epoch 2, Loss G:  3.5117,Loss D: -0.3016
Epoch 3, Loss G:  2.1619,Loss D: -0.5713
Epoch 4, Loss G:  0.9847,Loss D:  0.1010
Epoch 5, Loss G:  0.6198,Loss D:  0.0789
Epoch 6, Loss G:  0.1710,Loss D:  0.0959
Epoch 7, Loss G:  0.3236,Loss D: -0.1554
Epoch 8, Loss G:  0.2317,Loss D: -0.0765
Epoch 9, Loss G: -0.0127,Loss D:  0.0275
Epoch 10, Loss G:  0.1477,Loss D: -0.0353
Epoch 11, Loss G:  0.0997,Loss D: -0.0129
Epoch 12, Loss G:  0.0066,Loss D: -0.0486
Epoch 13, Loss G:  0.0351,Loss D: -0.0805
Epoch 14, Loss G: -0.1399,Loss D: -0.0021
Epoch 15, Loss G: -0.1503,Loss D: -0.0518
Epoch 16, Loss G: -0.2306,Loss D: -0.0234
Epoch 17, Loss G: -0.2986,Loss D:  0.0469
Epoch 18, Loss G: -0.1941,Loss D: -0.0560
Epoch 19, Loss G: -0.3794,Loss D:  0.0000
Epoch 20, Loss G: -0.2763,Loss D:  0.0368
   batsmanIdx  bowlerIdx  ballNum  ballsRemaining  runs   runRate  numWickets  \
0         906        224        8              75    81  1.955153           4   
1        4159        433       17              31   126  1.799280           9   
2         229        351      192              66    82  1.608527           5   
3        1926        962       63               0   117  1.658105           0   
4         286        431      128               1    36  1.605079           0   

   runsMomentum  perfIndex  isWinner  
0      0.146670   6.937595         1  
1      0.160534  10.904346         1  
2      0.516010  11.698128         1  
3      0.380986  11.914613         0  
4      0.112255   5.392120         0  
(30000, 10)
1
Epoch 1, Loss G:  7.9977,Loss D: -0.3592
Epoch 2, Loss G:  3.7418,Loss D: -0.3371
Epoch 3, Loss G:  1.6685,Loss D: -0.3211
Epoch 4, Loss G:  1.0539,Loss D: -0.3495
Epoch 5, Loss G:  0.4664,Loss D: -0.0907
Epoch 6, Loss G:  0.4004,Loss D: -0.1208
Epoch 7, Loss G:  0.3250,Loss D: -0.1482
Epoch 8, Loss G:  0.1753,Loss D:  0.0169
Epoch 9, Loss G:  0.1382,Loss D:  0.0661
Epoch 10, Loss G:  0.1509,Loss D: -0.1023
Epoch 11, Loss G: -0.0235,Loss D:  0.0210
Epoch 12, Loss G: -0.1636,Loss D: -0.0124
Epoch 13, Loss G: -0.3370,Loss D: -0.0185
Epoch 14, Loss G: -0.3054,Loss D: -0.0085
Epoch 15, Loss G: -0.5142,Loss D:  0.0121
Epoch 16, Loss G: -0.3813,Loss D: -0.0921
Epoch 17, Loss G: -0.5838,Loss D:  0.0210
Epoch 18, Loss G: -0.4033,Loss D: -0.0181
Epoch 19, Loss G: -0.5711,Loss D:  0.0269
Epoch 20, Loss G: -0.4828,Loss D: -0.0830
   batsmanIdx  bowlerIdx  ballNum  ballsRemaining  runs   runRate  numWickets  \
0        2202        265      223              39    13  0.868927           0   
1        3641        856       35              59    26  2.236160           6   
2         676       2903      218              93    16  0.460693           1   
3        3482       3459       44             117   102  0.851471           8   
4        3046       3076       59               5    84  1.016824           2   

   runsMomentum  perfIndex  isWinner  
0      0.138586   4.733462         0  
1      0.124453   5.146831         1  
2      0.273168  10.106869         0  
3      0.129520   5.361127         0  
4      1.083525  25.677574         1  
(60000, 10)
...
...
11
Epoch 1, Loss G:  8.8362,Loss D: -0.7111
Epoch 2, Loss G:  4.1322,Loss D: -0.8468
Epoch 3, Loss G:  1.2782,Loss D:  0.1245
Epoch 4, Loss G:  1.1135,Loss D: -0.3588
Epoch 5, Loss G:  0.6033,Loss D: -0.1255
Epoch 6, Loss G:  0.6912,Loss D: -0.1906
Epoch 7, Loss G:  0.3340,Loss D: -0.1048
Epoch 8, Loss G:  0.3515,Loss D: -0.0730
Epoch 9, Loss G:  0.1702,Loss D:  0.0237
Epoch 10, Loss G:  0.1064,Loss D:  0.0632
Epoch 11, Loss G:  0.0884,Loss D: -0.0005
Epoch 12, Loss G:  0.0556,Loss D: -0.0607
Epoch 13, Loss G: -0.0917,Loss D: -0.0223
Epoch 14, Loss G: -0.1492,Loss D:  0.0258
Epoch 15, Loss G: -0.0986,Loss D: -0.0112
Epoch 16, Loss G: -0.1428,Loss D: -0.0060
Epoch 17, Loss G: -0.2225,Loss D: -0.0263
Epoch 18, Loss G: -0.2255,Loss D: -0.0328
Epoch 19, Loss G: -0.3482,Loss D:  0.0277
Epoch 20, Loss G: -0.2667,Loss D: -0.0721
   batsmanIdx  bowlerIdx  ballNum  ballsRemaining  runs   runRate  numWickets  \
0         367       1447      129              27    30  1.242120           2   
1        2481       1528      221               4    10  1.344024           2   
2        1034       3116      132              87   153  1.142750           3   
3        1201       2868      151              60   136  1.091638           1   
4        4327       3291      108              89    22  0.842775           2   

   runsMomentum  perfIndex  isWinner  
0      1.978739   6.393691         1  
1      0.539650   6.783990         0  
2      0.107156  12.154197         0  
3      3.193574  11.992059         0  
4      0.127507  12.210876         0  
(360000, 10)

E. Sample of the Synthetic data

synthetic_data = ctgan.sample(20000)
print(synthetic_data.head(100))

    batsmanIdx  bowlerIdx  ballNum  ballsRemaining  runs    runRate  \
0         1073       3059       72              72   149   2.230236   
1         3769       1443      106               7   137   0.881409   
2          448       3048      166               6   220   1.092504   
3         2969       1244      103              82   207  12.314862   
4          180       1372      125             111    14   1.310051   
..         ...        ...      ...             ...   ...        ...   
95        1521       1040      153               6   166   1.097363   
96        2366         62       25             114   119   0.910642   
97        3506       1736      100             118   140   1.640921   
98        3343       2347       47              54    50   0.696462   
99        1957       2888      136              27   153   1.315565   

    numWickets  runsMomentum  perfIndex  isWinner  
0            0      0.111707  17.466925         0  
1            1      0.130352  14.274113         0  
2            1      0.173541  11.076731         1  
3            1      0.218977   6.239951         0  
4            4      2.829380   9.183323         1  
..         ...           ...        ...       ...  
95           0      0.223437   7.011180         0  
96           1      0.451371  16.908120         1  
97           5      0.156936   9.217205         0  
98           6      0.124536   6.273091         0  
99           1      0.249329  14.221554         0  

[100 rows x 10 columns]

F. Evaluating the synthetic T20 match data

Here the quality of the synthetic data set is evaluated.

a) Statistical evaluation

Read the real T20 match data
Read the generated T20 synthetic match data

import pandas as pd

# Read the T20 match and synthetic match data
df = pd.read_csv('/kaggle/input/cricket1/t20.csv').  #1.2 million rows
synthetic=pd.read_csv('/kaggle/input/synthetic/synthetic.csv')   #300K

# Randomly sample 1000 rows, and generate stats
df1=df.sample(n=1000)
real=df1.describe()
realData_stats=real.transpose
print(realData_stats)

synthetic1=synthetic.sample(n=1000)
synthetic=synthetic1.describe()
syntheticData_stats=synthetic.transpose
syntheticData_stats

a) Stats of real T20 match data

<bound method DataFrame.transpose of         batsmanIdx    bowlerIdx      ballNum  ballsRemaining         runs  \
count  1000.000000  1000.000000  1000.000000     1000.000000  1000.000000   
mean   2323.940000  1776.481000   118.165000       59.236000    77.649000   
std    1329.703046  1011.470703    70.564291       35.312934    49.098763   
min       8.000000    13.000000     1.000000        1.000000    -2.000000   
25%    1134.750000   850.000000    58.000000       28.750000    39.000000   
50%    2265.000000  1781.500000   117.000000       59.000000    72.000000   
75%    3510.000000  2662.250000   178.000000       89.000000   111.000000   
max    4738.000000  3481.000000   265.000000      127.000000   246.000000   

           runRate   numWickets  runsMomentum    perfIndex     isWinner  
count  1000.000000  1000.000000   1000.000000  1000.000000  1000.000000  
mean      1.734979     2.614000      0.310568     9.580386     0.499000  
std       5.698104     2.267189      0.686171     4.530856     0.500249  
min      -2.000000     0.000000      0.071429     0.000000     0.000000  
25%       1.009063     1.000000      0.105769     6.666667     0.000000  
50%       1.272727     2.000000      0.141026     9.236842     0.000000  
75%       1.546891     4.000000      0.250000    12.146735     1.000000  
max     166.000000    10.000000     10.000000    30.800000     1.000000

b) Stats of Synthetic T20 match data

     
           batsmanIdx    bowlerIdx      ballNum  ballsRemaining         runs  \
count  1000.000000  1000.000000  1000.000000     1000.000000  1000.000000   
mean   2304.135000  1760.776000   116.081000       50.102000    74.357000   
std    1342.348684  1003.496003    72.019228       35.795236    48.103446   
min       2.000000    15.000000    -4.000000       -2.000000    -1.000000   
25%    1093.000000   881.000000    46.000000       18.000000    30.000000   
50%    2219.500000  1763.500000   116.000000       45.000000    75.000000   
75%    3496.500000  2644.750000   180.250000       77.000000   112.000000   
max    4718.000000  3481.000000   253.000000      124.000000   222.000000   

           runRate   numWickets  runsMomentum    perfIndex     isWinner  
count  1000.000000  1000.000000   1000.000000  1000.000000  1000.000000  
mean      1.637225     3.096000      0.336540     9.278073     0.507000  
std       1.691060     2.640408      0.502346     4.727677     0.500201  
min      -4.388339     0.000000      0.083351    -0.902991     0.000000  
25%       1.077789     1.000000      0.115770     5.731931     0.000000  
50%       1.369655     2.000000      0.163085     9.104328     1.000000  
75%       1.660477     5.000000      0.311586    12.619318     1.000000  
max      23.757001    10.000000      4.630908    29.829497     1.000000

c) Plotting the Generator and Discriminator loss

import pandas as pd

# CTGAN prints out a new line for each epoch
epochs_output = str(output).split('\n')

# CTGAN separates the values with commas
raw_values = [line.split(',') for line in epochs_output]
loss_values = pd.DataFrame(raw_values)[:-1] # convert to df and delete last row (empty)

# Rename columns
loss_values.columns = ['Epoch', 'Generator Loss', 'Discriminator Loss']

# Extract the numbers from each column 
loss_values['Epoch'] = loss_values['Epoch'].str.extract('(\d+)').astype(int)
loss_values['Generator Loss'] = loss_values['Generator Loss'].str.extract('([-+]?\d*\.\d+|\d+)').astype(float)
loss_values['Discriminator Loss'] = loss_values['Discriminator Loss'].str.extract('([-+]?\d*\.\d+|\d+)').astype(float)

# the result is a row for each epoch that contains the generator and discriminator loss
loss_values.head()

	Epoch	Generator Loss	Discriminator Loss
0	1	8.0158	-0.3840
1	2	4.6748	-0.9589
2	3	1.1503	-0.0066
3	4	1.5593	-0.8148
4	5	0.6734	-0.1425
5	6	0.5342	-0.2202
6	7	0.4539	-0.1462
7	8	0.2907	-0.0155
8	9	0.2399	0.0172
9	10	0.1520	-0.0236

import plotly.graph_objects as go

# Plot loss function
fig = go.Figure(data=[go.Scatter(x=loss_values['Epoch'], y=loss_values['Generator Loss'], name='Generator Loss'),
                      go.Scatter(x=loss_values['Epoch'], y=loss_values['Discriminator Loss'], name='Discriminator Loss')])


# Update the layout for best viewing
fig.update_layout(template='plotly_white',
                    legend_orientation="h",
                    legend=dict(x=0, y=1.1))

title = 'CTGAN loss function for T20 dataset - ' 
fig.update_layout(title=title, xaxis_title='Epoch', yaxis_title='Loss')
fig.show()

G. Qualitative evaluation of Synthetic data

a) Quality of continuous columns in synthetic data

KSComplement -This metric computes the similarity of a real column vs. a synthetic column in terms of the column shapes.The KSComplement uses the Kolmogorov-Smirnov statistic. Closer to 1.0 is good and 0 is worst

from sdmetrics.single_column import KSComplement
numerical_columns=['ballNum','ballsRemaining','runs','runRate','numWickets','runsMomentum','perfIndex']
total_score = 0
for column_name in numerical_columns:
    column_score = KSComplement.compute(df[column_name], synthetic[column_name])
    total_score += column_score
    print('Column:', column_name, ', Score: ', column_score)

print('\nAverage: ', total_score/len(numerical_columns))

Column: ballNum , Score:  0.9502754283367316
Column: ballsRemaining , Score:  0.8770284103276166
Column: runs , Score:  0.9136464248633367
Column: runRate , Score:  0.9183841670732166
Column: numWickets , Score:  0.9016209114638712
Column: runsMomentum , Score:  0.8773491702213716
Column: perfIndex , Score:  0.9173808852778924

Average:  0.9079550567948624

b) Quality of categorical columns

This statistic measures the quality of generated categorical columns. 1 is best and 0 is worst

categorical_columns=['batsmanIdx','bowlerIdx']
from sdmetrics.single_column import TVComplement

total_score = 0
for column_name in categorical_columns:
    column_score = TVComplement.compute(df[column_name], synthetic[column_name])
    total_score += column_score
    print('Column:', column_name, ', Score: ', column_score)

print('\nAverage: ', total_score/len(categorical_columns))

Column: batsmanIdx , Score:  0.8436263499539245
Column: bowlerIdx , Score:  0.7356177407921669

Average:  0.7896220453730457

The performance is decent but not excellent. I was unable to execute more epochs as it it required larger than the memory allowed

c) Correlation similarity

This metric measures the correlation between a pair of numerical columns and computes the similarity between the real and synthetic data – it compares the trends of 2D distributions. Best 1.0 and 0.0 is worst

import itertools
from sdmetrics.column_pairs import CorrelationSimilarity

total_score = 0
total_pairs = 0
for pair in itertools.combinations(numerical_columns,2):
    col_A, col_B = pair
    score = CorrelationSimilarity.compute(df[[col_A, col_B]], synthetic[[col_A, col_B]])
    print('Columns:', pair, ' Score:', score)
    total_score += score
    total_pairs += 1

print('\nAverage: ', total_score/total_pairs)

Columns: ('ballNum', 'ballsRemaining')  Score: 0.7153942317384889
Columns: ('ballNum', 'runs')  Score: 0.8838043045134777
Columns: ('ballNum', 'runRate')  Score: 0.8710243133637056
Columns: ('ballNum', 'numWickets')  Score: 0.7978515509750435
Columns: ('ballNum', 'runsMomentum')  Score: 0.8956281260834316
Columns: ('ballNum', 'perfIndex')  Score: 0.9275145840528048
Columns: ('ballsRemaining', 'runs')  Score: 0.9566928975064546
Columns: ('ballsRemaining', 'runRate')  Score: 0.9127313819127167
Columns: ('ballsRemaining', 'numWickets')  Score: 0.6770737279315224
Columns: ('ballsRemaining', 'runsMomentum')  Score: 0.7939260278412358
Columns: ('ballsRemaining', 'perfIndex')  Score: 0.8694582252638351
Columns: ('runs', 'runRate')  Score: 0.999593795992159
Columns: ('runs', 'numWickets')  Score: 0.9510731832916608
Columns: ('runs', 'runsMomentum')  Score: 0.9956131422133428
Columns: ('runs', 'perfIndex')  Score: 0.9742931845536701
Columns: ('runRate', 'numWickets')  Score: 0.8859830711832263
Columns: ('runRate', 'runsMomentum')  Score: 0.9174744874779561
Columns: ('runRate', 'perfIndex')  Score: 0.9491100087911353
Columns: ('numWickets', 'runsMomentum')  Score: 0.8989709776329797
Columns: ('numWickets', 'perfIndex')  Score: 0.7178946968801441
Columns: ('runsMomentum', 'perfIndex')  Score: 0.9744441623018661

Average:  0.8840738134048025

d) Category coverage

This metric measures whether a synthetic column covers all the possible categories that are present in a real column. 1.0 is best , 0 is worst

from sdmetrics.single_column import CategoryCoverage

total_score = 0
for column_name in categorical_columns:
    column_score = CategoryCoverage.compute(df[column_name], synthetic[column_name])
    total_score += column_score
    print('Column:', column_name, ', Score: ', column_score)

print('\nAverage: ', total_score/len(categorical_columns))

Column: batsmanIdx , Score:  0.9533951919021509
Column: bowlerIdx , Score:  0.9913966160022942

Average:  0.9723959039522225

H. Augmenting the T20 match data set

In this final part I augment my T20 match data set with the generated synthetic T20 data set.

import pandas as pd
from numpy import savetxt
import tensorflow as tf
from tensorflow import keras
import pandas as pd
import numpy as np


from keras.layers import Input, Embedding, Flatten, Dense, Reshape, Concatenate, Dropout
from keras.models import Model
import matplotlib.pyplot as plt

# Read real and synthetic data
df = pd.read_csv('/kaggle/input/cricket1/t20.csv')
synthetic=pd.read_csv('/kaggle/input/synthetic/synthetic.csv')

# Augment the data. Concatenate real & synthetic data
df1=pd.concat([df,synthetic])

# Create training and test samples
print("Shape of dataframe=",df1.shape)
train_dataset = df1.sample(frac=0.8,random_state=0)
test_dataset = df1.drop(train_dataset.index)
train_dataset1 = train_dataset[['batsmanIdx','bowlerIdx','ballNum','ballsRemaining','runs','runRate','numWickets','runsMomentum','perfIndex']]
test_dataset1 = test_dataset[['batsmanIdx','bowlerIdx','ballNum','ballsRemaining','runs','runRate','numWickets','runsMomentum','perfIndex']]
train_dataset1
train_labels = train_dataset.pop('isWinner')
test_labels = test_dataset.pop('isWinner')
print(train_dataset1.shape)

a=train_dataset1.describe()
stats=a.transpose
print(a)

a) Create A Deep Learning Model in Keras

from numpy.random import seed
seed(33)
tf.random.set_seed(432)
# create input layers for each of the predictors
batsmanIdx_input = Input(shape=(1,), name='batsmanIdx')
bowlerIdx_input = Input(shape=(1,), name='bowlerIdx')
ballNum_input = Input(shape=(1,), name='ballNum')
ballsRemaining_input = Input(shape=(1,), name='ballsRemaining')
runs_input = Input(shape=(1,), name='runs')
runRate_input = Input(shape=(1,), name='runRate')
numWickets_input = Input(shape=(1,), name='numWickets')
runsMomentum_input = Input(shape=(1,), name='runsMomentum')
perfIndex_input = Input(shape=(1,), name='perfIndex')

no_of_unique_batman=len(df1["batsmanIdx"].unique()) 
print(no_of_unique_batman)
no_of_unique_bowler=len(df1["bowlerIdx"].unique()) 
print(no_of_unique_bowler)

embedding_size_bat = no_of_unique_batman ** (1/4)
print(embedding_size_bat)
embedding_size_bwl = no_of_unique_bowler ** (1/4)
print(embedding_size_bwl)

# create embedding layer for the categorical predictor
batsmanIdx_embedding = Embedding(input_dim=no_of_unique_batman+1, output_dim=16,input_length=1)(batsmanIdx_input)
print(batsmanIdx_embedding)
batsmanIdx_flatten = Flatten()(batsmanIdx_embedding)
print(batsmanIdx_flatten)
bowlerIdx_embedding = Embedding(input_dim=no_of_unique_bowler+1, output_dim=16,input_length=1)(bowlerIdx_input)
bowlerIdx_flatten = Flatten()(bowlerIdx_embedding)
print(bowlerIdx_flatten)
# concatenate all the predictors
x = keras.layers.concatenate([batsmanIdx_flatten,bowlerIdx_flatten, ballNum_input, ballsRemaining_input, runs_input, runRate_input, numWickets_input, runsMomentum_input, perfIndex_input])
print(x.shape)
# add hidden layers
x = Dense(96, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(64, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(32, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(16, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(8, activation='relu')(x)
x = Dropout(0.1)(x)
# add output layer
output = Dense(1, activation='sigmoid', name='output')(x)
print(output.shape)
# create model
model = Model(inputs=[batsmanIdx_input,bowlerIdx_input, ballNum_input, ballsRemaining_input, runs_input, runRate_input, numWickets_input, runsMomentum_input, perfIndex_input], outputs=output)
model.summary()
# compile model
#optimizer=keras.optimizers.Adam(learning_rate=.01, beta_1=0.1, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=True)
#optimizer=keras.optimizers.RMSprop(learning_rate=0.001, rho=0.2, momentum=0.2, epsilon=1e-07)
#optimizer=keras.optimizers.SGD(learning_rate=.01,momentum=0.1) #- Works without dropout
#optimizer = tf.keras.optimizers.RMSprop(0.01)
#optimizer=keras.optimizers.SGD(learning_rate=.01,momentum=0.1)
#optimizer=keras.optimizers.RMSprop(learning_rate=.005, rho=0.1, momentum=0, epsilon=1e-07)

optimizer=keras.optimizers.Adam(learning_rate=.015, beta_1=0.9, beta_2=0.999, epsilon=1e-07, amsgrad=True)

model.compile(optimizer=optimizer, loss='binary_crossentropy', metrics=['accuracy'])

# train the model
history=model.fit([train_dataset1['batsmanIdx'],train_dataset1['bowlerIdx'],train_dataset1['ballNum'],train_dataset1['ballsRemaining'],train_dataset1['runs'],
           train_dataset1['runRate'],train_dataset1['numWickets'],train_dataset1['runsMomentum'],train_dataset1['perfIndex']], train_labels, epochs=20, batch_size=1024,
          validation_data = ([test_dataset1['batsmanIdx'],test_dataset1['bowlerIdx'],test_dataset1['ballNum'],test_dataset1['ballsRemaining'],test_dataset1['runs'],
           test_dataset1['runRate'],test_dataset1['numWickets'],test_dataset1['runsMomentum'],test_dataset1['perfIndex']],test_labels), verbose=1)

plt.plot(history.history["loss"])
plt.plot(history.history["val_loss"])
plt.title("model loss")
plt.ylabel("loss")
plt.xlabel("epoch")
plt.legend(["train", "test"], loc="upper left")
plt.show()

==================================================================================================
Total params: 144,497
Trainable params: 144,497
Non-trainable params: 0
__________________________________________________________________________________________________
Epoch 1/20
1219/1219 [==============================] - 15s 11ms/step - loss: 0.6285 - accuracy: 0.6372 - val_loss: 0.5164 - val_accuracy: 0.7606
Epoch 2/20
1219/1219 [==============================] - 14s 11ms/step - loss: 0.5594 - accuracy: 0.7121 - val_loss: 0.4920 - val_accuracy: 0.7663
Epoch 3/20
1219/1219 [==============================] - 14s 12ms/step - loss: 0.5338 - accuracy: 0.7244 - val_loss: 0.4541 - val_accuracy: 0.7878
Epoch 4/20
1219/1219 [==============================] - 14s 11ms/step - loss: 0.5176 - accuracy: 0.7317 - val_loss: 0.4226 - val_accuracy: 0.7933
Epoch 5/20
1219/1219 [==============================] - 13s 11ms/step - loss: 0.4966 - accuracy: 0.7420 - val_loss: 0.4547 - val_accuracy: 0.7
...
...
poch 18/20
1219/1219 [==============================] - 14s 11ms/step - loss: 0.4300 - accuracy: 0.7747 - val_loss: 0.3536 - val_accuracy: 0.8288
Epoch 19/20
1219/1219 [==============================] - 14s 12ms/step - loss: 0.4269 - accuracy: 0.7766 - val_loss: 0.3565 - val_accuracy: 0.8302
Epoch 20/20
1219/1219 [==============================] - 14s 11ms/step - loss: 0.4259 - accuracy: 0.7775 - val_loss: 0.3498 - val_accuracy: 0.831

As can be seen the accuracy with augmented dataset is around 0.77, while without it I was getting 0.867 with just the real data. This degradation is probably due to the folllowing reasons

Only a fraction of the dataset was used for training. This was not representative of the data distribution for CTGAN to correctly synthesise data
The number of epochs had to be kept low to prevent Kaggle/Colab from crashing

I. Conclusion

This post shows how we can generate synthetic T20 match data to augment real T20 match data. Assuming we have sufficient processing power we should be able to generate synthetic data for augmenting our data set. This should improve the accuracy of the Win Probabily Deep Learning model.

References

Also see

To see all posts click Index of posts

GooglyPlusPlus: Win Probability using Deep Learning and player embeddings

In my last post ‘GooglyPlusPlus now with Win Probability Analysis for all T20 matches‘ I had discussed the performance of my ML models, created with and without player embeddings, in computing the Win Probability of T20 matches. With batsman & bowler embeddings I got much better performance than without the embeddings

glmnet – Accuracy – 0.73
Random Forest (RF) – Accuracy – 0.92

While the Random Forest gave excellent accuracy, it was bulky and also took an unusually long time to predict the Win Probability of a single T20 match. The above 2 ML models were built using R’s Tidymodels. glmnet was fast, but I wanted to see if I could create a ML model that was better, lighter and faster. I had initially tried to use Tensorflow, Keras in Python but then abandoned it, since I did not know how to port the Deep Learning model to R and use in my app GooglyPlusPlus.

But later, since I was stuck with a bulky Random Forest model, I decided to again explore options for saving the Keras Deep Learning model and loading it in R. I found out that saving the model as .h5, we can load it in R and use it for predictions. Hence, I rebuilt a Deep Learning model using Keras, Python with player embeddings and I got excellent performance. The DL model was light and had an accuracy 0.8639 with an ROC_AUC of 0.964 which was great!

GooglyPlusPlus uses data from Cricsheet and is based on my R package yorkr

You can try out this latest version of GooglyPlusPlus at gpp2023-1

Here are the steps

A. Build a Keras Deep Learning model

a. Import necessary packages

import pandas as pd
import numpy as np
from zipfile import ZipFile
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
from tensorflow.keras import regularizers
from pathlib import Path
import matplotlib.pyplot as plt

b, Upload the data of all 9 T20 leagues (BBL, CPL, IPL, T20 (men) , T20(women), NTB, CPL, SSM, WBB)

# Read all T20 leagues 
df1=pd.read_csv('t20.csv')
print("Shape of dataframe=",df1.shape)

# Create training and test data set
train_dataset = df1.sample(frac=0.8,random_state=0)
test_dataset = df1.drop(train_dataset.index)
train_dataset1 = train_dataset[['batsmanIdx','bowlerIdx','ballNum','ballsRemaining','runs','runRate','numWickets','runsMomentum','perfIndex']]
test_dataset1 = test_dataset[['batsmanIdx','bowlerIdx','ballNum','ballsRemaining','runs','runRate','numWickets','runsMomentum','perfIndex']]
train_dataset1

# Set the target data
train_labels = train_dataset.pop('isWinner')
test_labels = test_dataset.pop('isWinner')
train_dataset1

a=train_dataset1.describe()
stats=a.transpose
a

c. Create a Deep Learning ML model using batsman & bowler embeddings

import pandas as pd
import numpy as np
from keras.layers import Input, Embedding, Flatten, Dense
from keras.models import Model
from keras.layers import Input, Embedding, Flatten, Dense, Reshape, Concatenate, Dropout
from keras.models import Model

# Set seed
tf.random.set_seed(432)

# create input layers for each of the predictors
batsmanIdx_input = Input(shape=(1,), name='batsmanIdx')
bowlerIdx_input = Input(shape=(1,), name='bowlerIdx')
ballNum_input = Input(shape=(1,), name='ballNum')
ballsRemaining_input = Input(shape=(1,), name='ballsRemaining')
runs_input = Input(shape=(1,), name='runs')
runRate_input = Input(shape=(1,), name='runRate')
numWickets_input = Input(shape=(1,), name='numWickets')
runsMomentum_input = Input(shape=(1,), name='runsMomentum')
perfIndex_input = Input(shape=(1,), name='perfIndex')

# Set the embedding size as the 4th root of unique batsmen, bowlers
no_of_unique_batman=len(df1["batsmanIdx"].unique()) 
no_of_unique_bowler=len(df1["bowlerIdx"].unique()) 
embedding_size_bat = no_of_unique_batman ** (1/4)
embedding_size_bwl = no_of_unique_bowler ** (1/4)


# create embedding layer for the categorical predictor
batsmanIdx_embedding = Embedding(input_dim=no_of_unique_batman+1, output_dim=16,input_length=1)(batsmanIdx_input)
batsmanIdx_flatten = Flatten()(batsmanIdx_embedding)
bowlerIdx_embedding = Embedding(input_dim=no_of_unique_bowler+1, output_dim=16,input_length=1)(bowlerIdx_input)
bowlerIdx_flatten = Flatten()(bowlerIdx_embedding)

# concatenate all the predictors
x = keras.layers.concatenate([batsmanIdx_flatten,bowlerIdx_flatten, ballNum_input, ballsRemaining_input, runs_input, runRate_input, numWickets_input, runsMomentum_input, perfIndex_input])

# add hidden layers
# Use dropouts for regularisation
x = Dense(64, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(32, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(16, activation='relu')(x)
x = Dropout(0.1)(x)
x = Dense(8, activation='relu')(x)
x = Dropout(0.1)(x)

# add output layer
output = Dense(1, activation='sigmoid', name='output')(x)
print(output.shape)

# create a DL model
model = Model(inputs=[batsmanIdx_input,bowlerIdx_input, ballNum_input, ballsRemaining_input, runs_input, runRate_input, numWickets_input, runsMomentum_input, perfIndex_input], outputs=output)
model.summary()

# compile model
optimizer=keras.optimizers.Adam(learning_rate=.01, beta_1=0.9, beta_2=0.999, epsilon=1e-07, decay=0.0, amsgrad=True)

model.compile(optimizer=optimizer, loss='binary_crossentropy', metrics=['accuracy'])

# train the model
history=model.fit([train_dataset1['batsmanIdx'],train_dataset1['bowlerIdx'],train_dataset1['ballNum'],train_dataset1['ballsRemaining'],train_dataset1['runs'],
           train_dataset1['runRate'],train_dataset1['numWickets'],train_dataset1['runsMomentum'],train_dataset1['perfIndex']], train_labels, epochs=40, batch_size=1024,
          validation_data = ([test_dataset1['batsmanIdx'],test_dataset1['bowlerIdx'],test_dataset1['ballNum'],test_dataset1['ballsRemaining'],test_dataset1['runs'],
           test_dataset1['runRate'],test_dataset1['numWickets'],test_dataset1['runsMomentum'],test_dataset1['perfIndex']],test_labels), verbose=1)

plt.plot(history.history["loss"])
plt.plot(history.history["val_loss"])
plt.title("model loss")
plt.ylabel("loss")
plt.xlabel("epoch")
plt.legend(["train", "test"], loc="upper left")
plt.show()

Model: "model_5"
__________________________________________________________________________________________________
 Layer (type)                   Output Shape         Param #     Connected to                     
==================================================================================================
 batsmanIdx (InputLayer)        [(None, 1)]          0           []                               
                                                                                                  
 bowlerIdx (InputLayer)         [(None, 1)]          0           []                               
                                                                                                  
 embedding_10 (Embedding)       (None, 1, 16)        75888       ['batsmanIdx[0][0]']             
                                                                                                  
 embedding_11 (Embedding)       (None, 1, 16)        55808       ['bowlerIdx[0][0]']              
                                                                                                  
 flatten_10 (Flatten)           (None, 16)           0           ['embedding_10[0][0]']           
                                                                                                  
 flatten_11 (Flatten)           (None, 16)           0           ['embedding_11[0][0]']           
                                                                                                  
 ballNum (InputLayer)           [(None, 1)]          0           []                               
                                                                                                  
 ballsRemaining (InputLayer)    [(None, 1)]          0           []                               
                                                                                                  
 runs (InputLayer)              [(None, 1)]          0           []                               
                                                                                                  
 runRate (InputLayer)           [(None, 1)]          0           []                               
                                                                                                  
 numWickets (InputLayer)        [(None, 1)]          0           []                               
                                                                                                  
 runsMomentum (InputLayer)      [(None, 1)]          0           []                               
                                                                                                  
 perfIndex (InputLayer)         [(None, 1)]          0           []                               
                                                                                                  
 concatenate_5 (Concatenate)    (None, 39)           0           ['flatten_10[0][0]',             
                                                                  'flatten_11[0][0]',             
                                                                  'ballNum[0][0]',                
                                                                  'ballsRemaining[0][0]',         
                                                                  'runs[0][0]',                   
                                                                  'runRate[0][0]',                
                                                                  'numWickets[0][0]',             
                                                                  'runsMomentum[0][0]',           
                                                                  'perfIndex[0][0]']              
                                                                                                  
 dense_19 (Dense)               (None, 64)           2560        ['concatenate_5[0][0]']          
                                                                                                  
 dropout_19 (Dropout)           (None, 64)           0           ['dense_19[0][0]']               
                                                                                                  
 dense_20 (Dense)               (None, 32)           2080        ['dropout_19[0][0]']             
                                                                                                  
 dropout_20 (Dropout)           (None, 32)           0           ['dense_20[0][0]']               
                                                                                                  
 dense_21 (Dense)               (None, 16)           528         ['dropout_20[0][0]']             
                                                                                                  
 dropout_21 (Dropout)           (None, 16)           0           ['dense_21[0][0]']               
                                                                                                  
 dense_22 (Dense)               (None, 8)            136         ['dropout_21[0][0]']             
                                                                                                  
 dropout_22 (Dropout)           (None, 8)            0           ['dense_22[0][0]']               
                                                                                                  
 output (Dense)                 (None, 1)            9           ['dropout_22[0][0]']             
                                                                                                  
==================================================================================================
Total params: 137,009
Trainable params: 137,009
Non-trainable params: 0
__________________________________________________________________________________________________
Epoch 1/40
937/937 [==============================] - 11s 10ms/step - loss: 0.5683 - accuracy: 0.6968 - val_loss: 0.4480 - val_accuracy: 0.7708
Epoch 2/40
937/937 [==============================] - 9s 10ms/step - loss: 0.4477 - accuracy: 0.7721 - val_loss: 0.4305 - val_accuracy: 0.7833
Epoch 3/40
937/937 [==============================] - 9s 10ms/step - loss: 0.4229 - accuracy: 0.7832 - val_loss: 0.3984 - val_accuracy: 0.7936
...
...
937/937 [==============================] - 10s 10ms/step - loss: 0.2909 - accuracy: 0.8627 - val_loss: 0.2943 - val_accuracy: 0.8613
Epoch 38/40
937/937 [==============================] - 10s 10ms/step - loss: 0.2892 - accuracy: 0.8633 - val_loss: 0.2933 - val_accuracy: 0.8621
Epoch 39/40
937/937 [==============================] - 10s 10ms/step - loss: 0.2889 - accuracy: 0.8638 - val_loss: 0.2941 - val_accuracy: 0.8620
Epoch 40/40
937/937 [==============================] - 10s 11ms/step - loss: 0.2886 - accuracy: 0.8639 - val_loss: 0.2929 - val_accuracy: 0.8621

d. Compute and plot the ROC-AUC for the above model

from sklearn.metrics import roc_curve

# Select a random sample set
tf.random.set_seed(59)
train = df1.sample(frac=0.9,random_state=0)
test = df1.drop(train_dataset.index)
test_dataset1 = test[['batsmanIdx','bowlerIdx','ballNum','ballsRemaining','runs','runRate','numWickets','runsMomentum','perfIndex']]
test_labels = test.pop('isWinner')

# Compute the predicted values
y_pred_keras = model.predict([test_dataset1['batsmanIdx'],test_dataset1['bowlerIdx'],test_dataset1['ballNum'],test_dataset1['ballsRemaining'],test_dataset1['runs'],
           test_dataset1['runRate'],test_dataset1['numWickets'],test_dataset1['runsMomentum'],test_dataset1['perfIndex']]).ravel()

# Compute TPR & FPR
fpr_keras, tpr_keras, thresholds_keras = roc_curve(test_labels, y_pred_keras)

fpr_keras, tpr_keras, thresholds_keras = roc_curve(test_labels, y_pred_keras)
from sklearn.metrics import auc

# Plot the Area Under the Curve (AUC)
auc_keras = auc(fpr_keras, tpr_keras)
plt.figure(1)
plt.plot([0, 1], [0, 1], 'k--')
plt.plot(fpr_keras, tpr_keras, label='Keras (area = {:.3f})'.format(auc_keras))
plt.xlabel('False positive rate')
plt.ylabel('True positive rate')
plt.title('ROC curve')
plt.legend(loc='best')
plt.show()

The ROC_AUC for the Deep Learning Model is 0.946 as seen below

e. Save the Keras model for use in Python

from keras.models import Model
model.save("wpDL.h5")

f. Load the model in R using rhdf5 package for use in GooglyPlusPlus

library(rhdf5)
dl_model <- load_model_hdf5('wpDL.h5')

This was a huge success for me to be able to create the Deep Learning model in Python and use it in my Shiny app GooglyPlusPlus. The Deep Learning Keras model is light-weight and extremely fast.

The Deep Learning model has now been integrated into GooglyPlusPlus. Now you can check the Win Probability using both a) glmnet (Logistic Regression with lasso regularisation) b) Keras Deep Learning model with dropouts as regularisation

In addition I have created 2 features based on Win Probability (WP)

i) Win Probability (Side-by-side – Plot(interactive) : With this functionality the 1st and 2nd innings will be side-by-side. When the 1st innings is played by team 1, the Win Probability of team 2 = 100 – WP (team1). Similarly, when the 2nd innings is being played by team 2, the Win Probability of team1 = 100 – WP (team 2)

ii) Win Probability (Overlapping) – Plot (static): With this functionality the Win Probabilities of both team1(1st innings) & team 2 (2nd innings) are displayed overlapping, so that we can see how the probabilities vary ball-by-ball.

Note: Since the same UI is used for all match functions I had to re-use the Plot(interactive) and Plot(static) radio buttons for Win Probability (Side-by-side) and Win Probability(Overlapping) respectively

Here are screenshots using both ML models with both functionality for some random matches

B) ICC T20 Men World Cup – Netherland-South Africa- 2022-11-06

i) Match Worm wicket chart

ii) Win Probability with LR (Side-by-Side- Plot(interactive))

iii) Win Probability LR (Overlapping- Plot(static))

iv) Win Probability Deep Learning (Side-by-side – Plot(interactive)

In the 213th ball of the innings South Africa was slightly ahead of Netherlands. After that they crashed and burned!

v) Win Probability Deep Learning (Overlapping – Plot (static)

It can be seen that in the 94th ball of both innings South Africa was ahead of Netherlands before the eventual slump.

C) Intl. T20 (Women) India – New Zealand – 2020 – 02 – 27

Here is an interesting match between India and New Zealand T20 Women’s teams. NZ successfully chased the India’s total in a wildly swinging fortunes. See the charts below

i) Match Worm Wicket chart

ii) Win Probability with LR (Side-by-side – Plot (interactive)

iii) Win Probability with LR (Overlapping – Plot (static)

iv) Win Probability with DL model (Side-by-side – Plot (interactive))

v) Win Probability with DL model (Overlapping – Plot (static))

The above functionality in plotting the Win Probability using LR or DL with both options (Side-by-side or Overlapping) is available for all 9 T20 leagues currently supported by GooglyPlusPlus.

Go ahead and give gpp2023-1 a try!!!

Do also check out my other posts’

To see all posts click Index of posts

GooglyPlusPlus now with Win Probability Analysis for all T20 matches

In my 2 earlier posts Computing Win-Probability of T20 matches and Boosting Win Probability accuracy with player embeddings I had discussed the approaches to computing ball-by-ball Win Probability of a T20 match. My best ML models were.

glmnet – Logistic Regression(LR) with lasso regularization and penalty – Accuracy – 0.73
Random Forest (RF) – Accuracy – 0.92

Incidentally, both these models can be used on live streaming ball-by-ball data if available

I have now integrated the trained ML Logistic Regression model with penalty into my Shiny app GooglyPlusPlus. Unfortunately, the Random Forest model, besides being computationally intensive is also heavy-weight (1.29GB) when compared to LR model which is just 91.2 MB. So, I was not able to upload the Random Forest model to Shiny as the memory allowed exceeded that allowed in my paid subscription.

However, I will demonstrate the performance of both models, LR ( in my Web app) and RF (in my local machine). Incidentally the Random Forest model takes a long time to load and even longer (~90 secs) to compute the Win Probability of a T20 match, while the LR model computes in a few seconds. Interestingly, I find the LR model’s Win Probability more intuitive and explainable than the Random Forest. Possibly, the RF model overfits. I need to explore this more. Anyway, take a look at some interesting Win Probability Charts (fortune swings of teams!!!) over the course of the T20 match.

You can try out this latest version here at GooglyPlusPlus !!

Some major upsets in the ICC T20 World Cup, 2022

A) Netherlands vs South Africa – 2022-11-06

B) Zimbabwe vs Pakistan – 2022-10-27

1a) Netherlands vs South Africa – ICC 2022-11-06 (Worm-wicket chart)

Netherlands shocked South Africa and ended South Africa’s hopes for a place in the semi-finals. The match worm-wicket chart for this match is shown below

The 2 circled areas are where the South Africa lost the plot around the 8th over (~120+48=168) and 15th over (~120+90=210)

Around 205-215 ball of the innings South Africa started to lose

1b) Netherlands vs South Africa – ICC 2022-11-06 – Logistic Regression with regularisation (Shiny)

1c) 1b) Netherlands vs South Africa – ICC 2022-11-06 – Random Forest (not in Web app, local)

If you notice, for some reason, Random Forest model decided that Netherland was on the winning side, right from the start. Why would this happen? Possibly overfitting, I presume…

2a) Zimbabwe vs Pakistan – ICC 2022-10-27 Worm-wicket chart

Pakistan seemed to be cruising along with finally 11 runs in the last over, and for some reason they panicked and lost.

2a) Zimbabwe vs Pakistan -ICC 2022 – 2022-10-27 – Logistic Regression with regularisation (Shiny)

It can be seen that Pakistan did seem to have the upper hand , save the last over.

2a) Zimbabwe vs Pakistan ICC 2022-10-27 – Random Forest (not in Web app, local)

Again the Random Forest model implies that Zimbabwe was on a winning foot except in brief stretches for e.g ball 248 of the innings

So while the accuracy of Random Forest model is better by about ~20% I feel it is the Logistic Regression with penalty has generalised better and is more intuitive. Meanwhile, I will see if I can improve LR or try another model which can provide better accuracy besides generalising well

Henceforth, I will only be using the LR model that is in the Shiny app

3a) England vs New Zealand T20 Women – 2021-09-04

Another close match till the 15th over. After that England’s seems to have had a slower strike rate and lost

3b) England vs New Zealand T20 Women – 2021-09-04 – Logistic Regression

4a) Chennai Super Kings vs Gujarat Titans (IPL 2022) – Worm wicket chart

4a) Chennai Super Kings vs Gujarat Titans (IPL 2022) – Logistic Regression

5a) Islamabad United vs Peshawar Zalmi -2021-06-17 – Worm wicket chart

This match seems to be close, with both worms inter-twined almost all the way

5b) Islamabad United vs Peshawar Zalmi -2021-06-17 – Logistic Regression

According to the model Peshawar Zalmi lost the game around 14-15th over

Feel free to play around with the latest GooglyPlusPlus

Conclusion

Meanwhile I will try to come with a better model which executes fast, generalises well and is accurate. Tall order, no doubt!!!

Till such time play around with GooglyPlusPlus

Also check out my other posts

To see all posts click Index of posts

Boosting Win Probability accuracy with player embeddings

In my previous post Computing Win Probability of T20 matches I had discussed various approaches on computing Win Probability of T20 matches. I had created ML models with glmnet and random forest using TidyModels. This was what I had achieved

glmnet : accuracy – 0.67 and sensitivity/specificity – 0.68/0.65
random forest : accuracy – 0.737 and roc_auc- 0.834
DL model with Keras in Python : accuracy – 0.73

I wanted to see if the performance of the models could be further improved. I got a suggestion from a AI/DL whizkid, who is close to me, to include embeddings for batsmen and bowlers. He felt that win percentage is influenced by which batsman faces which bowler.

So, I started to explore this idea. Embeddings can be used to convert categorical variables to a vector of continuous floating point numbers.Fortunately R’s Tidymodels, has a convenient functionality to create embeddings. By including embeddings for batsman, bowler the performance of my ML models improved vastly. Now the performance is

glmnet : accuracy – 0.728 and roc_auc – 0.81
random forest : accuracy – 0.927 and roc_auc – 0.98
mlp-dnn :accuracy – 0.762 and roc_auc – 0.854

As can be seem there is almost a 20% increase in accuracy with random forests with embeddings over the model without embeddings. Moreover, the feature importance which is plotted below shows that the bowler and batsman embeddings have a significant influence on the Win Probability

Note: The data for this analysis is taken from Cricsheet and has been processed with my R package yorkr.

A. Win Probability using GLM with penalty and player embeddings

Here Generalised Linear Model (GLMNET) for Logistic Regression is used. In the GLMNET the regularisation path is computed for the lasso or elastic net penalty at a grid of values for the regularisation parameter lambda. glmnet is extremely fast and gave an accuracy of 0.72 for an roc_auc of 0.81 with batsman, bowler embeddings. This was good improvement over my earlier implementation with glmnet without the batsman & bowler embeddings which had a

Read the data

a) Read the data from 9 T20 leagues (BBL, CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB) and create a single data frame of ball-by-ball data. Display the data frame

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)  
library(embed)

# Helper packages
library(readr)       # for importing data
library(vip) 

df1=read.csv("output3/matchesBBL3.csv")
df2=read.csv("output3/matchesCPL3.csv")
df3=read.csv("output3/matchesIPL3.csv")
df4=read.csv("output3/matchesNTB3.csv")
df5=read.csv("output3/matchesPSL3.csv")
df6=read.csv("output3/matchesSSM3.csv")
df7=read.csv("output3/matchesT20M3.csv")
df8=read.csv("output3/matchesT20W3.csv")
df9=read.csv("output3/matchesWBB3.csv")

#Bind all dataframes together
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)
glimpse(df)
Rows: 1,199,115
Columns: 10
$ batsman        <chr> "JD Smith", "M Klinger", "M Klinger", "M Klinger", "JD …
$ bowler         <chr> "NM Hauritz", "NM Hauritz", "NM Hauritz", "NM Hauritz",…

$ ballNum        <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, …
$ ballsRemaining <int> 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, …
$ runs           <int> 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 13, 14, 16, 18, 18,…

$ runRate        <dbl> 1.0000000, 0.5000000, 0.6666667, 0.7500000, 0.6000000, …
$ numWickets     <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
$ runsMomentum   <dbl> 0.08800000, 0.08870968, 0.08943089, 0.09016393, 0.09090…
$ perfIndex      <dbl> 11.000000, 5.500000, 7.333333, 8.250000, 6.600000, 5.50…
$ isWinner       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…


df %>% 
  count(isWinner) %>% 
  mutate(prop = n/sum(n))
  isWinner      n      prop
1        
0 614237 0.5122419
2        
1 584878 0.4877581

2) Create training.validation and test sets

b) Split to training, validation and test sets. The dataset is initially split into training and test in the ratio 80%:20%. The training data is again split into training and validation in the ratio 80:20

set.seed(123)
splits      <- initial_split(df,prop = 0.80)
splits
<Training/Testing/Total>
<959292/239823/1199115>
df_other <- training(splits)
df_test  <- testing(splits)

set.seed(234)
val_set <- validation_split(df_other,prop = 0.80)
val_set
# A tibble: 1 × 2
  splits                  
id        
  <list>                  <chr>     
1 <split [767433/191859]> validation

3) Create pre-processing recipe

a) Normalise the following predictors

ballNum
ballsRemaining
runs
runRate
numWickets
runsMomentum
perfIndex

b) Create floating point embeddings for

batsman
bowler

4) Create a Logistic Regression Workflow by adding the GLM model and the recipe

5) Create grid of elastic penalty values for regularisation

6) Train all 30 models

7) Plot the ROC of the model against the penalty

# Use all 12 cores
cores <- parallel::detectCores()
cores
# Create a Logistic Regression model with penalty
lr_mod <- 
  logistic_reg(penalty = tune(), mixture = 1) %>% 
  set_engine("glmnet",num.threads = cores)

# Create pre-processing recipe
lr_recipe <- 
  recipe(isWinner ~ ., data = df_other) %>%
  step_embed(batsman,bowler, outcome = vars(isWinner)) %>%  step_normalize(ballNum,ballsRemaining,runs,runRate,numWickets,runsMomentum,perfIndex) 

# Set the workflow by adding the GLM model with the recipe
lr_workflow <- 
  workflow() %>% 
  add_model(lr_mod) %>% 
  add_recipe(lr_recipe)

# Create a grid for the elastic net penalty
lr_reg_grid <- tibble(penalty = 10^seq(-4, -1, length.out = 30))
lr_reg_grid %>% top_n(-5) 
# A tibble: 5 × 1
   penalty
     
<dbl>
1 0.0001  
2 0.000127
3 0.000161
4 0.000204
5 0.000259

lr_reg_grid %>% top_n(5)  # highest penalty values
# A tibble: 5 × 1
  penalty
    <dbl>
1  0.0386
2  0.0489
3  0.0621
4  0.0788
5  0.1

# Train 30 penalized models
lr_res <- 
  lr_workflow %>% 
  tune_grid(val_set,
            grid = lr_reg_grid,
            control = control_grid(save_pred = TRUE),
            metrics = metric_set(accuracy,roc_auc))

# Plot the penalty versus ROC
lr_plot <- 
  lr_res %>% 
  collect_metrics() %>% 
  ggplot(aes(x = penalty, y = mean)) + 
  geom_point() + 
  geom_line() + 
  ylab("Area under the ROC Curve") +
  scale_x_log10(labels = scales::label_number())

lr_plot

The Penalty vs ROC plot is shown below

8) Display the ROC_AUC of the top models with the penalty

9) Select the model with the best ROC_AUC and the associated penalty. It can be seen the best mean ROC_AUC is 0.81 and the associated penalty is 0.000530

top_models <-
  lr_res %>% 
  show_best("roc_auc", n = 15) %>% 
  arrange(penalty) 
top_models

# A tibble: 15 × 7
    penalty .metric .estimator  mean     n std_err .config              
      <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
 1 0.0001   roc_auc binary     0.810     1      NA Preprocessor1_Model01
 2 0.000127 roc_auc binary     0.810     1      NA Preprocessor1_Model02
 3 0.000161 roc_auc binary     0.810     1      NA Preprocessor1_Model03
 4 0.000204 roc_auc binary     0.810     1      NA Preprocessor1_Model04
 5 0.000259 roc_auc binary     0.810     1      NA Preprocessor1_Model05
 6 0.000329 roc_auc binary     0.810     1      NA Preprocessor1_Model06
 7 0.000418 roc_auc binary     0.810     1      NA Preprocessor1_Model07
 8 0.000530 roc_auc binary     0.810     1      NA Preprocessor1_Model08
 9 0.000672 roc_auc binary     0.810     1      NA Preprocessor1_Model09
10 0.000853 roc_auc binary     0.810     1      NA Preprocessor1_Model10
11 0.00108  roc_auc binary     0.810     1      NA Preprocessor1_Model11
12 0.00137  roc_auc binary     0.810     1      NA Preprocessor1_Model12
13 0.00174  roc_auc binary     0.809     1      NA Preprocessor1_Model13
14 0.00221  roc_auc binary     0.809     1      NA Preprocessor1_Model14
15 0.00281  roc_auc binary     0.809     1      NA Preprocessor1_Model15

#Picking the best model and the corresponding penalty
lr_best <- 
  lr_res %>% 
  collect_metrics() %>% 
  arrange(penalty) %>% 
  slice(8)
lr_best
# A tibble: 1 × 7
   
   penalty .metric .estimator  mean     n std_err .config              
     <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                

1 0.000530 roc_auc binary     0.810     1      NA Preprocessor1_Model08

# Collect predictions and generate the AUC curve
lr_auc <- 
  lr_res %>% 
  collect_predictions(parameters = lr_best) %>% 
  roc_curve(isWinner, .pred_0) %>% 
  mutate(model = "Logistic Regression")

autoplot(lr_auc)

7) Plot the Area under the Curve (AUC).

10) Build the final model with the best LR parameters value as found in lr_best

a) The best performance was for a penalty of 0.000530

b) The accuracy achieved is 0.72. Clearly using the embeddings for batsman, bowlers improves on the performance of the GLM model without the embeddings. The accuracy achieved was 0.72 whereas previously it was 0.67 see (Computing Win Probability of T20 Matches)

c) Create a fit with the best parameters

d) The accuracy is 72.8% and the ROC_AUC is 0.813

# Create a model with the penalty for best ROC_AUC
last_lr_mod <- 
  logistic_reg(penalty = 0.000530, mixture = 1) %>% 
  set_engine("glmnet",num.threads = cores,importance = "impurity")

#Update the workflow with this model
last_lr_workflow <- 
  lr_workflow %>% 
  update_model(last_lr_mod)

#Create a fit
set.seed(345)
last_lr_fit <- 
  last_lr_workflow %>% 
  last_fit(splits)

#Generate accuracy, roc_auc
last_lr_fit %>% 
  collect_metrics()
# A tibble: 2 × 4
  .metric  .estimator .estimate .config             
  
<chr>    <chr>          <dbl> <chr>               
1 accuracy binary         0.728 Preprocessor1_Model1

2 roc_auc  binary         0.813 Preprocessor1_Model1

11) Plot the feature importance

It can be seen that bowler and batsman embeddings are the most significant for the prediction followed by runRate.

runRate –

runRate in 1st innings

requiredRunRate in 2nd innings

12) Plot the ROC characteristics

last_lr_fit %>% 
  collect_predictions() %>% 
  roc_curve(isWinner, .pred_0) %>% 
  autoplot()

13) Generate a confusion matrix

14) Create a final Generalised Linear Model for Logistic Regression with the penalty of 0.000530

15) Save the model

# generate predictions from the test set
test_predictions <- last_lr_fit %>% collect_predictions()
test_predictions

# generate a confusion matrix
test_predictions %>% 
  conf_mat(truth = isWinner, estimate = .pred_class)

Truth
Prediction     0     1
         
0                  90105 32658
         
1                  32572 84488

final_lr_model <- fit(last_lr_workflow, df_other)

final_lr_model

obj_size(final_lr_model)
146.51 MB


butcher::weigh(final_lr_model)
A tibble: 305 × 2
object                                  size
<chr>                                  <dbl>
  1 pre.actions.recipe.recipe.steps.terms1  57.9
2 pre.actions.recipe.recipe.steps.terms2  57.9
3 pre.actions.recipe.recipe.steps.terms3  57.9


cleaned_lm <- butcher::axe_env(final_lr_model, verbose = TRUE)
#✔ Memory released: "1.04 kB"
#✔ Memory released: "1.62 kB"

saveRDS(cleaned_lm, "cleanedLR.rds")

16) Compute Ball-by-ball Win Probability

Chennai Super Kings-Lucknow Super Giants-2022-03-31

16a) The corresponding Worm-wicket graph for this match is as below

Chennai Super Kings-Lucknow Super Giants-2022-03-31

B) Win Probability using Random Forest with player embeddings

In the 2nd approach I use Random Forest with batsman and bowler embeddings. The performance of the model with embeddings is quantum jump from the earlier performance without embeddings. However, the random forest is also computationally intensive.

1) Read the data

a) Read the data from 9 T20 leagues (BBL, CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB) and create a single data frame of ball-by-ball data. Display the data frame

2) Create training.validation and test sets

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)  
library(tidymodels)  
library(embed)

# Helper packages
library(readr)       # for importing data
library(vip) 
library(ranger)

# Read all the 9 T20 leagues
df1=read.csv("output3/matchesBBL3.csv")
df2=read.csv("output3/matchesCPL3.csv")
df3=read.csv("output3/matchesIPL3.csv")
df4=read.csv("output3/matchesNTB3.csv")
df5=read.csv("output3/matchesPSL3.csv")
df6=read.csv("output3/matchesSSM3.csv")
df7=read.csv("output3/matchesT20M3.csv")
df8=read.csv("output3/matchesT20W3.csv")
df9=read.csv("output3/matchesWBB3.csv")

# Bind into a single dataframe
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)

set.seed(123)
df$isWinner = as.factor(df$isWinner)

#Split data into training, validation and test sets
splits      <- initial_split(df,prop = 0.80)
df_other <- training(splits)
df_test  <- testing(splits)
set.seed(234)
val_set <- validation_split(df_other, prop = 0.80)
val_set

2) Create a Random Forest model tuning for number of predictor nodes at each decision node (mtry) and minimum number of predictor nodes (min_n)

3) Use the ranger engine and set up for classification

4) Set up the recipe and include batsman and bowler embeddings

5) Create a workflow and add the recipe and the random forest model with the tuning parameters

# Use all 12 cores parallely
cores <- parallel::detectCores()
cores
[1] 12

# Create the random forest model with mtry and min as tuning parameters
rf_mod <- 
  rand_forest(mtry = tune(), min_n = tune(), trees = 1000) %>% 
  set_engine("ranger", num.threads = cores) %>% 
  set_mode("classification")

# Setup the recipe with batsman and bowler embeddings
rf_recipe <- 
  recipe(isWinner ~ ., data = df_other) %>% 
  step_embed(batsman,bowler, outcome = vars(isWinner)) 

# Create the random forest workflow
rf_workflow <- 
  workflow() %>% 
  add_model(rf_mod) %>% 
  add_recipe(rf_recipe)

rf_mod
# show what will be tuned
extract_parameter_set_dials(rf_mod)

set.seed(345)
# specify which values meant to tune

# Build the model
rf_res <- 
  rf_workflow %>% 
  tune_grid(val_set,
            grid = 10,
            control = control_grid(save_pred = TRUE),
            metrics = metric_set(accuracy,roc_auc))

# Pick the best  roc_auc and the associated tuning parameters
rf_res %>% 
  show_best(metric = "roc_auc")
# A tibble: 5 × 8
   mtry min_n .metric .estimator  mean     n std_err .config              
  <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
1     4     4 roc_auc binary     0.980     1      NA Preprocessor1_Model08
2     9     8 roc_auc binary     0.979     1      NA Preprocessor1_Model03

3     8    16 roc_auc binary     0.974     1      NA Preprocessor1_Model10
4     7    22 roc_auc binary     0.969     1      NA Preprocessor1_Model09

5     5    19 roc_auc binary     0.969     1      NA Preprocessor1_Model06

rf_res %>% 
  show_best(metric = "accuracy")
# A tibble: 5 × 8
   
mtry min_n .metric  .estimator  mean     n std_err .config              
  <int> <int> <chr>    <chr>      <dbl> <int>   <dbl> <chr>                
1  4     4 accuracy binary    0.927     1      NA Preprocessor1_Model08

2  9     8 accuracy binary    0.926     1      NA Preprocessor1_Model03
3  8    16 accuracy binary    0.915     1      NA Preprocessor1_Model10
4  7    22 accuracy binary    0.906     1      NA Preprocessor1_Model09

5  5    19 accuracy binary    0.904     1      NA Preprocessor1_Model0

6) Select all models with the best roc_auc. It can be seen that the best roc_auc is 0.980 for mtry=4 and min_n=4

7) Get the model with the highest accuracy. The highest accuracy achieved is 0.927 or 92.7. This accuracy is also for mtry=4 and min_n=4

# Pick the best  roc_auc and the associated tuning parameters
rf_res %>% 
  show_best(metric = "roc_auc")
# A tibble: 5 × 8
   mtry min_n .metric .estimator  mean     n std_err .config              
  <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>                
1     4     4 roc_auc binary     0.980     1      NA Preprocessor1_Model08
2     9     8 roc_auc binary     0.979     1      NA Preprocessor1_Model03

3     8    16 roc_auc binary     0.974     1      NA Preprocessor1_Model10
4     7    22 roc_auc binary     0.969     1      NA Preprocessor1_Model09

5     5    19 roc_auc binary     0.969     1      NA Preprocessor1_Model06

# Display the accuracy of the models in descending order and the parameters
rf_res %>% 
  show_best(metric = "accuracy")
# A tibble: 5 × 8
   
mtry min_n .metric  .estimator  mean     n std_err .config              
  <int> <int> <chr>    <chr>      <dbl> <int>   <dbl> <chr>                
1  4     4 accuracy binary    0.927     1      NA Preprocessor1_Model08

2  9     8 accuracy binary    0.926     1      NA Preprocessor1_Model03
3  8    16 accuracy binary    0.915     1      NA Preprocessor1_Model10
4  7    22 accuracy binary    0.906     1      NA Preprocessor1_Model09

5  5    19 accuracy binary    0.904     1      NA Preprocessor1_Model0

8) Select the model with the best parameters for accuracy mtry=4 and min_n=4. For this the accuracy is 0.927. For this configuration the roc_auc is also the best at 0.980

9) Plot the Area Under the Curve (AUC). It can be seen that this model performs really well and it hugs the top left.

# Pick the best model
rf_best <- 
  rf_res %>% 
  select_best(metric = "accuracy")

# The best model has mtry=4 and min=4
rf_best
     mtry min_n .config              
  <int> <int> <chr>                
1     4     4      Preprocessor1_Model08

#Plot AUC
rf_auc <- 
  rf_res %>% 
  collect_predictions(parameters = rf_best) %>% 
  roc_curve(isWinner, .pred_0) %>% 
  mutate(model = "Random Forest")

autoplot(rf_auc)

10) Create the final model with the best parameters

11) Execute the final fit

12) Plot feature importance, The bowler and batsman embedding followed by perfIndex and runRate are features that contribute the most to the Win Probability

last_rf_mod <- 
  rand_forest(mtry = 4, min_n = 4, trees = 1000) %>% 
  set_engine("ranger", num.threads = cores, importance = "impurity") %>% 
  set_mode("classification")

# the last workflow
last_rf_workflow <- 
  rf_workflow %>% 
  update_model(last_rf_mod)

set.seed(345)
last_rf_fit <- 
  last_rf_workflow %>% 
  last_fit(splits)

last_rf_fit %>% 
  collect_metrics()

  .metric  .estimator .estimate .config             
  <chr>    <chr>          <dbl> <chr>               

1 accuracy binary         0.944 Preprocessor1_Model1
2 roc_auc  binary         0.988 Preprocessor1_Model1

last_rf_fit %>% 
  extract_fit_parsnip() %>% 
  vip(num_features = 9)

13) Plot the ROC curve for the best fit

# Plot the ROC for the final model
last_rf_fit %>% 
  collect_predictions() %>% 
  roc_curve(isWinner, .pred_0) %>% 
  autoplot()

14) Create a confusion matrix

We can see that the number of false positives and false negatives is very low

15) Create the final fit with the Random Forest Model

# generate predictions from the test set
test_predictions <- last_rf_fit %>% collect_predictions()
test_predictions

   id               .pred_0 .pred_1  .row .pred_class isWinner .config          
   <chr>              <dbl>   <dbl> <int> <fct>       <fct>    <chr>            
 1 train/test split   0.838  0.162      1 0           0       Preprocessor1_Mo…
 2 
train/test split   0.463  0.537     11 1           0        Preprocessor1_Mo…
 3 
train/test split   0.846  0.154     14 0           0        Preprocessor1_Mo…
 4 
train/test split   0.839  0.161     22 0           0        Preprocessor1_Mo…
 5 
train/test split   0.846  0.154     36 0           0        Preprocessor1_Mo…
 6 
train/test split   0.848  0.152     37 0           0        Preprocessor1_Mo…
 7 
train/test split   0.731  0.269     39 0           0        Preprocessor1_Mo…
 8 
train/test split   0.972  0.0281    40 0           0        Preprocessor1_Mo…
 9 
train/test split   0.655  0.345     42 0           0        Preprocessor1_Mo…
10 
train/test split   0.662  0.338     43 0           0        Preprocessor1_Mo…

# generate a confusion matrix
test_predictions %>% 
  conf_mat(truth = isWinner, estimate = .pred_class)

          Truth
Prediction      0      1
         
          0 116576   7096
         
          1   6391 109760

# Create the final model
final_model <- fit(last_rf_workflow, df_other)

16) Computing Win Probability with Random Forest Model for match

Pakistan-India-2022-10-23

17) Worm -wicket graph of match

Pakistan-India-2022-10-23

C) Win Probability using MLP – Deep Neural Network (DNN) with player embeddings

In this approach the MLP package of Tidymodels was used. Multi-layer perceptron (MLP) with Deep Neural Network (DNN) was used to compute the Win Probability using player embeddings. An accuracy of 0.76 was obtained

1) Read the data

a) Read the data from 9 T20 leagues (BBL, CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB) and create a single data frame of ball-by-ball data. Display the data frame

2) Create training.validation and test sets

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)    
library(embed)

# Helper packages
library(readr)       # for importing data
library(vip) 
library(ranger)

df1=read.csv("output3/matchesBBL3.csv")
df2=read.csv("output3/matchesCPL3.csv")
df3=read.csv("output3/matchesIPL3.csv")
df4=read.csv("output3/matchesNTB3.csv")
df5=read.csv("output3/matchesPSL3.csv")
df6=read.csv("output3/matchesSSM3.csv")
df7=read.csv("output3/matchesT20M3.csv")
df8=read.csv("output3/matchesT20W3.csv")
df9=read.csv("output3/matchesWBB3.csv")

df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)


set.seed(123)
df$isWinner = as.factor(df$isWinner)
splits      <- initial_split(df,prop = 0.80)
df_other <- training(splits)
df_test  <- testing(splits)
set.seed(234)
val_set <- validation_split(df_other, 
                            prop = 0.80)
val_set

3) Create a Deep Neural Network recipe

Normalize parameters
Add embeddings for batsman, bowler

4) Set the MLP-DNN hyperparameters

epochs=100
hidden units =5
dropout regularization =0.1

5) Fit on Training data

cores <- parallel::detectCores()
cores

nn_recipe <- 
  recipe(isWinner ~ ., data = df_other) %>% 
step_normalize(ballNum,ballsRemaining,runs,runRate,numWickets,runsMomentum,perfIndex) %>%
  step_embed(batsman,bowler, outcome = vars(isWinner)) %>%
  prep(training = df_other, retain = TRUE) 

# For validation:
test_normalized <- bake(nn_recipe, new_data = df_test)

set.seed(57974)
# Set the hyper parameters for DNN
# Use Keras
# Fit on training data
nnet_fit <-
  mlp(epochs = 100, hidden_units = 5, dropout = 0.1) %>%
  set_mode("classification") %>% 
  # Also set engine-specific `verbose` argument to prevent logging the results: 
  set_engine("keras", verbose = 0) %>%
  fit(isWinner ~ ., data = bake(nn_recipe, new_data = df_other))

nnet_fit
parsnip model object
Model:"sequential"

____________________________________________________________________________

Layer (type)                                           Output Shape                                    Param #            
============================================================================
dense (Dense)                                           (None, 5)                                          60                 
____________________________________________________________________________

dense_1 (Dense)                                         (None, 5)                                          30                 
____________________________________________________________________________
dropout (Dropout)                                       (None, 5)                                          0                  
____________________________________________________________________________
dense_2 (Dense)                                         (None, 2)                                          12                 
============================================================================
Total params: 102
Trainable params: 102
Non-trainable params: 0

6) Test on Test data

Check ROC_AUC. It is 0.854
Check accuracy. The MLP-DNN gives a decent performance with an acuracy of 0.76
Compute the Confusion Matrix

# Validate on test data
val_results <- 
  df_test %>%
  bind_cols(
    predict(nnet_fit, new_data = test_normalized),
    predict(nnet_fit, new_data = test_normalized, type = "prob")
  )
val_results 

# Check roc_auc
val_results %>% roc_auc(truth = isWinner, .pred_0)
  .metric .estimator .estimate
  
   <chr>   <chr>          <dbl>
1 roc_auc binary         0.854

# Check accuracy
val_results %>% accuracy(truth = isWinner, .pred_class)
  .metric  .estimator .estimate
  <chr>    <chr>          <dbl>
1 accuracy binary         0.762

# Display confusion matrix
val_results %>% conf_mat(truth = isWinner, .pred_class)
          Truth
Prediction     
           0     1        
       0 97419 31564       
       1 25548 85292

Conclusion

Of the 3 ML models, glmnet, random forest and Multi-layer Perceptron DNN, random forest had the best performance
Random Forest ML model with batsman, bowler embeddings was able to achieve an accuracy of 92.4% and a ROC_AUC of 0.98 with very low false positives, negatives. This was a quantum jump from my earlier random forest model without embeddings which had an accuracy of 73.7% and an ROC_AUC of 0.834
The glmnet and NN models are fairly light weight. Random Forest is computationally very intensive.

Check out my other posts

To see all posts click Index of posts

Computing Win-Probability of T20 matches

I am late to the ‘Win probability’ computation for T20 matches, but managed to jump on to this bus with this post. Win Probability analysis and computation have been around for some time and are used in baseball, NFL, soccer hockey and others. On T20 cricket, the following posts from White Ball Analytics & Sports Data Science were good pointers to the general approach. The data for the Win Probability computation is taken from Cricsheet.

My initial Machine Learning models could not do better than 62% accuracy. I created a data set of ~830 IPL matches which roughly came to about 280,000 rows of ball-by-ball match data but I could not move beyond 62%. Addition of T20 men moved the needle to 64% accuracy. I spent time tuning Deep Learning networks using Tensorflow and Keras. Finally, I added T20 data from 9 T20 leagues – IPL, T20 men, T20 women, BBL, CPL, NTB, PSL, WBB, SSM. I had one large data set of 1.2 million rows of ball by ball data. The data frame looks like

I created a data frame for each match from ball Num 1 to ballNum ~240 for the 1st and 2nd innings of the match. My initial set of features were ballNum, runs, runRate, numWickets. The target variable isWinner= {0,1} depending on whether the team has won or lost the match.

The features

ballNum – ball number for 1 ~ 240+ in data frame. 1 – 120+ for 1st innings and 120+ – 240+ in 2nd innings including noballs, wides etc.
runs = cumulative runs scored at the ball count
runRate = cumulative runs scored/ ballNum (for 1st innings) and runs= required runs/ball Num for 2nd innings
numWickets = wickets lost

The target variable isWinner can take values {0,1} depending whether the team won or lost

With this initial dataframe, even though I had close to 1.2 million rows of ball by ball data of T20 matches my best performance with vanilla Logistic regression & SVM in Python was about 64% accuracy.

# Read all the data from 9 T20 leagues
# BBL,CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB
df1=pd.read_csv('matchesT20M.csv')
df2=pd.read_csv('matchesIPL.csv')
df3=pd.read_csv('matchesBBL.csv')
df4=pd.read_csv('matchesCPL.csv')
df5=pd.read_csv('matchesNTB.csv')
df6=pd.read_csv('matchesPSL.csv')
df7=pd.read_csv('matchesSSM.csv')
df8=pd.read_csv('matchesT20W.csv')
df9=pd.read_csv('matchesWBB.csv')

# Create one large dataframe
df10=pd.concat([df1,df2,df3,df4,df5,df6,df7,df8,df9])
print("Shape of dataframe=",df10.shape)
print("#####################################")
stats=check_values(df10)
print("#####################################")
model_fit(df10)
#norm_model_fit(df,stats)
svm_model_fit(df10)

Shape of dataframe= (1206901, 6)
#####################################
Null values: False
It contains 0 infinite values

Accuracy of Logistic regression classifier on training set: 0.63
Accuracy of Logistic regression classifier on test set: 0.64
Accuracy: 0.64
Precision: 0.62
Recall: 0.65
F1: 0.64


Accuracy of Linear SVC classifier on training set: 0.52
Accuracy of Linear SVC classifier on test set: 0.52

With Tensorflow/Keras the performance was about 67%. I tried several things

Normalisation
Tried different learning rates
Different optimisers – SGD, RMSProp, Adam
Changed depth and width of Neural Network

However I did not get much improvement. Finally I decided to do some Feature engineering. I added 2 new features

a) Runs Momentum : This feature is based on the fact that more the wickets in hand, the more freely the batsmen can make risky strokes, hence increasing the momentum of the runs, This is calculated as

runsMomentum = (11 – numWickets)/balls remaining

b) Performance Index: This feature is the product of the run rate x wickets in hand. In other words, if the strike rate is good and fewer wickets lost at the point in the match, then the performance index is higher at that point in the match will be higher

The final set of features chosen were as below

I had also included the balls Remaining in the innings. Now with this set of features I decided to execute Tensorflow/Keras and do a GridSearch with different learning rates, optimisers. After a couple of hours of computation I got an accuracy of 0.73. I needed to be able to read the ML model in R which required installation of Tensorflow, reticulate and Keras in RStudio and I had several issues. Since I hit a roadblock I moved to regular R models

I performed WIn Probability computation in the following ways

A) Win Probability with Vanilla Logistic Regression (R)

With vanilla Logistic Regression in R using the ‘glm’ package I got an accuracy of 0.67, sensitivity of 0.68 and specificity of 0.65 as shown below

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)

# Read all the data from 9 T20 leagues
# BBL,CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB
df1=read.csv("output2/matchesBBL2.csv")
df2=read.csv("output2/matchesCPL2.csv")
df3=read.csv("output2/matchesIPL2.csv")
df4=read.csv("output2/matchesNTB2.csv")
df5=read.csv("output2/matchesPSL2.csv")
df6=read.csv("output2/matchesSSM2.csv")
df7=read.csv("output2/matchesT20M2.csv")
df8=read.csv("output2/matchesT20W2.csv")
df9=read.csv("output2/matchesWBB2.csv")

# Create one large dataframe
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)

# Helper function to split into training/test
trainTestSplit <- function(df,trainPercent,seed1){
  ## Sample size percent
  samp_size <- floor(trainPercent/100 * nrow(df))
  ## set the seed 
  set.seed(seed1)
  idx <- sample(seq_len(nrow(df)), size = samp_size)
  idx
  
}

train_idx <- trainTestSplit(df,trainPercent=80,seed=5)
train <- df[train_idx, ]

test <- df[-train_idx, ]
# Fit a generalized linear logistic model, 
fit=glm(isWinner~.,family=binomial,data=train,control = list(maxit = 50))

a=predict(fit,newdata=train,type="response")
# Set response >0.5 as 1 and <=0.5 as 0
b=as.factor(ifelse(a>0.5,1,0))
# Compute the confusion matrix for training data

confusionMatrix(
  factor(b, levels = 0:1),
  factor(train$isWinner, levels = 0:1)
)

Confusion Matrix and Statistics

          Reference
Prediction    
  0      1
         0 339938 160336
         1 154236 310217
                                         
               Accuracy : 0.6739         
                 95% CI : (0.673, 0.6749)
    No Information Rate : 0.5122         
    P-Value [Acc > NIR] : < 2.2e-16      
                                         
                  Kappa : 0.3473         
                                         
 Mcnemar's Test P-Value : < 2.2e-16      
                                         
            Sensitivity : 0.6879         
            Specificity : 0.6593         
         Pos Pred Value : 0.6795         
         Neg Pred Value : 0.6679         
             Prevalence : 0.5122         
         Detection Rate : 0.3524         
   Detection Prevalence : 0.5186         
      Balanced Accuracy : 0.6736         
                                         
       'Positive' Class : 0      

# This can be saved and loaded as    
saveRDS(fit, "glm.rds")
ml_model <- readRDS("glm.rds")

Using the above ML model on Deccan Chargers vs Chennai Super on 27-04-2009 the Win Probability as the match progresses is as below

The Worm wicket graph of this match shows it was a closely fought match

B) Win Probability using Random Forests with Tidy Models – R

Initially I tried Tidy models with tuning for glmnet. The best I got was 0.67. However, I got an excellent performance using TidyModels with Random Forests. I am using Tidy Models for the first time and I have been blown away with how logically it is constructed, much like dplyr & ggplot2.

library(dplyr)
library(caret)
library(e1071)
library(ggplot2)
library(tidymodels)  

# Helper packages
library(readr)       # for importing data
library(vip) 
library(ranger)
# Read all the data from 9 T20 leagues
# BBL,CPL, IPL, NTB, PSL, SSM, T20 Men, T20 Women, WBB

df1=read.csv("output2/matchesBBL2.csv")
df2=read.csv("output2/matchesCPL2.csv")
df3=read.csv("output2/matchesIPL2.csv")
df4=read.csv("output2/matchesNTB2.csv")
df5=read.csv("output2/matchesPSL2.csv")
df6=read.csv("output2/matchesSSM2.csv")
df7=read.csv("output2/matchesT20M2.csv")
df8=read.csv("output2/matchesT20W2.csv")
df9=read.csv("output2/matchesWBB2.csv")

# Create one large dataframe
df=rbind(df1,df2,df3,df4,df5,df6,df7,df8,df9)

dim(df)
[1] 
1205909       8

# Take a peek at the dataset
glimpse(df)
$ ballNum        <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28…
$ ballsRemaining <int> 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 1…
$ runs           <int> 1, 1, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 13, 14, 16, 18, 18, 18, 24, 24, 24, 26, 26, 32, 32, 33, 34, 34, 3…
$ runRate        <dbl> 1.0000000, 0.5000000, 0.6666667, 0.7500000, 0.6000000, 0.5000000, 0.5714286, 0.5000000, 0.5555556, 0.…
$ numWickets     <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,…
$ runsMomentum   <dbl> 0.08800000, 0.08870968, 0.08943089, 0.09016393, 0.09090909, 0.09166667, 0.09243697, 0.09322034, 0.094…
$ perfIndex      <dbl> 11.000000, 5.500000, 7.333333, 8.250000, 6.600000, 5.500000, 6.285714, 5.500000, 6.111111, 5.000000, …
$ isWinner       <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…

df %>% 
  count(isWinner) %>% 
  mutate(prop = n/sum(n))

set.seed(123)
df$isWinner = as.factor(df$isWinner)

# Split the data into training and test set in 80%:20%
splits      <- initial_split(df,prop = 0.80)
df_other <- training(splits)
df_test  <- testing(splits)

# Create a validation set from training set in 80%:20%
set.seed(234)
val_set <- validation_split(df_other, 
                            prop = 0.80)
val_set

# Setup for Random forest using Ranger for classification
# Set up cores for parallel execution
cores <- parallel::detectCores()
cores

#Set up Random Forest engine
rf_mod <- 
  rand_forest(mtry = tune(), min_n = tune(), trees = 1000) %>% 
  set_engine("ranger", num.threads = cores) %>% 
  set_mode("classification")

rf_mod
# The Random Forest engine includes mtry which is number of predictor 
# variables required at each decision  tree with min_n the minimum number # of 
Random Forest Model Specification (classification)

Main Arguments:
  mtry = tune()
  trees = 1000
  min_n = tune()

Engine-Specific Arguments:
  num.threads = cores

Computational engine: ranger


# Setup the predictors and target variable
# Normalise all predictors. Random Forest don't need normalization but
# I have done it anyway
rf_recipe <-
  recipe(isWinner ~ ., data = df_other) %>% 
  step_normalize(all_predictors())

# Create workflow adding the ML model and recipe
rf_workflow <- 
  workflow() %>% 
  add_model(rf_mod) %>% 
  add_recipe(rf_recipe)

# The tune is done for 5 different values of the tuning parameters.
# Metrics include accuracy and roc_auc
rf_res <- 
  rf_workflow %>% 
  tune_grid(val_set,
            grid = 5,
            control = control_grid(save_pred = TRUE),
            metrics = metric_set(accuracy,roc_auc))

$ Pick the best of ROC/AUC
rf_res %>% 
  show_best(metric = "roc_auc")

We can see that when mtry (number of predictors) is 5 or 7 the ROC_AUC is 0.834 which is quite good

# A tibble: 5 × 8
   mtry min_n .metric .estimator  mean     n std_err .config             
  <int> <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>               
1     5    26 roc_auc binary     0.834     1      NA Preprocessor1_Model5
2     7    36 roc_auc binary     0.834     1      NA Preprocessor1_Model3
3     2    17 roc_auc binary     0.833     1      NA Preprocessor1_Model4
4     1    20 roc_auc binary     0.832     1      NA Preprocessor1_Model2
5     5     6 roc_auc binary     0.825     1      NA Preprocessor1_Model1


# Select the model with highest accuracy
rf_res %>% 
  show_best(metric = "accuracy")
   mtry min_n .metric  .estimator  mean     n std_err .config             
  <int> <int> <chr>    <chr>      <dbl> <int>   <dbl> <chr>               
1     7    36 accuracy binary     0.737     1      NA Preprocessor1_Model3
2     5    26 accuracy binary     0.736     1      NA Preprocessor1_Model5
3     1    20 accuracy binary     0.736     1      NA Preprocessor1_Model2
4     2    17 accuracy binary     0.735     1      NA Preprocessor1_Model4
5     5     6 accuracy binary     0.731     1      NA Preprocessor1_Model1

# The model with mtry (number of predictors) is 7 has the best accuracy. 
# Hence the best model has mtry=7 and min_n=36

rf_best <- 
  rf_res %>% 
  select_best(metric = "accuracy")

# Display the best model
rf_best
# A tibble: 1 × 3
   mtry min_n .config             
  <int> <int> <chr>               
1     7    36 Preprocessor1_Model3


rf_res %>% 
  collect_predictions()
   id         .pred_class  .row  mtry min_n .pred_0  .pred_1 isWinner .config             
   <chr>      <fct>       <int> <int> <int>   <dbl>    <dbl> <fct>    <chr>               
 1 validation 1               1     5     6 0.497   0.503    0        Preprocessor1_Model1
 2 validation 1               9     5     6 0.00753 0.992    1        Preprocessor1_Model1
 3 validation 0              10     5     6 0.627   0.373    0        Preprocessor1_Model1
 4 validation 0              16     5     6 0.998   0.002    0        Preprocessor1_Model1
 5 validation 1              18     5     6 0.270   0.730    1        Preprocessor1_Model1
 6 validation 0              23     5     6 0.899   0.101    0        Preprocessor1_Model1
 7 validation 1              26     5     6 0.452   0.548    1        Preprocessor1_Model1
 8 validation 0              30     5     6 0.657   0.343    1        Preprocessor1_Model1
 9 validation 0              34     5     6 0.576   0.424    0        Preprocessor1_Model1
10 validation 0              35     5     6 1.00    0.000167 0        Preprocessor1_Model1

rf_auc <- 
  rf_res %>% 
  collect_predictions(parameters = rf_best) %>% 
  roc_curve(isWinner, .pred_0) %>% 
  mutate(model = "Random Forest")

autoplot(rf_auc)

The Final Model

# Create the final Random Forest model with mtry=7 and min_n=36
# engine as "ranger" for classification
last_rf_mod <- 
  rand_forest(mtry = 7, min_n = 36, trees = 1000) %>% 
  set_engine("ranger", num.threads = cores, importance = "impurity") %>% 
  set_mode("classification")


# the last workflow is updated with the final model
last_rf_workflow <- 
  rf_workflow %>% 
  update_model(last_rf_mod)

set.seed(345)
last_rf_fit <- 
  last_rf_workflow %>% 
  last_fit(splits)

# Collect metrics
last_rf_fit %>% 
  collect_metrics()
  .metric  .estimator .estimate .config             
  <chr>    <chr>          <dbl> <chr>               
1 accuracy binary         0.739 Preprocessor1_Model1
2 roc_auc  binary         0.837 Preprocessor1_Model1

The Random Forest model gives an accuracy of 0.739 and ROC_AUC of .837 which I think is quite good. This is roughly what I got with Tensorflow/Keras

# Get the feature importance 
last_rf_fit %>% 
  extract_fit_parsnip() %>% 
  vip(num_features = 7)

Interestingly the feature that I engineered seems to have the maximum importancce namely Performance Index which is a product of Run rate x Wicket in Hand. I would have thought numWickets would be important but in T20 match probably is is not.

 generate predictions from the test set
test_predictions <- last_rf_fit %>% collect_predictions()
> test_predictions
# A tibble: 241,182 × 7
id               .pred_0 .pred_1  .row .pred_class isWinner .config             
<chr>              <dbl>   <dbl> <int> <fct>       <fct>    <chr>               
  1 train/test split   0.496   0.504     1 1           0        Preprocessor1_Model1
2 train/test split   0.640   0.360    11 0           0        Preprocessor1_Model1
3 train/test split   0.596   0.404    14 0           0        Preprocessor1_Model1
4 train/test split   0.287   0.713    22 1           0        Preprocessor1_Model1
5 train/test split   0.616   0.384    28 0           0        Preprocessor1_Model1
6 train/test split   0.516   0.484    36 0           0        Preprocessor1_Model1
7 train/test split   0.754   0.246    37 0           0        Preprocessor1_Model1
8 train/test split   0.641   0.359    39 0           0        Preprocessor1_Model1
9 train/test split   0.811   0.189    40 0           0        Preprocessor1_Model1
10 train/test split   0.618   0.382    42 0           0        Preprocessor1_Model1


# generate a confusion matrix
test_predictions %>% 
  conf_mat(truth = isWinner, estimate = .pred_class)

          Truth
Prediction     0     1
         0 92173 31623
         1 31320 86066

# Create the final model on the train/test data
final_model <- fit(last_rf_workflow, df_other)

# Final model
final_model
══ Workflow [trained] ════════════════════════════════════════════════════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: rand_forest()

── Preprocessor ──────────────────────────────────────────────────────────────────────────────────────────────────────────────
1 Recipe Step

• step_normalize()

── Model ─────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
Ranger result

Call:
 ranger::ranger(x = maybe_data_frame(x), y = y, mtry = min_cols(~7,      x), num.trees = ~1000, min.node.size = min_rows(~36, x),      num.threads = ~cores, importance = ~"impurity", verbose = FALSE,      seed = sample.int(10^5, 1), probability = TRUE) 

Type:                             Probability estimation 
Number of trees:                  1000 
Sample size:                      964727 
Number of independent variables:  7 
Mtry:                             7 
Target node size:                 36 
Variable importance mode:         impurity 
Splitrule:                        gini 
OOB prediction error (Brier s.):  0.1631303

The Random Forest Model’s performance has been quite impressive and probably requires further exploration.

# Saving and loading the model
save(final_model, file = "fit.rda")
load("fit.rda")

#Predicting the Win Probability of CSK vs DD match on 12 May 2012

Comparing this with the Worm wicket graph of this match we see that DD had no chance at all

C) Win Probability with Tensorflow/Keras with Grid Search – Python

I spent a fair amount of time tuning the hyper parameters of the Keras Deep Learning Network. Finally did go for the Grid Search. Incidentally I did ask ChatGPT to suggest code snippets for GridSearch which it promptly did!!!

import pandas as pd
import numpy as np
from zipfile import ZipFile
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
from tensorflow.keras import regularizers
from sklearn.model_selection import GridSearchCV

# Define the model
def create_model(optimizer='adam'):
    tf.random.set_seed(4)
    model = tf.keras.Sequential([
        keras.layers.Dense(32, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
        keras.layers.Dense(16, activation=tf.nn.relu),
        keras.layers.Dense(8, activation=tf.nn.relu),
        keras.layers.Dense(1,activation=tf.nn.sigmoid)
    ])

    # Since this is binary classification use binary_crossentropy
    model.compile(loss='binary_crossentropy',
                    optimizer=optimizer,
                    metrics='accuracy')
    return(model)

    # Create a KerasClassifier object
model = keras.wrappers.scikit_learn.KerasClassifier(build_fn=create_model)

# Define the grid of hyperparameters to search over
batch_size = [1024]
epochs = [40]
learning_rate = [0.01, 0.001, 0.0001]
optimizer = ['SGD', 'RMSprop', 'Adagrad', 'Adadelta', 'Adam', 'Adamax', 'Nadam']

param_grid = dict(dict(optimizer=optimizer,batch_size=batch_size, epochs=epochs) )
# Create the grid search object
grid_search = GridSearchCV(estimator=model, param_grid=param_grid, cv=3)

# Fit the grid search object to the training data
grid_search.fit(normalized_train_data, train_labels)

# Print the best hyperparameters
print('Best hyperparameters:', grid_search.best_params_)
# summarize results
print("Best: %f using %s" % (grid_search.best_score_, grid_search.best_params_))
means = grid_search.cv_results_['mean_test_score']
stds = grid_search.cv_results_['std_test_score']
params = grid_search.cv_results_['params']
for mean, stdev, param in zip(means, stds, params):
    print("%f (%f) with: %r" % (mean, stdev, param))

The best worked out to be the optimiser ‘Nadam’ with a learning rate of 0.001

import matplotlib.pyplot as plt
# Create a model
tf.random.set_seed(4)
model = tf.keras.Sequential([
    keras.layers.Dense(32, activation=tf.nn.relu, input_shape=[len(train_dataset1.keys())]),
    keras.layers.Dense(16, activation=tf.nn.relu),
    keras.layers.Dense(8, activation=tf.nn.relu),
    keras.layers.Dense(1,activation=tf.nn.sigmoid)
  ])

# Use the Nadam optimiser
optimizer=keras.optimizers.Nadam(learning_rate=.001, beta_1=0.9, beta_2=0.999, epsilon=1e-07, decay=0.0)

# Since this is binary classification use binary_crossentropy
model.compile(loss='binary_crossentropy',
                optimizer=optimizer,
                metrics='accuracy')

# Fit 
#history=model.fit(
#  train_dataset1, train_labels,batch_size=1024,
#  epochs=40, validation_data=(test_dataset1,test_labels), verbose=1)
history=model.fit(
  normalized_train_data, train_labels,batch_size=1024,
  epochs=40, validation_data=(normalized_test_data,test_labels), verbose=1)

Epoch 37/40
943/943 [==============================] - 3s 3ms/step - loss: 0.4971 - accuracy: 0.7310 - val_loss: 0.4968 - val_accuracy: 0.7357
Epoch 38/40
943/943 [==============================] - 3s 3ms/step - loss: 0.4970 - accuracy: 0.7310 - val_loss: 0.4974 - val_accuracy: 0.7378
Epoch 39/40
943/943 [==============================] - 4s 4ms/step - loss: 0.4970 - accuracy: 0.7309 - val_loss: 0.4994 - val_accuracy: 0.7296
Epoch 40/40
943/943 [==============================] - 3s 3ms/step - loss: 0.4969 - accuracy: 0.7311 - val_loss: 0.4998 - val_accuracy: 0.7300
plt.plot(history.history["loss"])
plt.plot(history.history["val_loss"])
plt.title("model loss")
plt.ylabel("loss")
plt.xlabel("epoch")
plt.legend(["train", "test"], loc="upper left")
plt.show()

Conclusion

So, the Keras Deep Learning Network gives about the same performance of Random Forest in Tidy Models. But I went with R Random Forest as it was easier to save and load the model for use with my data. Also, I am not sure whether the performance of the ML model can be improved beyond a point. However, I will continue to explore.

Watch this space!!!

Also see

To see all posts click Index of posts

References

Using embeddings, collaborative filtering with Deep Learning to analyse T20 players

There is a school of thought which considers that total runs scored and strike rate for a batsman, or total wickets taken and economy rate for a bowler, do not tell the whole story. This is true to a fair extent. The runs scored or the wickets taken could have been against weaker teams and hence the runs, strike rate or the wickets and economy rate alone do not capture all the performance details of the batsman or bowler. A technique to determine the performance of batsmen against different bowlers and identify the batsman’s possible performance even against bowlers he/she has not yet faced could be done with collaborative filtering. Collaborative filtering, with embeddings can also be used to group players with similar characteristics. Similarly, we could also identify the performance of bowlers versus different batsmen. Hence we need to look at average runs, SR and total wickets, ER with the lens of batsmen, bowlers against similar opposition. This is where collaborative filtering is useful.

The table below shows the performance of all batsman against all bowlers in the table below. The row in the table below is the batsman and the column is the bowler, with the value in the cell is the total Runs scored by the batsman against the bowler in all matches. Note the values are 0 for batsmen who have not yet faced specific bowlers. The table is fairly sparse.

Table A

Similarly, we can compute the performance of all bowlers against all batsmen as in the table below. Here the row is the bowler, the column batsman and the value in the cell is the number of times the bowler got the batsman’s wicket. As before the data is sparsely populated

This problem of computing batsman’s performance against bowlers or vice versa, is identical to the user vs movie rating problem used in collaborative filtering. For e.g we could consider

This above problem depicted could be computed using collaborative filtering with embeddings. We could assign sequential numbers for the batsmen from 1 to M, and for the bowlers from 1 to N. The total runs scored could be represented only for the rows where there are values. One way to solve this problem in Machine Learning is to use One Hot Encoding (OHE), where we assign values for each row and each column and map the values of the table with values of the cell for each combination. But this would take a enormous computation time and memory. The solution to this is use vector embeddings. Here embeddings could be used for capturing the sparse tensors between the batsmen, bowlers, runs scored or vice versa between bowlers against batsmen and the wickets taken. We only need to consider the cells for which values exist. An embedding is a relatively low-dimensional space, into which you can translate high-dimensional vectors. An embedding captures some of the semantics of the input by placing semantically similar inputs close together in the embedding space.

a) To compute bowler performances and identify similarities between bowlers the following embedding in the Deep Learning Network was used

To compute batsmen similarities a similar Deep Learning network for bowler vs batsmen is used

I had earlier created another post Player Performance Estimation using AI Collaborative Filtering for batsman and bowler recommendation, using R package Recommender Lab. However, I was not too happy with the results I got with this R package. When I searched the net for material on using embeddings for collaborative filtering, most of material on the web on movie lens or word2vec are repetitive and have no new material. Finally, this short video lecture from Developer Google on Embeddings provided the most clarity.

I have created 4 Colab notebooks to identify player similarities (recommendations)

a) Batsman similarities IPL

b) Batsman similarities T20

c) Bowler similarities IPL

d) Bowler similarities T20

For creating the model I have used all the data for T20 and IPL from so that I get the best results. The data is from Cricsheet. I have also used Google’s Embeddings Projector to display batsman and bowler embedding to and to group similar players

All the Colab notebooks and the data associated with the code are available in Github. Feel free to download and execute them. See if you get better performance. I tried a wide variety of hyperparameters – learning rate, width and depth of nodes per layer, number of layers, gradient methods etc.

You can download all the code & data from Github at embeddings

A) Batsman Recommender IPL (BatsmanRecommenderIPLA.ipynb)

Steps for creating the model

a) Upload bowler vs batsmen with times wicket was taken for batsman. This will be a sparse matrix

b) Assign integer indices for bowlers, batsmen

c) Add additional input features balls, runs conceded and Economy rate

d) Minimise loss for wickets taken for the bowler using SGD

e) Display embeddings of similar batsmen using Tensorboard projector

a) Upload data

Upload data file
2. Remove rows where wickets = 0

from google.colab import files
import io
uploaded = files.upload()
df2 = pd.read_csv(io.BytesIO(uploaded['bowlerVsBatsmanIPLE.csv']))
print(df2.shape)
df2 = df2.loc[df2['wicketTaken']!= 0]
print(df2.shape)

uploaded = files.upload()
df6 = pd.read_csv(io.BytesIO(uploaded['bowlerVsBatsmanIPLAll.csv']))
df6

Out[14]:

	bowler1	batsman1	balls	runsConceded	ER
0	A Ashish Reddy	DJG Sammy	1	0	0.000000
1	A Ashish Reddy	G Gambhir	10	17	10.200000
2	A Ashish Reddy	JEC Franklin	2	0	0.000000
3	A Ashish Reddy	LRPL Taylor	5	6	7.200000
4	A Ashish Reddy	MA Agarwal	3	7	14.000000
…	…	…	…	…	…
8550	Z Khan	Vishnu Vinod	4	8	12.000000
8551	Z Khan	VS Malik	3	5	10.000000
8552	Z Khan	W Jaffer	7	3	2.571429
8553	Z Khan	YK Pathan	22	35	9.545455
8554	Z Khan	Yuvraj Singh	12	12	6.000000

b) Create integer dictionaries for batsmen & bowlers

bowlers = df3["bowler1"].unique().tolist()
bowlers
# Create dictionary of bowler to index
bowlers2index = {x: i for i, x in enumerate(bowlers)}
bowlers2index
#Create dictionary of index tp bowler
index2bowlers = {i: x for i, x in enumerate(bowlers)}
index2bowlers


batsmen = df3["batsman1"].unique().tolist()
batsmen
# Create dictionary of batsman to index
batsmen2index = {x: i for i, x in enumerate(batsmen)}
batsmen2index
# Create dictionary of index to batsman
index2batsmen = {i: x for i, x in enumerate(batsmen)}
index2batsmen

#Map bowler, batsman to respective indices
df3["bowler"] = df3["bowler1"].map(bowlers2index)
df3["batsman"] = df3["batsman1"].map(batsmen2index)
df3
num_bowlers =len(bowlers2index)
num_batsmen = len(batsmen2index)
df3["wicketTaken"] = df3["wicketTaken"].values.astype(np.float32)
df3
# min and max ratings will be used to normalize the ratings later
min_wicketTaken = min(df3["wicketTaken"])
max_wicketTaken = max(df3["wicketTaken"])

print(
    "Number of bowlers: {}, Number of batsmen: {}, Min wicketsTaken: {}, Max wicketsTaken: {}".format(
        num_bowlers, num_batsmen, min_wicketTaken, max_wicketTaken
    )
)

c) Concatenate additional features

df3
df6
df31=pd.concat([df3,df6],axis=1)
df31

d) Create a Tensorflow/Keras deep learning mode. Minimise using Mean Squared Error using Stochastic Gradient Descent. I used ‘dropouts’ to regularise the model to keep validation loss within limits

tf.random.set_seed(4)
vector_size=len(batsmen2index)

df4=df31[['bowler','batsman','wicketTaken','balls','runsConceded','ER']]
df4
train_dataset = df4.sample(frac=0.9,random_state=0)
test_dataset = df4.drop(train_dataset.index)

train_dataset1 = train_dataset[['bowler','batsman','balls','runsConceded','ER']]
test_dataset1 = test_dataset[['bowler','batsman','balls','runsConceded','ER']]
train_stats = train_dataset1.describe()
train_stats = train_stats.transpose()
#print(train_stats)

train_labels = train_dataset.pop('wicketTaken')
test_labels = test_dataset.pop('wicketTaken')

# Create a Deep Learning model with keras
model = tf.keras.Sequential([
    tf.keras.layers.Embedding(vector_size,16,input_length=5),
    tf.keras.layers.Flatten(),
    keras.layers.Dropout(.2),
    keras.layers.Dense(16),
 
    keras.layers.Dense(8,activation=tf.nn.relu),
    
    keras.layers.Dense(4,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Print the model summary
#model.summary()
# Use the Adam optimizer with a learning rate of 0.01
#optimizer=keras.optimizers.Adam(learning_rate=.0009, beta_1=0.5, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=True)
#optimizer=keras.optimizers.RMSprop(learning_rate=0.01, rho=0.2, momentum=0.2, epsilon=1e-07)
#optimizer=keras.optimizers.SGD(learning_rate=.009,momentum=0.1) - Works without dropout
optimizer=keras.optimizers.SGD(learning_rate=.01,momentum=0.1)

model.compile(loss='mean_squared_error',
                optimizer=optimizer,
                )

 # Setup the training parameters
#model.compile(loss='binary_crossentropy',optimizer='rmsprop',metrics=['accuracy'])
# Create a model
history=model.fit(
  train_dataset1, train_labels,batch_size=32,
  epochs=40, validation_data = (test_dataset1,test_labels), verbose=1)

e) Plot losses

f) Predict wickets that will be taken by bowlers against random batsmen


df5= df4[['bowler','batsman','balls','runsConceded','ER']]
test1 = df5.sample(n=10)
test1.shape
for i in range(test1.shape[0]):
      print('Bowler :', index2bowlers.get(test1.iloc[i,0]), ", Batsman : ",index2batsmen.get(test1.iloc[i,1]), '- Times wicket Prediction:',model.predict(test1.iloc[[i]]))
1/1 [==============================] - 0s 90ms/step
Bowler : Harbhajan Singh , Batsman :  AM Nayar - Times wicket Prediction: [[1.0114906]]
1/1 [==============================] - 0s 18ms/step
Bowler : T Natarajan , Batsman :  Arshdeep Singh - Times wicket Prediction: [[0.98656166]]
1/1 [==============================] - 0s 19ms/step
Bowler : KK Ahmed , Batsman :  A Mishra - Times wicket Prediction: [[1.0504484]]
1/1 [==============================] - 0s 24ms/step
Bowler : M Muralitharan , Batsman :  F du Plessis - Times wicket Prediction: [[1.0941994]]
1/1 [==============================] - 0s 25ms/step
Bowler : SK Warne , Batsman :  DR Smith - Times wicket Prediction: [[1.0679393]]
1/1 [==============================] - 0s 28ms/step
Bowler : Mohammad Nabi , Batsman :  Ishan Kishan - Times wicket Prediction: [[1.403399]]
1/1 [==============================] - 0s 32ms/step
Bowler : R Bhatia , Batsman :  DJ Thornely - Times wicket Prediction: [[0.89399755]]
1/1 [==============================] - 0s 26ms/step
Bowler : SP Narine , Batsman :  MC Henriques - Times wicket Prediction: [[1.1997008]]
1/1 [==============================] - 0s 19ms/step
Bowler : AS Rajpoot , Batsman :  K Gowtham - Times wicket Prediction: [[0.9911405]]
1/1 [==============================] - 0s 21ms/step
Bowler : K Rabada , Batsman :  P Simran Singh - Times wicket Prediction: [[1.0064855]]

g) The embedding can be visualised using Google’s Embedding Projector, which identifies other batsmen who have similar characteristics. Here Cosine Similarity is used for grouping similar batsmen of IPL

The closest neighbor for AB De Villiers in IPL is SK Raina, then Rohit Sharma as seen in the visualisation below

B. Bowler Recommender T20 (BowlerRecommenderT20M1A.ipynb)

Similar to how batsman was set up,

The steps are

a) Upload data for T20 Batsman vs Bowler with Total runs scored. This will be a sparse matrix

b) Create integer dictionaries for batsman & bowler

c) Add additional features like fours, sixes and strike rate

d) Minimise loss for wicket taken

e) Display embeddings of bowlers using Tensorboard Embeddings Projector

Minimizing the loss for wicket taken using SGD

tf.random.set_seed(4)
vector_size=len(batsman2index)

#Normalize target variable
df4=df31[['bowler','batsman','totalRuns','fours','sixes','ballsFaced']]
df4['normalizedRuns'] = (df4['totalRuns'] -df4['totalRuns'].mean())/df4['totalRuns'].std()
print(df4)
train_dataset = df4.sample(frac=0.8,random_state=0)
test_dataset = df4.drop(train_dataset.index)
train_dataset1 = train_dataset[['batsman','bowler','fours','sixes','ballsFaced']]
test_dataset1 = test_dataset[['batsman','bowler','fours','sixes','ballsFaced']]

train_labels = train_dataset.pop('normalizedRuns')
test_labels = test_dataset.pop('normalizedRuns')
train_labels
print(train_dataset1)

# Create a Deep Learning model with keras
model = tf.keras.Sequential([
    tf.keras.layers.Embedding(vector_size,16,input_length=5),
    tf.keras.layers.Flatten(),
    keras.layers.Dropout(.2),
    keras.layers.Dense(16),
 
    keras.layers.Dense(8,activation=tf.nn.relu),
    
    keras.layers.Dense(4,activation=tf.nn.relu),
    keras.layers.Dense(1)
  ])

# Print the model summary
#model.summary()
# Use the Adam optimizer with a learning rate of 0.01
#optimizer=keras.optimizers.Adam(learning_rate=.0009, beta_1=0.5, beta_2=0.999, epsilon=None, decay=0.0, amsgrad=True)
#optimizer=keras.optimizers.RMSprop(learning_rate=0.001, rho=0.2, momentum=0.2, epsilon=1e-07)
#optimizer=keras.optimizers.SGD(learning_rate=.009,momentum=0.1) - Works without dropout
optimizer=keras.optimizers.SGD(learning_rate=.01,momentum=0.1)

model.compile(loss='mean_squared_error',
                optimizer=optimizer,
                )

 # Setup the training parameters
#model.compile(loss='binary_crossentropy',optimizer='rmsprop',metrics=['accuracy'])
# Create a model
history=model.fit(
  train_dataset1, train_labels,batch_size=32,
  epochs=40, validation_data = (test_dataset1,test_labels), verbose=1)

model.predict(train_dataset1[1:10])
df5= df4[['batsman','bowler','fours','sixes','ballsFaced']]
test1 = df5.sample(n=10)
model.predict(test1)
#(model.predict(test1)* df4['totalRuns'].std()) + df4['totalRuns'].mean()
for i in range(test1.shape[0]):
        print('Batsman :', index2batsman.get(test1.iloc[i,0]), ", Bowler : ",index2bowler.get(test1.iloc[i,1]), '- Total runs Prediction:',(model.predict(test1.iloc[i])* df4['totalRuns'].std()) + df4['totalRuns'].mean())
1/1 [==============================] - 0s 396ms/step
1/1 [==============================] - 0s 112ms/step
1/1 [==============================] - 0s 183ms/step
Batsman : G Chohan , Bowler :  Khawar Ali - Total runs Prediction: [[1.8883028]]
1/1 [==============================] - 0s 56ms/step
Batsman : Umar Akmal , Bowler :  LJ Wright - Total runs Prediction: [[9.305391]]
1/1 [==============================] - 0s 68ms/step
Batsman : M Shumba , Bowler :  Simi Singh - Total runs Prediction: [[19.662743]]
1/1 [==============================] - 0s 30ms/step
Batsman : CH Gayle , Bowler :  RJW Topley - Total runs Prediction: [[16.854687]]
1/1 [==============================] - 0s 39ms/step
Batsman : BA King , Bowler :  Taskin Ahmed - Total runs Prediction: [[3.5154686]]
1/1 [==============================] - 0s 102ms/step
Batsman : KD Shah , Bowler :  Avesh Khan - Total runs Prediction: [[8.411661]]
1/1 [==============================] - 0s 38ms/step
Batsman : ST Jayasuriya , Bowler :  SCJ Broad - Total runs Prediction: [[5.867449]]
1/1 [==============================] - 0s 45ms/step
Batsman : AB de Villiers , Bowler :  Saeed Ajmal - Total runs Prediction: [[15.150892]]
1/1 [==============================] - 0s 46ms/step
Batsman : SV Samson , Bowler :  J Little - Total runs Prediction: [[10.44426]]
1/1 [==============================] - 0s 102ms/step
Batsman : Zawar Farid , Bowler :  GJ Delany - Total runs Prediction: [[1.9770675]]

Identifying similar bowlers using Embeddings Projector for T20

Bhuvaneshwar Kumar’s performance is closest to CR Woakes

Note: Incidentally the accuracy in the above model was not too good. I may work on this again later!

C) Bowler Embeddings IPL – Grouping similar bowlers of IPL with Embeddings Projector (BowlerRecommenderIPLA.ipynb)

D) Batting Embeddings T20 – Grouping similar batsmen of T20 (BatsmanRecommenderT20MA.ipynb)

The Tensorboard Pmbeddings projector is also interesting. There are multiple ways the data can be visualised namely UMAP, T-SNE, PCA(included). You could play with it.

As mentioned above the Colab notebooks and data are available at Github embeddings

The ability to identify batsmen & bowlers who would perform similarly against specific bowling attacks coupled with the average runs & strike rate should give a good measure of a player’s performance.

Take a look at some of my other posts

To see all posts click Index of posts

Near Real-time Analytics of ICC Men’s T20 World Cup with GooglyPlusPlus

In my last post GooglyPlusPlus gets ready for ICC Men’s T20 World Cup, I had mentioned that GooglyPlusPlus was preparing for the big event the ICC Men’s T20 World cup. Now that the T20 World cup is underway, my Shiny app in R, GooglyPlusPlus ,will be generating near real-time analytics of matches completed the previous day. Besides the app can also do historical analysis of players, teams and matches.

The whole process is automated. A cron job will execute every day, in the morning, which will automatically download the matches of the previous day from Cricsheet, unzip them, start a pipeline which will transform and process the match data into necessary folders and finally upload the newly acquired data into my Shiny app. Hence, you will be able to access all the breathless, pulsating cricketing action in timeless, interactive plots and tables which will capture all aspects of Men’s T20 matches, namely batsman, bowler performance, match analysis, team-vs-team, team-vs-all teams besides ranking of batsmen & bowlers. Since the data is cumulative, all the analytics are historical and current.

Check out GooglyPlusPlus!!

The data for GooglyPlusPlus is taken from Cricsheet

Interest in cricket, has mushroomed in recent times around the world, with the addition of new formats which started with ODI, T20, T10, 100 ball and so on. There are leagues which host these matches at different levels around the world. While GooglyPlusPlus, provides near real-time analytics of Men’s T20 World cup, we can clearly envision a big data platform which ingests matches daily from multiple cricket formats, leagues around the world generating real-time and near real-time analytics which are essential these days to selection of teams at different levels through auctions. For more discussion on this see my posts

We could imagine a Data Lake, into which are ingested data from the different cricket formats, leagues through appropriate technology connectors. Once the data is ingested, we could have data pipelines, based on Azure ADF, Apache NiFi, Apache Airflow or Amazon EMR etc., to transform, process and enhance the data, generating real-time analytics on the fly. Recent formats like T20, T10 require more urgency in strategic thinking based on scoring within limited overs, or containing batsmen from going on a rampage within the set of overs, the analytics on a fly may help the coach to modify the batting or bowling lineup at points in match. In this context see my earlier post Using Linear Programming (LP) for optimizing bowling change or batting lineup in T20 cricket

All of these are not just possible, but are likely to become reality as more and more formats, leagues and cricket data proliferate around the world.

This post, focuses on generating near-real time analytics for ICC Men’s T20 World Cup using GooglyPlusPlus. Included below, is a sampling of the analytics that you can perform for analysing the matches. In addition you can do all the analysis included in my post GooglyPlusPlus gets ready for ICC Men’s T20 World Cup

Namibia-Sri Lanka-16 Oct 2022 : Match Worm graph

The opening match between Namibia vs Sri Lanka resulted in an upset. We can see this in the match worm-wicket graph below

2. Scotland vs West Indies – 17 Oct 2022: Batsmen vs Bowlers

George Munsey was the top scorer for Scotland and was instrumental in the win against WI. His performance against West Indies bowlers is shown below. Note, the charts are interactive

3. Zimbabwe vs Ireland – 17 Oct 2022 : Team Runs vs SR

Sikander Raza of Zimbabwe with 82 runs with the strike rate ~ 170

4. United Arab Emirates vs Netherlands – 16 Oct 2022: Team runs across 20 overs

UAE pipped Netherlands in the middle overs and were able to win by 1 ball and 3 wickets

5. Scotland vs Ireland – 19 Oct 2022 : Team Runs vs SR Middle overs plot

Curtis Campher snatched the game away from Scotland with his stellar performance in middle and death overs

6. UAE vs Namibia : 20 Oct 2022 : Team Wickets vs ER plot

Basoor Hameed and Zahoor Khan got 2 wickets apiece with an economy rate of ~5.00 but still they were not able to stop UAE from stealing a win

7. Overall Runs vs SR in T20 World Cup 2022

It is too early to rank the players, nevertheless in the current T20 World Cup, MP O’Dowd (Netherlands), BKG Mendis (Sri Lanka) and JN Frylinck(Namibia) are the top 3 batsmen with good runs and Strike Rate

8. Overall Wickets over ER in T20 World Cup 2022

The top 3 bowlers so far in T20 World Cup 2022 are a) BFW de Leede (Netherlands) b) PWH De Silva (Sri Lanka) c) KP Meiyappan (UAE) with a total of 7,7, and 6 wickets respectively

Note: Besides the match analysis GooglyPlusPlus also provides detailed analysis of batsmen, bowlers, matches as above, team-vs-team, team-vs-all teams, ranking of batsmen & bowlers etc. For more details see my post GooglyPlusPlus gets ready for ICC Men’s T20 World Cup

Do visit GooglyPlusPlus everyday to check out the cricketing actions of matches gone by. You can also follow me on twitter @tvganesh_85 for daily highlights.