cricketr adapts to the Twenty20 International!


Introduction

This should be last in the series of posts based on my R package cricketr. That is, unless some bright idea comes trotting along and light bulbs go on around my head.

In this post cricketr adapts to the Twenty20 International format. Now cricketr can handle stats from all 3 formats of the game namely Test matches, ODIs and Twenty20 International from ESPN Cricinfo. You should be able to install the package from GitHub and use the many of the functions available in the package.

Please be mindful of the ESPN Cricinfo Terms of Use

You can also read this post at Rpubs as twenty20-cricketr. Download this report as a PDF file from twenty20-cricketr.pdf

I have chosen the Top 4 batsmen and top 4 bowlers based on ICC rankings and/or number of matches played.

Batsmen

  1. Virat Kohli (Ind)
  2. Faf du Plessis (SA)
  3. A J Finch (Aus)
  4. Brendon McCullum (Aus)

Bowlers

  1. Samuel Badree (WI)
  2. Sunil Narine (WI)
  3. Ravichander Ashwin (Ind)
  4. Ajantha Mendis (SL)

I have explained the plots and added my own observations. Please feel free to draw your conclusions!

The data for a particular player can be obtained with the getPlayerData() function. To do you will need to go to ESPN CricInfo Player and type in the name of the player for e.g Virat Kohli, Sunil Narine etc. This will bring up a page which have the profile number for the player e.g. for Virat Kohli this would be http://www.espncricinfo.com/india/content/player/253802.html. Hence, Sachin’s profile is 253802. This can be used to get the data for Virat Kohli as shown below

library(devtools)
install_github("tvganesh/cricketr")
library(cricketr)

The data for a particular player can be obtained with the getPlayerData() function. To do you will need to go to ESPN CricInfo Player and type in the name of the player for e.g Virat Kohli, Sunil Narine etc. This will bring up a page which have the profile number for the player e.g. for Virat Kohli this would be http://www.espncricinfo.com/india/content/player/253802.html. Hence, Kohlis profile is 253802. This can be used to get the data for Virat Kohli as shown below

kohli <- getPlayerDataTT(253802,dir="..",file="kohli.csv",type="batting")

The analysis is included below

Analyses of Batsmen

The following plots gives the analysis of the 4 ODI batsmen

  1. Virat Kohli (Ind) – Innings-26, Runs-972, Average-46.28,Strike Rate-131.70
  2. Faf du Plessis (SA) – Innings-24, Runs-805, Average-42.36,Strike Rate-135.75
  3. A J Finch (Aus) – Innings-22, Runs-756, Average-39.78,Strike Rate-152.41
  4. Brendon McCullum (NZ) – Innings-70, Runs-2140, Average-35.66,Strike Rate-136.21

Plot of 4s, 6s and the scoring rate in ODIs

The 3 charts below give the number of

  1. 4s vs Runs scored
  2. 6s vs Runs scored
  3. Balls faced vs Runs scored A regression line is fitted in each of these plots for each of the ODI batsmen

A. Virat Kohli
– The 1st plot shows that Kohli approximately hits about 5 4’s on his way to the 50s
– The 2nd box plot of no of 6s and runs shows the range of runs when Kohli scored 1,2 or 4 6s. The dark line in the box shows the average runs when he scored those number of 6s. So when he scored 1 6 the average runs he scored was 45
– The 3rd plot shows the number of runs scored against the balls faced. It can be seen when Kohli faced 50 balls he had scored around ~ 70 runs

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./kohli.csv","Kohli")
batsman6s("./kohli.csv","Kohli")
batsmanScoringRateODTT("./kohli.csv","Kohli")

kohli-4s6sSR-1

dev.off()
## null device 
##           1

B. Faf du Plessis

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./plessis.csv","Du Plessis")
batsman6s("./plessis.csv","Du Plessis")
batsmanScoringRateODTT("./plessis.csv","Du Plessss")

plessis-4s6SR-1

dev.off()
## null device 
##           1

C. A J Finch

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./finch.csv","A J Finch")
batsman6s("./finch.csv","A J Finch")
batsmanScoringRateODTT("./finch.csv","A J Finch")

finch-4s6sSR-1

dev.off()
## null device 
##           1

D. Brendon McCullum

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./mccullum.csv","McCullum")
batsman6s("./mccullum.csv","McCullum")
batsmanScoringRateODTT("./mccullum.csv","McCullum")

mccullum-4s6sout-1

dev.off()
## null device 
##           1

Relative Mean Strike Rate

This plot shows the Mean Strike Rate of the batsman in each run range. It can be seen the A J Finch has the best strike rate followed by B McCullum.

par(mar=c(4,4,2,2))
frames <- list("./kohli.csv","./plessis.csv","finch.csv","mccullum.csv")
names <- list("Kohli","Du Plessis","Finch","McCullum")
relativeBatsmanSRODTT(frames,names)

plot-1-1

Relative Runs Frequency Percentage

The plot below provides the average runs scored in each run range 0-5,5-10,10-15 etc. Clearly Kohli has the most runs scored in most of the runs ranges. . This is also evident in the fact that Kohli has the highest average. He is followed by McCullum

frames <- list("./kohli.csv","./plessis.csv","finch.csv","mccullum.csv")
names <- list("Kohli","Du Plessis","Finch","McCullum")
relativeRunsFreqPerfODTT(frames,names)

plot-2-1

Percent 4’s,6’s in total runs scored

The plot below shows the percentage of runs scored by way of 4s and 6s for each batsman. Du Plessis has the highest percentage of 4s, McCullum has the highest 6s. Finch has the highest percentage of 4s & 6s – 25.37 + 15.64= 41.01%

rames <- list("./kohli.csv","./plessis.csv","finch.csv","mccullum.csv")
names <- list("Kohli","Du Plessis","Finch","McCullum")
runs4s6s <-batsman4s6s(frames,names)

plot-46s-1

print(runs4s6s)
##                Kohli Du Plessis Finch McCullum
## Runs(1s,2s,3s) 64.29      64.55 58.99    61.45
## 4s             27.78      24.38 25.37    22.87
## 6s              7.94      11.07 15.64    15.69

3D plot of Runs vs Balls Faced and Minutes at Crease

The plot is a scatter plot of Runs vs Balls faced and Minutes at Crease. A prediction plane is then fitted based on the Balls Faced and Minutes at Crease to give the runs scored

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./kohli.csv","Kohli")
battingPerf3d("./plessis.csv","Du Plessis")

plot-3-1

dev.off()
## null device 
##           1
par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./finch.csv","A J Finch")
battingPerf3d("./mccullum.csv","McCullum")

plot-4-1

dev.off()
## null device 
##           1

Predicting Runs given Balls Faced and Minutes at Crease

A hypothetical Balls faced and Minutes at Crease is used to predict the runs scored by each batsman based on the computed prediction plane

BF <- seq( 5, 70,length=10)
Mins <- seq(5,70,length=10)
newDF <- data.frame(BF,Mins)

kohli <- batsmanRunsPredict("./kohli.csv","Kohli",newdataframe=newDF)
plessis <- batsmanRunsPredict("./plessis.csv","Du Plessis",newdataframe=newDF)
finch <- batsmanRunsPredict("./finch.csv","A J Finch",newdataframe=newDF)
mccullum <- batsmanRunsPredict("./mccullum.csv","McCullum",newdataframe=newDF)

The predicted runs is displayed. As can be seen Finch has the best overall strike rate followed by McCullum.

batsmen <-cbind(round(kohli$Runs),round(plessis$Runs),round(finch$Runs),round(mccullum$Runs))
colnames(batsmen) <- c("Kohli","Du Plessis","Finch","McCullum")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns
##    BallsFaced MinsAtCrease Kohli Du Plessis Finch McCullum
## 1           5            5     2          1     5        3
## 2          12           12    12         10    22       16
## 3          19           19    22         19    40       28
## 4          27           27    31         28    57       41
## 5          34           34    41         37    74       54
## 6          41           41    51         47    91       66
## 7          48           48    60         56   108       79
## 8          56           56    70         65   125       91
## 9          63           63    79         74   142      104
## 10         70           70    89         84   159      117

Highest runs likelihood

The plots below the runs likelihood of batsman. This uses K-Means Kohli has the highest likelihood of scoring runs 34.2% likely to score 66 runs. Du Plessis has 25% likelihood to score 53 runs, A. Virat Kohli

batsmanRunsLikelihood("./kohli.csv","Kohli")

kohli-lh-1

## Summary of  Kohli 's runs scoring likelihood
## **************************************************
## 
## There is a 23.08 % likelihood that Kohli  will make  10 Runs in  10 balls over 13  Minutes 
## There is a 42.31 % likelihood that Kohli  will make  29 Runs in  23 balls over  30  Minutes 
## There is a 34.62 % likelihood that Kohli  will make  66 Runs in  47 balls over 63  Minutes

B. Faf Du Plessis

batsmanRunsLikelihood("./plessis.csv","Du Plessis")

plessis-l-1

## Summary of  Du Plessis 's runs scoring likelihood
## **************************************************
## 
## There is a 62.5 % likelihood that Du Plessis  will make  14 Runs in  11 balls over 19  Minutes 
## There is a 25 % likelihood that Du Plessis  will make  53 Runs in  40 balls over  50  Minutes 
## There is a 12.5 % likelihood that Du Plessis  will make  94 Runs in  61 balls over 90  Minutes

C. A J Finch

batsmanRunsLikelihood("./finch.csv","A J Finch")

finch-lh,cache-TRUE-1

## Summary of  A J Finch 's runs scoring likelihood
## **************************************************
## 
## There is a 20 % likelihood that A J Finch  will make  95 Runs in  54 balls over 70  Minutes 
## There is a 25 % likelihood that A J Finch  will make  42 Runs in  27 balls over  35  Minutes 
## There is a 55 % likelihood that A J Finch  will make  8 Runs in  8 balls over 12  Minutes

D. Brendon McCullum

batsmanRunsLikelihood("./mccullum.csv","McCullum")

mccullum-1

## Summary of  McCullum 's runs scoring likelihood
## **************************************************
## 
## There is a 50.72 % likelihood that McCullum  will make  11 Runs in  10 balls over 13  Minutes 
## There is a 28.99 % likelihood that McCullum  will make  36 Runs in  27 balls over  37  Minutes 
## There is a 20.29 % likelihood that McCullum  will make  74 Runs in  48 balls over 70  Minutes

Moving Average of runs over career

The moving average for the 4 batsmen indicate the following. It must be noted that there is not sufficient data yet on Twenty20 Internationals. Kpohli, Du Plessis and Finch average only 26 innings while McCullum has close to 70. So the moving average while an indication will regress towards the mean over time.

  1. The moving average of Kohli and Du Plessis is on the way up.
  2. McCullum has a consistent performance while Finch had a brief burst in 2013-2014
par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanMovingAverage("./kohli.csv","Kohli")
batsmanMovingAverage("./plessis.csv","Du Plessis")
batsmanMovingAverage("./finch.csv","A J Finch")
batsmanMovingAverage("./mccullum.csv","McCullum")

sdgm-ma-1

dev.off()
## null device 
##           1

Analysis of bowlers

  1. Samuel Badree (WI) – Innings-22, Runs -464, Wickets – 31, Econ Rate : 5.39
  2. Sunil Narine (WI)- Innings-31,Runs-666, Wickets – 38 , Econ Rate : 5.70
  3. Ravichander Ashwin (Ind)- Innings-26, Runs- 732, Wickets – 25, Econ Rate : 7.32
  4. Ajantha Mendis (SL)- Innings-39, Runs – 952,Wickets – 66, Econ Rate : 6.45

The plot shows the frequency with which the bowlers have taken 1,2,3 etc wickets. The most wickets taken is by Ajantha Mendis (6 wickets)

Wicket Frequency percentage

This plot gives the percentage of wickets for each wickets (1,2,3…etc)

par(mfrow=c(1,4))
par(mar=c(4,4,2,2))
bowlerWktsFreqPercent("./badree.csv","Badree")
bowlerWktsFreqPercent("./mendis.csv","Mendis")
bowlerWktsFreqPercent("./narine.csv","Narine")
bowlerWktsFreqPercent("./ashwin.csv","Ashwin")

relBowlFP-1

dev.off()
## null device 
##           1

Wickets Runs plot

The plot below gives a boxplot of the runs ranges for each of the wickets taken by the bowlers. The ends of the box indicate the 25% and 75% percentile of runs scored for the wickets taken and the dark balck line is the average runs conceded.

par(mfrow=c(1,4))
par(mar=c(4,4,2,2))
bowlerWktsRunsPlot("./badree.csv","Badree")
bowlerWktsRunsPlot("./mendis.csv","Mendis")
bowlerWktsRunsPlot("./narine.csv","Narine")
bowlerWktsRunsPlot("./ashwin.csv","Ashwin")

wktsrun-1

dev.off()
## null device 
##           1

This plot below shows the average number of deliveries needed by the bowler to take the wickets (1,2,3 etc)

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerWktRateTT("./badree.csv","Badree")
bowlerWktRateTT("./mendis.csv","Mendis")

wktsrate1-1

dev.off()
## null device 
##           1
par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerWktRateTT("./narine.csv","Narine")
bowlerWktRateTT("./ashwin.csv","Ashwin")

wktsrate2-1

dev.off()
## null device 
##           1

Relative bowling performance

The plot below shows that Narine has the most wickets in the 2 -4 range followed by Mendis

frames <- list("./badree.csv","./mendis.csv","narine.csv","ashwin.csv")
names <- list("Badree","Mendis","Narine","Ashwin")
relativeBowlingPerf(frames,names)

relBowlPerf-1

Relative Economy Rate against wickets taken

The economy rate can be deduced as follows from the plot below. Narine has a good economy rate around 1 & 4 wickets, Ashwin around 2 wickets and Badree around 3. wickets

frames <- list("./badree.csv","./mendis.csv","narine.csv","ashwin.csv")
names <- list("Badree","Mendis","Narine","Ashwin")
relativeBowlingERODTT(frames,names)

relBowlER-1

Relative Wicket Rate

The relative wicket rate plots the mean number of deliveries needed to take the wickets namely (1,2,3,4). For e.g. Narine needed an average of 22 deliveries to take 1 wicket and 22.5,23.2, 24 deliveries to take 2,3 & 4 wickets respectively

frames <- list("./badree.csv","./mendis.csv","narine.csv","ashwin.csv")
names <- list("Badree","Mendis","Narine","Ashwin")
relativeWktRateTT(frames,names)

relBowlWktRate-1

Moving average of wickets over career

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
bowlerMovingAverage("./badree.csv","Badree")
bowlerMovingAverage("./mendis.csv","Mendis")
bowlerMovingAverage("./narine.csv","Narine")
bowlerMovingAverage("./ashwin.csv","Ashwin")
## null device 
##           1

jsba-bowlma-1

Key findings

Here are some key conclusions

Twenty 20 batsmen

  1. Kohli has the a very consistent performance scoring high runs in the different run ranges. Kohli also has a 34.2% likelihood to score 6 runs. He is followed by McCullum for consisten performance
  2. Finch has a best strike rate followed by McCullum.
  3. Du Plessis has the highest percentage of 4s and McCullum has the percentage of 6s. Finch is superior in the percentage of runs scored in 4s and 6s
  4. For a hypothetical balls faced and minutes at crease, Finch does best followed by McCullum
  5. Kohli’s & Du Plessis Twenty20 career is on a upswing. Can they maintain the momentum. McCullum is consistent

Twenty20 bowlers

  1. Narine has the highest wickets percentage for different wickets taken followed by Mendis
  2. Mendis has taken 1,2,3,4,6 wickets in 24 deliveries
  3. Narine has the lowest economy rate for 1 & 4 wickets, Ashwin for 2 wickets and Badree for 3 wickets. Mendis is comparatively expensive
  4. Narine needed the least deliveries to get 1 (22.5) & 2 (23.2) wickets, Mendis needed 20.5 deliveries and Ashwin 19 deliveries for 4 wickets

Key takeaways 1. If all the above batsment and bowlers were in the same team we expect

  1. Finch would be most useful when the run rate has to be greatly accelerated followed by McCullum
  2. If the need is to consolidate, then Kohli is the best man for the job followed by McCullum
  3. Overall McCullum is the best bet for Twenty20
  4. When it comes to bowling Narine wins hands down as he has the most wickets, a good economy rate and a very good attack rate. So Narine is great bet for providing a vital breakthrough.

Also see my other posts in R

  1. Introducing cricketr! : An R package to analyze performances of cricketers
  2. cricketr plays the ODIs!
  3. A peek into literacy in India: Statistical Learning with R
  4. A crime map of India in R – Crimes against women
  5. Analyzing cricket’s batting legends – Through the mirage with R
  6. Mirror, mirror . the best batsman of them all?

You may also like

  1. A closer look at “Robot Horse on a Trot” in Android
  2. What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
  3. Bend it like Bluemix, MongoDB with autoscaling – Part 2
  4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
  5. TWS-4: Gossip protocol: Epidemics and rumors to the rescue
  6. Deblurring with OpenCV:Weiner filter reloaded
  7. Architecting a cloud based IP Multimedia System (IMS)

cricketr plays the ODIs!


Introduction

In this post my package ‘cricketr’ takes a swing at One Day Internationals(ODIs). Like test batsman who adapt to ODIs with some innovative strokes, the cricketr package has some additional functions and some modified functions to handle the high strike and economy rates in ODIs. As before I have chosen my top 4 ODI batsmen and top 4 ODI bowlers

You can also read this post at Rpubs as odi-cricketr. Dowload this report as a PDF file from odi-cricketr.pdf

Batsmen

  1. Virendar Sehwag (Ind)
  2. AB Devilliers (SA)
  3. Chris Gayle (WI)
  4. Glenn Maxwell (Aus)

Bowlers

  1. Mitchell Johnson (Aus)
  2. Lasith Malinga (SL)
  3. Dale Steyn (SA)
  4. Tim Southee (NZ)

I have sprinkled the plots with a few of my comments. Feel free to draw your conclusions! The analysis is included below

The profile for Virender Sehwag is 35263. This can be used to get the ODI data for Sehwag. For a batsman the type should be “batting” and for a bowler the type should be “bowling” and the function is getPlayerDataOD()

library(devtools)
install_github("tvganesh/cricketr")
library(cricketr)

The One day data for a particular player can be obtained with the getPlayerDataOD() function. To do you will need to go to ESPN CricInfo Player and type in the name of the player for e.g Virendar Sehwag, etc. This will bring up a page which have the profile number for the player e.g. for Virendar Sehwag this would be http://www.espncricinfo.com/india/content/player/35263.html. Hence, Sehwag’s profile is 35263. This can be used to get the data for Virat Sehwag as shown below

sehwag <- getPlayerDataOD(35263,dir="..",file="sehwag.csv",type="batting")

Analyses of Batsmen

The following plots gives the analysis of the 4 ODI batsmen

  1. Virendar Sehwag (Ind) – Innings – 245, Runs = 8586, Average=35.05, Strike Rate= 104.33
  2. AB Devilliers (SA) – Innings – 179, Runs= 7941, Average=53.65, Strike Rate= 99.12
  3. Chris Gayle (WI) – Innings – 264, Runs= 9221, Average=37.65, Strike Rate= 85.11
  4. Glenn Maxwell (Aus) – Innings – 45, Runs= 1367, Average=35.02, Strike Rate= 126.69

Plot of 4s, 6s and the scoring rate in ODIs

The 3 charts below give the number of

  1. 4s vs Runs scored
  2. 6s vs Runs scored
  3. Balls faced vs Runs scored

A regression line is fitted in each of these plots for each of the ODI batsmen A. Virender Sehwag

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./sehwag.csv","Sehwag")
batsman6s("./sehwag.csv","Sehwag")
batsmanScoringRateODTT("./sehwag.csv","Sehwag")

sehwag-4s6sSR-1

dev.off()
## null device 
##           1

B. AB Devilliers

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./devilliers.csv","Devillier")
batsman6s("./devilliers.csv","Devillier")
batsmanScoringRateODTT("./devilliers.csv","Devillier")

devillier-4s6SR-1

dev.off()
## null device 
##           1

C. Chris Gayle

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./gayle.csv","Gayle")
batsman6s("./gayle.csv","Gayle")
batsmanScoringRateODTT("./gayle.csv","Gayle")

gayle-4s6sSR-1

dev.off()
## null device 
##           1

D. Glenn Maxwell

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./maxwell.csv","Maxwell")
batsman6s("./maxwell.csv","Maxwell")
batsmanScoringRateODTT("./maxwell.csv","Maxwell")

maxwell-4s6sout-1

dev.off()
## null device 
##           1

Relative Mean Strike Rate

In this first plot I plot the Mean Strike Rate of the batsmen. It can be seen that Maxwell has a awesome strike rate in ODIs. However we need to keep in mind that Maxwell has relatively much fewer (only 45 innings) innings. He is followed by Sehwag who(most innings- 245) also has an excellent strike rate till 100 runs and then we have Devilliers who roars ahead. This is also seen in the overall strike rate in above

par(mar=c(4,4,2,2))
frames <- list("./sehwag.csv","./devilliers.csv","gayle.csv","maxwell.csv")
names <- list("Sehwag","Devilliers","Gayle","Maxwell")
relativeBatsmanSRODTT(frames,names)

plot-1-1

Relative Runs Frequency Percentage

Sehwag leads in the percentage of runs in 10 run ranges upto 50 runs. Maxwell and Devilliers lead in 55-66 & 66-85 respectively.

frames <- list("./sehwag.csv","./devilliers.csv","gayle.csv","maxwell.csv")
names <- list("Sehwag","Devilliers","Gayle","Maxwell")
relativeRunsFreqPerfODTT(frames,names)

plot-2-1

Percentage of 4s,6s in the runs scored

The plot below shows the percentage of runs made by the batsmen by ways of 1s,2s,3s, 4s and 6s. It can be seen that Sehwag has the higheest percent of 4s (33.36%) in his overall runs in ODIs. Maxwell has the highest percentage of 6s (13.36%) in his ODI career. If we take the overall 4s+6s then Sehwag leads with (33.36 +5.95 = 39.31%),followed by Gayle (27.80+10.15=37.95%)

Percent 4’s,6’s in total runs scored

The plot below shows the contrib

frames <- list("./sehwag.csv","./devilliers.csv","gayle.csv","maxwell.csv")
names <- list("Sehwag","Devilliers","Gayle","Maxwell")
runs4s6s <-batsman4s6s(frames,names)

plot-46s-1

print(runs4s6s)
##                Sehwag Devilliers Gayle Maxwell
## Runs(1s,2s,3s)  60.69      67.39 62.05   62.11
## 4s              33.36      24.28 27.80   24.53
## 6s               5.95       8.32 10.15   13.36
 

Runs forecast

The forecast for the batsman is shown below.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanPerfForecast("./sehwag.csv","Sehwag")
batsmanPerfForecast("./devilliers.csv","Devilliers")
batsmanPerfForecast("./gayle.csv","Gayle")
batsmanPerfForecast("./maxwell.csv","Maxwell")

swcr-perf-1

dev.off()
## null device 
##           1

3D plot of Runs vs Balls Faced and Minutes at Crease

The plot is a scatter plot of Runs vs Balls faced and Minutes at Crease. A prediction plane is fitted

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./sehwag.csv","V Sehwag")
battingPerf3d("./devilliers.csv","AB Devilliers")

plot-3-1

dev.off()
## null device 
##           1
par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./gayle.csv","C Gayle")
battingPerf3d("./maxwell.csv","G Maxwell")

plot-4-1

dev.off()
## null device 
##           1

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, 200,length=10)
Mins <- seq(30,220,length=10)
newDF <- data.frame(BF,Mins)

sehwag <- batsmanRunsPredict("./sehwag.csv","Sehwag",newdataframe=newDF)
devilliers <- batsmanRunsPredict("./devilliers.csv","Devilliers",newdataframe=newDF)
gayle <- batsmanRunsPredict("./gayle.csv","Gayle",newdataframe=newDF)
maxwell <- batsmanRunsPredict("./maxwell.csv","Maxwell",newdataframe=newDF)

The fitted model is then used to predict the runs that the batsmen will score for a hypotheticial Balls faced and Minutes at crease. It can be seen that Maxwell sets a searing pace in the predicted runs for a given Balls Faced and Minutes at crease followed by Sehwag. But we have to keep in mind that Maxwell has only around 1/5th of the innings of Sehwag (45 to Sehwag’s 245 innings). They are followed by Devilliers and then finally Gayle

batsmen <-cbind(round(sehwag$Runs),round(devilliers$Runs),round(gayle$Runs),round(maxwell$Runs))
colnames(batsmen) <- c("Sehwag","Devilliers","Gayle","Maxwell")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns
##    BallsFaced MinsAtCrease Sehwag Devilliers Gayle Maxwell
## 1          10           30     11         12    11      18
## 2          31           51     33         32    28      43
## 3          52           72     55         52    46      67
## 4          73           93     77         71    63      92
## 5          94          114    100         91    81     117
## 6         116          136    122        111    98     141
## 7         137          157    144        130   116     166
## 8         158          178    167        150   133     191
## 9         179          199    189        170   151     215
## 10        200          220    211        190   168     240

Highest runs likelihood

The plots below the runs likelihood of batsman. This uses K-Means It can be seen that Devilliers has almost 27.75% likelihood to make around 90+ runs. Gayle and Sehwag have 34% to make 40+ runs. A. Virender Sehwag

A. Virender Sehwag

batsmanRunsLikelihood("./sehwag.csv","Sehwag")

smith-1

## Summary of  Sehwag 's runs scoring likelihood
## **************************************************
## 
## There is a 35.22 % likelihood that Sehwag  will make  46 Runs in  44 balls over 67  Minutes 
## There is a 9.43 % likelihood that Sehwag  will make  119 Runs in  106 balls over  158  Minutes 
## There is a 55.35 % likelihood that Sehwag  will make  12 Runs in  13 balls over 18  Minutes

B. AB Devilliers

batsmanRunsLikelihood("./devilliers.csv","Devilliers")

warner-1

## Summary of  Devilliers 's runs scoring likelihood
## **************************************************
## 
## There is a 30.65 % likelihood that Devilliers  will make  44 Runs in  43 balls over 60  Minutes 
## There is a 29.84 % likelihood that Devilliers  will make  91 Runs in  88 balls over  124  Minutes 
## There is a 39.52 % likelihood that Devilliers  will make  11 Runs in  15 balls over 21  Minutes

C. Chris Gayle

batsmanRunsLikelihood("./gayle.csv","Gayle")

cook,cache-TRUE-1

## Summary of  Gayle 's runs scoring likelihood
## **************************************************
## 
## There is a 32.69 % likelihood that Gayle  will make  47 Runs in  51 balls over 72  Minutes 
## There is a 54.49 % likelihood that Gayle  will make  10 Runs in  15 balls over  20  Minutes 
## There is a 12.82 % likelihood that Gayle  will make  109 Runs in  119 balls over 172  Minutes

D. Glenn Maxwell

batsmanRunsLikelihood("./maxwell.csv","Maxwell")

oot-1

## Summary of  Maxwell 's runs scoring likelihood
## **************************************************
## 
## There is a 34.38 % likelihood that Maxwell  will make  39 Runs in  29 balls over 35  Minutes 
## There is a 15.62 % likelihood that Maxwell  will make  89 Runs in  55 balls over  69  Minutes 
## There is a 50 % likelihood that Maxwell  will make  6 Runs in  7 balls over 9  Minutes

Average runs at ground and against opposition

A. Virender Sehwag

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./sehwag.csv","Sehwag")
batsmanAvgRunsOpposition("./sehwag.csv","Sehwag")

avgrg-1-1

dev.off()
## null device 
##           1

B. AB Devilliers

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./devilliers.csv","Devilliers")
batsmanAvgRunsOpposition("./devilliers.csv","Devilliers")

avgrg-2-1

dev.off()
## null device 
##           1

C. Chris Gayle

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./gayle.csv","Gayle")
batsmanAvgRunsOpposition("./gayle.csv","Gayle")

avgrg-3-1

dev.off()
## null device 
##           1

D. Glenn Maxwell

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./maxwell.csv","Maxwell")
batsmanAvgRunsOpposition("./maxwell.csv","Maxwell")

avgrg-4-1

dev.off()
## null device 
##           1

Moving Average of runs over career

The moving average for the 4 batsmen indicate the following

1. The moving average of Devilliers and Maxwell is on the way up.
2. Sehwag shows a slight downward trend from his 2nd peak in 2011
3. Gayle maintains a consistent 45 runs for the last few years

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanMovingAverage("./sehwag.csv","Sehwag")
batsmanMovingAverage("./devilliers.csv","Devilliers")
batsmanMovingAverage("./gayle.csv","Gayle")
batsmanMovingAverage("./maxwell.csv","Maxwell")

sdgm-ma-1

dev.off()
## null device 
##           1

Check batsmen in-form, out-of-form

  1. Maxwell, Devilliers, Sehwag are in-form. This is also evident from the moving average plot
  2. Gayle is out-of-form
checkBatsmanInForm("./sehwag.csv","Sehwag")
## *******************************************************************************************
## 
## Population size: 143  Mean of population: 33.76 
## Sample size: 16  Mean of sample: 37.44 SD of sample: 55.15 
## 
## Null hypothesis H0 : Sehwag 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Sehwag 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Sehwag 's Form Status: In-Form because the p value: 0.603525  is greater than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./devilliers.csv","Devilliers")
## *******************************************************************************************
## 
## Population size: 111  Mean of population: 43.5 
## Sample size: 13  Mean of sample: 57.62 SD of sample: 40.69 
## 
## Null hypothesis H0 : Devilliers 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Devilliers 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Devilliers 's Form Status: In-Form because the p value: 0.883541  is greater than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./gayle.csv","Gayle")
## *******************************************************************************************
## 
## Population size: 140  Mean of population: 37.1 
## Sample size: 16  Mean of sample: 17.25 SD of sample: 20.25 
## 
## Null hypothesis H0 : Gayle 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Gayle 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Gayle 's Form Status: Out-of-Form because the p value: 0.000609  is less than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./maxwell.csv","Maxwell")
## *******************************************************************************************
## 
## Population size: 28  Mean of population: 25.25 
## Sample size: 4  Mean of sample: 64.25 SD of sample: 36.97 
## 
## Null hypothesis H0 : Maxwell 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Maxwell 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Maxwell 's Form Status: In-Form because the p value: 0.948744  is greater than alpha=  0.05"
## *******************************************************************************************

Analysis of bowlers

  1. Mitchell Johnson (Aus) – Innings-150, Wickets – 239, Econ Rate : 4.83
  2. Lasith Malinga (SL)- Innings-182, Wickets – 287, Econ Rate : 5.26
  3. Dale Steyn (SA)- Innings-103, Wickets – 162, Econ Rate : 4.81
  4. Tim Southee (NZ)- Innings-96, Wickets – 135, Econ Rate : 5.33

Malinga has the highest number of innings and wickets followed closely by Mitchell. Steyn and Southee have relatively fewer innings.

To get the bowler’s data use

malinga <- getPlayerDataOD(49758,dir=".",file="malinga.csv",type="bowling")

Wicket Frequency percentage

This plot gives the percentage of wickets for each wickets (1,2,3…etc)

par(mfrow=c(1,4))
par(mar=c(4,4,2,2))
bowlerWktsFreqPercent("./mitchell.csv","J Mitchell")
bowlerWktsFreqPercent("./malinga.csv","Malinga")
bowlerWktsFreqPercent("./steyn.csv","Steyn")
bowlerWktsFreqPercent("./southee.csv","southee")

relBowlFP-1

dev.off()
## null device 
##           1

Wickets Runs plot

The plot below gives a boxplot of the runs ranges for each of the wickets taken by the bowlers. M Johnson and Steyn are more economical than Malinga and Southee corroborating the figures above

par(mfrow=c(1,4))
par(mar=c(4,4,2,2))

bowlerWktsRunsPlot("./mitchell.csv","J Mitchell")
bowlerWktsRunsPlot("./malinga.csv","Malinga")
bowlerWktsRunsPlot("./steyn.csv","Steyn")
bowlerWktsRunsPlot("./southee.csv","southee")

wktsrun-1

dev.off()
## null device 
##           1

Average wickets in different grounds and opposition

A. Mitchell Johnson

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./mitchell.csv","J Mitchell")
bowlerAvgWktsOpposition("./mitchell.csv","J Mitchell")

gr-1-1

dev.off()
## null device 
##           1

B. Lasith Malinga

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./malinga.csv","Malinga")
bowlerAvgWktsOpposition("./malinga.csv","Malinga")

gr-2-1

dev.off()
## null device 
##           1

C. Dale Steyn

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./steyn.csv","Steyn")
bowlerAvgWktsOpposition("./steyn.csv","Steyn")

gr-3-1

dev.off()
## null device 
##           1

D. Tim Southee

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./southee.csv","southee")
bowlerAvgWktsOpposition("./southee.csv","southee")

avgrg-4-1

dev.off()
## null device 
##           1

Relative bowling performance

The plot below shows that Mitchell Johnson and Southee have more wickets in 3-4 wickets range while Steyn and Malinga in 1-2 wicket range

frames <- list("./mitchell.csv","./malinga.csv","steyn.csv","southee.csv")
names <- list("M Johnson","Malinga","Steyn","Southee")
relativeBowlingPerf(frames,names)

relBowlPerf-1

Relative Economy Rate against wickets taken

Steyn had the best economy rate followed by M Johnson. Malinga and Southee have a poorer economy rate

frames <- list("./mitchell.csv","./malinga.csv","steyn.csv","southee.csv")
names <- list("M Johnson","Malinga","Steyn","Southee")
relativeBowlingERODTT(frames,names)

relBowlER-1

Moving average of wickets over career

Johnson and Steyn career vs wicket graph is on the up-swing. Southee is maintaining a reasonable record while Malinga shows a decline in ODI performance

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
bowlerMovingAverage("./mitchell.csv","M Johnson")
bowlerMovingAverage("./malinga.csv","Malinga")
bowlerMovingAverage("./steyn.csv","Steyn")
bowlerMovingAverage("./southee.csv","Southee")

jmss-bowlma-1

dev.off()
## null device 
##           1

Wickets forecast

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
bowlerPerfForecast("./mitchell.csv","M Johnson")
bowlerPerfForecast("./malinga.csv","Malinga")
bowlerPerfForecast("./steyn.csv","Steyn")
bowlerPerfForecast("./southee.csv","southee")

jsba-pfcst-1

dev.off()
## null device 
##           1

Check bowler in-form, out-of-form

All the bowlers are shown to be still in-form

checkBowlerInForm("./mitchell.csv","J Mitchell")
## *******************************************************************************************
## 
## Population size: 135  Mean of population: 1.55 
## Sample size: 15  Mean of sample: 2 SD of sample: 1.07 
## 
## Null hypothesis H0 : J Mitchell 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : J Mitchell 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "J Mitchell 's Form Status: In-Form because the p value: 0.937917  is greater than alpha=  0.05"
## *******************************************************************************************
checkBowlerInForm("./malinga.csv","Malinga")
## *******************************************************************************************
## 
## Population size: 163  Mean of population: 1.58 
## Sample size: 19  Mean of sample: 1.58 SD of sample: 1.22 
## 
## Null hypothesis H0 : Malinga 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Malinga 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Malinga 's Form Status: In-Form because the p value: 0.5  is greater than alpha=  0.05"
## *******************************************************************************************
checkBowlerInForm("./steyn.csv","Steyn")
## *******************************************************************************************
## 
## Population size: 93  Mean of population: 1.59 
## Sample size: 11  Mean of sample: 1.45 SD of sample: 0.69 
## 
## Null hypothesis H0 : Steyn 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Steyn 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Steyn 's Form Status: In-Form because the p value: 0.257438  is greater than alpha=  0.05"
## *******************************************************************************************
checkBowlerInForm("./southee.csv","southee")
## *******************************************************************************************
## 
## Population size: 86  Mean of population: 1.48 
## Sample size: 10  Mean of sample: 0.8 SD of sample: 1.14 
## 
## Null hypothesis H0 : southee 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : southee 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "southee 's Form Status: Out-of-Form because the p value: 0.044302  is less than alpha=  0.05"
## *******************************************************************************************

***************

Key findings

Here are some key conclusions ODI batsmen

  1. AB Devilliers has high frequency of runs in the 60-120 range and the highest average
  2. Sehwag has the most number of innings and good strike rate
  3. Maxwell has the best strike rate but it should be kept in mind that he has 1/5 of the innings of Sehwag. We need to see how he progress further
  4. Sehwag has the highest percentage of 4s in the runs scored, while Maxwell has the most 6s
  5. For a hypothetical Balls Faced and Minutes at creases Maxwell will score the most runs followed by Sehwag
  6. The moving average of indicates that the best is yet to come for Devilliers and Maxwell. Sehwag has a few more years in him while Gayle shows a decline in ODI performance and an out of form is indicated.

ODI bowlers

  1. Malinga has the highest played the highest innings and also has the highest wickets though he has poor economy rate
  2. M Johnson is the most effective in the 3-4 wicket range followed by Southee
  3. M Johnson and Steyn has the best overall economy rate followed by Malinga and Steyn 4 M Johnson and Steyn’s career is on the up-swing,Southee maintains a steady consistent performance, while Malinga shows a downward trend

Hasta la vista! I’ll be back!
Watch this space!

Also see my other posts in R

  1. Introducing cricketr! : An R package to analyze performances of cricketers
  2. cricketr digs the Ashes!
  3. A peek into literacy in India: Statistical Learning with R
  4. A crime map of India in R – Crimes against women
  5. Analyzing cricket’s batting legends – Through the mirage with R
  6. Mirror, mirror . the best batsman of them all?

You may also like

  1. A closer look at “Robot Horse on a Trot” in Android
  2. What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
  3. Bend it like Bluemix, MongoDB with autoscaling – Part 2
  4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
  5. TWS-4: Gossip protocol: Epidemics and rumors to the rescue
  6. Deblurring with OpenCV:Weiner filter reloaded

cricketr digs the Ashes!


Introduction

In some circles the Ashes is considered the ‘mother of all cricketing battles’. But, being a staunch supporter of all things Indian, cricket or otherwise, I have to say that the Ashes pales in comparison against a India-Pakistan match. After all, what are a few frowns and raised eyebrows at the Ashes in comparison to the seething emotions and reckless exuberance of Indian fans.

Anyway, the Ashes are an interesting duel and I have decided to do some cricketing analysis using my R package cricketr. For this analysis I have chosen the top 2 batsman and top 2 bowlers from both the Australian and English sides.

Batsmen

  1. Steven Smith (Aus) – Innings – 58 , Ave: 58.52, Strike Rate: 55.90
  2. David Warner (Aus) – Innings – 76, Ave: 46.86, Strike Rate: 73.88
  3. Alistair Cook (Eng) – Innings – 208 , Ave: 46.62, Strike Rate: 46.33
  4. J E Root (Eng) – Innings – 53, Ave: 54.02, Strike Rate: 51.30

Bowlers

  1. Mitchell Johnson (Aus) – Innings-131, Wickets – 299, Econ Rate : 3.28
  2. Peter Siddle (Aus) – Innings – 104 , Wickets- 192, Econ Rate : 2.95
  3. James Anderson (Eng) – Innings – 199 , Wickets- 406, Econ Rate : 3.05
  4. Stuart Broad (Eng) – Innings – 148 , Wickets- 296, Econ Rate : 3.08

It is my opinion if any 2 of the 4 in either team click then they will be able to swing the match in favor of their team.

I have interspered the plots with a few comments. Feel free to draw your conclusions!

The analysis is included below. Note: This post has also been hosted at Rpubs as cricketr digs the Ashes!
You can also download this analysis as a PDF file from cricketr digs the Ashes!

library(devtools)
install_github("tvganesh/cricketr")
library(cricketr)

Analyses of Batsmen

The following plots gives the analysis of the 2 Australian and 2 English batsmen. It must be kept in mind that Cooks has more innings than all the rest put together. Smith has the best average, and Warner has the best strike rate

Box Histogram Plot

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

batsmanPerfBoxHist("./smith.csv","S Smith")

swcr-boxhist-1

batsmanPerfBoxHist("./warner.csv","D Warner")

swcr-boxhist-2

batsmanPerfBoxHist("./cook.csv","A Cook")

swcr-boxhist-3

batsmanPerfBoxHist("./root.csv","JE Root")

swcr-boxhist-4

Plot os 4s, 6s and the type of dismissals

A. Steven Smith

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./smith.csv","S Smith")
batsman6s("./smith.csv","S Smith")
batsmanDismissals("./smith.csv","S Smith")

smith-4s6sout-1

dev.off()
## null device 
##           1

B. David Warner

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./warner.csv","D Warner")
batsman6s("./warner.csv","D Warner")
batsmanDismissals("./warner.csv","D Warner")

warner-4s6sout-1

dev.off()
## null device 
##           1

C. Alistair Cook

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./cook.csv","A Cook")
batsman6s("./cook.csv","A Cook")
batsmanDismissals("./cook.csv","A Cook")

cook-4s6sout-1

dev.off()
## null device 
##           1

D. J E Root

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./root.csv","JE Root")
batsman6s("./root.csv","JE Root")
batsmanDismissals("./root.csv","JE Root")

root-4s6sout-1

dev.off()
## null device 
##           1

Relative Mean Strike Rate

In this first plot I plot the Mean Strike Rate of the batsmen. It can be Warner’s has the best strike rate (hit outside the plot!) followed by Smith in the range 20-100. Root has a good strike rate above hundred runs. Cook maintains a good strike rate.

par(mar=c(4,4,2,2))
frames <- list("./smith.csv","./warner.csv","cook.csv","root.csv")
names <- list("Smith","Warner","Cook","Root")
relativeBatsmanSR(frames,names)

plot-1-1

Relative Runs Frequency Percentage

The plot below show the percentage contribution in each 10 runs bucket over the entire career.It can be seen that Smith pops up above the rest with remarkable regularity.COok is consistent over the entire range.

frames <- list("./smith.csv","./warner.csv","cook.csv","root.csv")
names <- list("Smith","Warner","Cook","Root")
relativeRunsFreqPerf(frames,names)

plot-2-1

Moving Average of runs over career

The moving average for the 4 batsmen indicate the following 1. S Smith is the most promising. There is a marked spike in Performance. Cook maintains a steady pace and is consistent over the years averaging 50 over the years.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanMovingAverage("./smith.csv","S Smith")
batsmanMovingAverage("./warner.csv","D Warner")
batsmanMovingAverage("./cook.csv","A Cook")
batsmanMovingAverage("./root.csv","JE Root")

swcr-ma-1

dev.off()
## null device 
##           1

Runs forecast

The forecast for the batsman is shown below. As before Cooks’s performance is really consistent across the years and the forecast is good for the years ahead. In Cook’s case it can be seen that the forecasted and actual runs are reasonably accurate

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanPerfForecast("./smith.csv","S Smith")
batsmanPerfForecast("./warner.csv","D Warner")
batsmanPerfForecast("./cook.csv","A Cook")
## Warning in HoltWinters(ts.train): optimization difficulties: ERROR:
## ABNORMAL_TERMINATION_IN_LNSRCH
batsmanPerfForecast("./root.csv","JE Root")

swcr-perf-1

dev.off()
## null device 
##           1

3D plot of Runs vs Balls Faced and Minutes at Crease

The plot is a scatter plot of Runs vs Balls faced and Minutes at Crease. A prediction plane is fitted

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./smith.csv","S Smith")
battingPerf3d("./warner.csv","D Warner")

plot-3-1

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./cook.csv","A Cook")
battingPerf3d("./root.csv","JE Root")

plot-4-1

dev.off()
## null device 
##           1

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)
smith <- batsmanRunsPredict("./smith.csv","S Smith",newdataframe=newDF)
warner <- batsmanRunsPredict("./warner.csv","D Warner",newdataframe=newDF)
cook <- batsmanRunsPredict("./cook.csv","A Cook",newdataframe=newDF)
root <- batsmanRunsPredict("./root.csv","JE Root",newdataframe=newDF)

The fitted model is then used to predict the runs that the batsmen will score for a given Balls faced and Minutes at crease. It can be seen that Warner sets a searing pace in the predicted runs for a given Balls Faced and Minutes at crease while Smith and Root are neck to neck in the predicted runs

batsmen <-cbind(round(smith$Runs),round(warner$Runs),round(cook$Runs),round(root$Runs))
colnames(batsmen) <- c("Smith","Warner","Cook","Root")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns
##    BallsFaced MinsAtCrease Smith Warner Cook Root
## 1          10           30     9     12    6    9
## 2          38           71    25     33   20   25
## 3          66          111    42     53   33   42
## 4          94          152    58     73   47   59
## 5         121          193    75     93   60   75
## 6         149          234    91    114   74   92
## 7         177          274   108    134   88  109
## 8         205          315   124    154  101  125
## 9         233          356   141    174  115  142
## 10        261          396   158    195  128  159
## 11        289          437   174    215  142  175
## 12        316          478   191    235  155  192
## 13        344          519   207    255  169  208
## 14        372          559   224    276  182  225
## 15        400          600   240    296  196  242

Highest runs likelihood

The plots below the runs likelihood of batsman. This uses K-Means. It can be seen Smith has the best likelihood around 40% of scoring around 41 runs, followed by Root who has 28.3% likelihood of scoring around 81 runs

A. Steven Smith

batsmanRunsLikelihood("./smith.csv","S Smith")
smith-1
## Summary of  S Smith 's runs scoring likelihood
## **************************************************
## 
## There is a 40 % likelihood that S Smith  will make  41 Runs in  73 balls over 101  Minutes 
## There is a 36 % likelihood that S Smith  will make  9 Runs in  21 balls over  27  Minutes 
## There is a 24 % likelihood that S Smith  will make  139 Runs in  237 balls over 338  Minutes

B. David Warner

batsmanRunsLikelihood("./warner.csv","D Warner")
warner-1
## Summary of  D Warner 's runs scoring likelihood
## **************************************************
## 
## There is a 11.11 % likelihood that D Warner  will make  134 Runs in  159 balls over 263  Minutes 
## There is a 63.89 % likelihood that D Warner  will make  17 Runs in  25 balls over  37  Minutes 
## There is a 25 % likelihood that D Warner  will make  73 Runs in  105 balls over 156  Minutes

C. Alastair Cook

batsmanRunsLikelihood("./cook.csv","A Cook")
cook,cache-TRUE-1
## Summary of  A Cook 's runs scoring likelihood
## **************************************************
## 
## There is a 27.72 % likelihood that A Cook  will make  64 Runs in  140 balls over 195  Minutes 
## There is a 59.9 % likelihood that A Cook  will make  15 Runs in  32 balls over  46  Minutes 
## There is a 12.38 % likelihood that A Cook  will make  141 Runs in  300 balls over 420  Minutes

D. J E Root

batsmanRunsLikelihood("./root.csv","JE Root")
oot-1
## Summary of  JE Root 's runs scoring likelihood
## **************************************************
## 
## There is a 28.3 % likelihood that JE Root  will make  81 Runs in  158 balls over 223  Minutes 
## There is a 7.55 % likelihood that JE Root  will make  179 Runs in  290 balls over  425  Minutes 
## There is a 64.15 % likelihood that JE Root  will make  16 Runs in  39 balls over 59  Minutes
 

Average runs at ground and against opposition

A. Steven Smith

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./smith.csv","S Smith")
batsmanAvgRunsOpposition("./smith.csv","S Smith")

avgrg-1-1

dev.off()
## null device 
##           1

B. David Warner

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./warner.csv","D Warner")
batsmanAvgRunsOpposition("./warner.csv","D Warner")

avgrg-2-1

dev.off()
## null device 
##           1

C. Alistair Cook

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./cook.csv","A Cook")
batsmanAvgRunsOpposition("./cook.csv","A Cook")

avgrg-3-1

dev.off()
## null device 
##           1

D. J E Root

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./root.csv","JE Root")
batsmanAvgRunsOpposition("./root.csv","JE Root")

avgrg-4-1

dev.off()
## null device 
##           1

Analysis of bowlers

  1. Mitchell Johnson (Aus) – Innings-131, Wickets – 299, Econ Rate : 3.28
  2. Peter Siddle (Aus) – Innings – 104 , Wickets- 192, Econ Rate : 2.95
  3. James Anderson (Eng) – Innings – 199 , Wickets- 406, Econ Rate : 3.05
  4. Stuart Broad (Eng) – Innings – 148 , Wickets- 296, Econ Rate : 3.08

Anderson has the highest number of inning and wickets followed closely by Broad and Mitchell who are in a neck to neck race with respect to wickets. Johnson is on the more expensive side though. Siddle has fewer innings but a good economy rate.

Wicket Frequency percentage

This plot gives the percentage of wickets for each wickets (1,2,3…etc)

par(mfrow=c(1,4))
par(mar=c(4,4,2,2))
bowlerWktsFreqPercent("./johnson.csv","Johnson")
bowlerWktsFreqPercent("./siddle.csv","Siddle")
bowlerWktsFreqPercent("./broad.csv","Broad")
bowlerWktsFreqPercent("./anderson.csv","Anderson")

relBowlFP-1

dev.off()
## null device 
##           1

Wickets Runs plot

The plot below gives a boxplot of the runs ranges for each of the wickets taken by the bowlers

par(mfrow=c(1,4))
par(mar=c(4,4,2,2))
bowlerWktsRunsPlot("./johnson.csv","Johnson")
bowlerWktsRunsPlot("./siddle.csv","Siddle")
bowlerWktsRunsPlot("./broad.csv","Broad")
bowlerWktsRunsPlot("./anderson.csv","Anderson")

wktsrun-1

dev.off()
## null device 
##           1

Average wickets in different grounds and opposition

A. Mitchell Johnson

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./johnson.csv","Johnson")
bowlerAvgWktsOpposition("./johnson.csv","Johnson")

gr-1-1

dev.off()
## null device 
##           1

B. Peter Siddle

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./siddle.csv","Siddle")
bowlerAvgWktsOpposition("./siddle.csv","Siddle")

gr-2-1

dev.off()
## null device 
##           1

C. Stuart Broad

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./broad.csv","Broad")
bowlerAvgWktsOpposition("./broad.csv","Broad")

gr-3-1

dev.off()
## null device 
##           1

D. James Anderson

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
bowlerAvgWktsGround("./anderson.csv","Anderson")
bowlerAvgWktsOpposition("./anderson.csv","Anderson")

gr-4-1

dev.off()
## null device 
##           1

Relative bowling performance

The plot below shows that Mitchell Johnson is the mopst effective bowler among the lot with a higher wickets in the 3-6 wicket range. Broad and Anderson seem to perform well in 2 wickets in comparison to Siddle but in 3 wickets Siddle is better than Broad and Anderson.

frames <- list("./johnson.csv","./siddle.csv","broad.csv","anderson.csv")
names <- list("Johnson","Siddle","Broad","Anderson")
relativeBowlingPerf(frames,names)

relBowlPerf-1

Relative Economy Rate against wickets taken

Anderson followed by Siddle has the best economy rates. Johnson is fairly expensive in the 4-8 wicket range.

frames <- list("./johnson.csv","./siddle.csv","broad.csv","anderson.csv")
names <- list("Johnson","Siddle","Broad","Anderson")
relativeBowlingER(frames,names)

relBowlER-1

Moving average of wickets over career

Johnson is on his second peak while Siddle is on the decline with respect to bowling. Broad and Anderson show improving performance over the years.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
bowlerMovingAverage("./johnson.csv","Johnson")
bowlerMovingAverage("./siddle.csv","Siddle")
bowlerMovingAverage("./broad.csv","Broad")
bowlerMovingAverage("./anderson.csv","Anderson")

jsba-bowlma-1

dev.off()
## null device 
##           1

Wickets forecast

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
bowlerPerfForecast("./johnson.csv","Johnson")
bowlerPerfForecast("./siddle.csv","Siddle")
bowlerPerfForecast("./broad.csv","Broad")
bowlerPerfForecast("./anderson.csv","Anderson")

jsba-bowlma-1

dev.off()
## null device 
##           1

Key findings

Here are some key conclusions

  1. Cook has the most number of innings and has been extremly consistent in his scores
  2. Warner has the best strike rate among the lot followed by Smith and Root
  3. The moving average shows a marked improvement over the years for Smith
  4. Johnson is the most effective bowler but is fairly expensive
  5. Anderson has the best economy rate followed by Siddle
  6. Johnson is at his second peak with respect to bowling while Broad and Anderson maintain a steady line and length in their career bowling performance


Also see my other posts in R

  1. Introducing cricketr! : An R package to analyze performances of cricketers
  2. Taking cricketr for a spin – Part 1
  3. A peek into literacy in India: Statistical Learning with R
  4. A crime map of India in R – Crimes against women
  5. Analyzing cricket’s batting legends – Through the mirage with R
  6. Masters of Spin: Unraveling the web with R
  7. Mirror, mirror . the best batsman of them all?

You may also like

  1. A crime map of India in R: Crimes against women
  2. What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
  3. Bend it like Bluemix, MongoDB with autoscaling – Part 2
  4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
  5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data
  6. Deblurring with OpenCV:Weiner filter reloaded

Taking cricketr for a spin – Part 1


“Curiouser and curiouser!” cried Alice
“The time has come,” the walrus said, “to talk of many things: Of shoes and ships – and sealing wax – of cabbages and kings”
“Begin at the beginning,”the King said, very gravely,“and go on till you come to the end: then stop.”
“And what is the use of a book,” thought Alice, “without pictures or conversation?”

            Excerpts from Alice in Wonderland by Lewis Carroll

Introduction

This post is a continuation of my previous post “Introducing cricketr! A R package to analyze the performances of cricketers.” In this post I take my package cricketr for a spin. For this analysis I focus on the Indian batting legends

– Sachin Tendulkar (Master Blaster)
– Rahul Dravid (The Will)
– Sourav Ganguly ( The Dada Prince)
– Sunil Gavaskar (Little Master)

This post is also hosted on RPubs – cricketr-1

library(devtools)
install_github("tvganesh/cricketr")
library(cricketr)

Box Histogram Plot

This plot shows a combined boxplot of the Runs ranges and a histogram of the Runs Frequency The plot below indicate the Tendulkar’s average is the highest. He is followed by Dravid, Gavaskar and then Ganguly

batsmanPerfBoxHist("./tendulkar.csv","Sachin Tendulkar")
tkps-boxhist-1

 

batsmanPerfBoxHist("./dravid.csv","Rahul Dravid")
tkps-boxhist-2

 

batsmanPerfBoxHist("./ganguly.csv","Sourav Ganguly")
tkps-boxhist-3

 

batsmanPerfBoxHist("./gavaskar.csv","Sunil Gavaskar")

 

tkps-boxhist-4

Relative Mean Strike Rate

In this first plot I plot the Mean Strike Rate of the batsmen. Tendulkar leads in the Mean Strike Rate for each runs in the range 100- 180. Ganguly has a very good Mean Strike Rate for runs range 40 -80

frames <- list("./tendulkar.csv","./dravid.csv","ganguly.csv","gavaskar.csv")
names <- list("Tendulkar","Dravid","Ganguly","Gavaskar")
relativeBatsmanSR(frames,names)

plot-1-1

Relative Runs Frequency Percentage

The plot below show the percentage contribution in each 10 runs bucket over the entire career.The percentage Runs Frequency is fairly close but Gavaskar seems to lead most of the way

frames <- list("./tendulkar.csv","./dravid.csv","ganguly.csv","gavaskar.csv")
names <- list("Tendulkar","Dravid","Ganguly","Gavaskar")
relativeRunsFreqPerf(frames,names)

plot-2-1

Moving Average of runs over career

The moving average for the 4 batsmen indicate the following – Tendulkar and Ganguly’s career has a downward trend and their retirement didn’t come too soon – Dravid and Gavaskar’s career definitely shows an upswing. They probably had a year or two left.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanMovingAverage("./tendulkar.csv","Tendulkar")
batsmanMovingAverage("./dravid.csv","Dravid")
batsmanMovingAverage("./ganguly.csv","Ganguly")
batsmanMovingAverage("./gavaskar.csv","Gavaskar")

tdsg-ma-1

dev.off()
## null device 
##           1

Runs forecast

The forecast for the batsman is shown below. The plots indicate that only Tendulkar seemed to maintain a consistency over the period while the rest seem to score less than their forecasted runs in the last 10% of the career

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanPerfForecast("./tendulkar.csv","Sachin Tendulkar")
batsmanPerfForecast("./dravid.csv","Rahul Dravid")
batsmanPerfForecast("./ganguly.csv","Sourav Ganguly")
batsmanPerfForecast("./gavaskar.csv","Sunil Gavaskar")

tdsg-perf-1

dev.off()
## null device 
##           1

Check for batsman in-form/out-of-form

The following snippet checks whether the batsman is in-inform or ouyt-of-form during the last 10% innings of the career. This is done by choosing the null hypothesis (h0) to indicate that the batsmen are in-form. Ha is the alternative hypothesis that they are not-in-form. The population is based on the 1st 90% of career runs. The last 10% is taken as the sample and a check is made on the lower tail to see if the sample mean is less than 95% confidence interval. If this difference is >0.05 then the batsman is considered out-of-form.

The computation show that Tendulkar was out-of-form while the other’s weren’t. While Dravid and Gavaskar’s moving average do show an upward trend the surprise is Ganguly. This could be that Ganguly was able to keep his average in the last 10% to with the 95$ confidence interval. It has to be noted that Ganguly’s average was much lower than Tendulkar

checkBatsmanInForm("./tendulkar.csv","Tendulkar")
## *******************************************************************************************
## 
## Population size: 294  Mean of population: 50.48 
## Sample size: 33  Mean of sample: 32.42 SD of sample: 29.8 
## 
## Null hypothesis H0 : Tendulkar 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Tendulkar 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Tendulkar 's Form Status: Out-of-Form because the p value: 0.000713  is less than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./dravid.csv","Dravid")
## *******************************************************************************************
## 
## Population size: 256  Mean of population: 46.98 
## Sample size: 29  Mean of sample: 43.48 SD of sample: 40.89 
## 
## Null hypothesis H0 : Dravid 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Dravid 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Dravid 's Form Status: In-Form because the p value: 0.324138  is greater than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./ganguly.csv","Ganguly")
## *******************************************************************************************
## 
## Population size: 169  Mean of population: 38.94 
## Sample size: 19  Mean of sample: 33.21 SD of sample: 32.97 
## 
## Null hypothesis H0 : Ganguly 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Ganguly 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Ganguly 's Form Status: In-Form because the p value: 0.229006  is greater than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./gavaskar.csv","Gavaskar")
## *******************************************************************************************
## 
## Population size: 125  Mean of population: 44.67 
## Sample size: 14  Mean of sample: 57.86 SD of sample: 58.55 
## 
## Null hypothesis H0 : Gavaskar 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Gavaskar 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Gavaskar 's Form Status: In-Form because the p value: 0.793276  is greater than alpha=  0.05"
## *******************************************************************************************
dev.off()
## null device 
##           1

3D plot of Runs vs Balls Faced and Minutes at Crease

The plot is a scatter plot of Runs vs Balls faced and Minutes at Crease. A prediction plane is fitted

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./tendulkar.csv","Tendulkar")
battingPerf3d("./dravid.csv","Dravid")

plot-3-1

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./ganguly.csv","Ganguly")
battingPerf3d("./gavaskar.csv","Gavaskar")

plot-4-1

dev.off()
## null device 
##           1

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)
tendulkar <- batsmanRunsPredict("./tendulkar.csv","Tendulkar",newdataframe=newDF)
dravid <- batsmanRunsPredict("./dravid.csv","Dravid",newdataframe=newDF)
ganguly <- batsmanRunsPredict("./ganguly.csv","Ganguly",newdataframe=newDF)
gavaskar <- batsmanRunsPredict("./gavaskar.csv","Gavaskar",newdataframe=newDF)

The fitted model is then used to predict the runs that the batsmen will score for a given Balls faced and Minutes at crease. It can be seen Tendulkar has a much higher Runs scored than all of the others.

Tendulkar is followed by Ganguly who we saw earlier had a very good strike rate. However it must be noted that Dravid and Gavaskar have a better average.

batsmen <-cbind(round(tendulkar$Runs),round(dravid$Runs),round(ganguly$Runs),round(gavaskar$Runs))
colnames(batsmen) <- c("Tendulkar","Dravid","Ganguly","Gavaskar")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns
##    BallsFaced MinsAtCrease Tendulkar Dravid Ganguly Gavaskar
## 1          10           30         7      1       7        4
## 2          38           71        23     14      21       17
## 3          66          111        39     27      35       30
## 4          94          152        54     40      50       43
## 5         121          193        70     54      64       56
## 6         149          234        86     67      78       69
## 7         177          274       102     80      93       82
## 8         205          315       118     94     107       95
## 9         233          356       134    107     121      108
## 10        261          396       150    120     136      121
## 11        289          437       165    134     150      134
## 12        316          478       181    147     165      147
## 13        344          519       197    160     179      160
## 14        372          559       213    173     193      173
## 15        400          600       229    187     208      186

Contribution to matches won and lost

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanContributionWonLost(35320,"Tendulkar")
batsmanContributionWonLost(28114,"Dravid")
batsmanContributionWonLost(28779,"Ganguly")
batsmanContributionWonLost(28794,"Gavaskar")

tdgg-1

Home and overseas performance

From the plot below Tendulkar and Dravid have a lot more matches both home and abroad and their performance has good both at home and overseas. Tendulkar has the best performance home and abroad and is consistent all across. Dravid is also cossistent at all venues. Gavaskar played fewer matches than Tendulkar & Dravid. The range of runs at home is higher than overseas, however the average is consistent both at home and abroad. Finally we have Ganguly.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanPerfHomeAway(35320,"Tendulkar")
batsmanPerfHomeAway(28114,"Dravid")
batsmanPerfHomeAway(28779,"Ganguly")
batsmanPerfHomeAway(28794,"Gavaskar")
tdgg-ha-1

Average runs at ground and against opposition

Tendulkar has above 50 runs average against Sri Lanka, Bangladesh, West Indies and Zimbabwe. The performance against Australia and England average very close to 50. Sydney, Port Elizabeth, Bloemfontein, Collombo are great huntings grounds for Tendulkar

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./tendulkar.csv","Tendulkar")
batsmanAvgRunsOpposition("./tendulkar.csv","Tendulkar")
avgrg-1-1

 

dev.off()
## null device 
##           1

Dravid plundered runs at Adelaide, Georgetown, Oval, Hamiltom etc. Dravid has above average against England, Bangaldesh, New Zealand, Pakistan, West Indies and Zimbabwe

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./dravid.csv","Dravid")
batsmanAvgRunsOpposition("./dravid.csv","Dravid")
avgrg-2-1

 

dev.off()
## null device 
##           1

Ganguly has good performance at the Oval, Rawalpindi, Johannesburg and Kandy. Ganguly averages 50 runs against England and Bangladesh.

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./ganguly.csv","Ganguly")
batsmanAvgRunsOpposition("./ganguly.csv","Ganguly")
avgrg-3-1

 

dev.off()
## null device 
##           1

The Oval, Sydney, Perth, Melbourne, Brisbane, Manchester are happy hunting grounds for Gavaskar. Gavaskar averages around 50 runs Australia, Pakistan, Sri Lanka, West Indies.

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
batsmanAvgRunsGround("./gavaskar.csv","Gavaskar")
batsmanAvgRunsOpposition("./gavaskar.csv","Gavaskar")
avgrg-4-1

 

dev.off()
## null device 
##           1

Key findings

Here are some key conclusions

  1. Tendulkar has the highest average among the 4. He is followed by Dravid, Gavaskar and Ganguly.
  2. Tendulkar’s predicted performance for a given number of Balls Faced and Minutes at Crease is superior to the rest
  3. Dravid averages above 50 against 6 countries
  4. West Indies and Australia are Gavaskar’s favorite batting grounds
  5. Ganguly has a very good Mean Strike Rate for the range 40-80 and Tendulkar from 100-180
  6. In home and overseas performance, Tendulkar is the best. Dravid and Gavaskar also have good performance overseas.
  7. Dravid and Gavaskar probably retired a year or two earlier while Tendulkar and Ganguly’s time was clearly up

Final thoughts

Tendulkar is clearly the greatest batsman India has produced as he leads in almost all aspects of batting – number of centuries, strike rate, predicted runs and home and overseas performance. Dravid follows Tendulkar with 48 centuries, consistent performance home and overseas and a career that was still green. Gavaskar has fewer matches than rest but his performance overseas is very good in those helmetless times. Finally we have Ganguly.

Dravid and Gavaskar had a few more years of great batting while Tendulkar and Ganguly’s career was on a decline.

Note:It is really not fair to include Gavaskar in the analysis as he played in a different era when helmets were not used, even against the fiery pace of Thomson, Lillee, Roberts, Holding etc. In addition Gavaskar did not play against some of the newer countries like Bangladesh and Zimbabwe where he could have amassed runs. Yet I wanted to include him and his performance is clearly excellent

Also see my other posts in R

  1. A peek into literacy in India: Statistical Learning with R
  2. A crime map of India in R – Crimes against women
  3. Analyzing cricket’s batting legends – Through the mirage with R
  4. Masters of Spin: Unraveling the web with R
  5. Mirror, mirror . the best batsman of them all?

You may also like

  1. A crime map of India in R: Crimes against women
  2. What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
  3. Bend it like Bluemix, MongoDB with autoscaling – Part 2
  4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
  5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data
  6. Deblurring with OpenCV:Weiner filter reloaded

Introducing cricketr! : An R package to analyze performances of cricketers


Yet all experience is an arch wherethro’
Gleams that untravell’d world whose margin fades
For ever and forever when I move.
How dull it is to pause, to make an end,
To rust unburnish’d, not to shine in use!

Ulysses by Alfred Tennyson

Introduction

This is an initial post in which I introduce a cricketing package ‘cricketr’ which I have created. This package was a natural culmination to my earlier posts on cricket and my completing 9 modules of Data Science Specialization, from John Hopkins University at Coursera. The thought of creating this package struck me some time back, and I have finally been able to bring this to fruition.

So here it is. My R package ‘cricketr!!!’

This package uses the statistics info available in ESPN Cricinfo Statsguru. The current version of this package only uses data from test cricket. I plan to develop functionality for One-day and Twenty20 cricket later.

You should be able to install the package from GitHub and use  many of the functions available in the package. Please be mindful of  ESPN Cricinfo Terms of Use

(Note: This page is also hosted as a GitHub page at cricketr and also at RPubs as cricketr: A R package for analyzing performances of cricketers

You can download this analysis as a PDF file from Introducing cricketr

 The cricketr package

The cricketr package has several functions that perform several different analyses on both batsman and bowlers. The package has functions that plot percentage frequency runs or wickets, runs likelihood for a batsman, relative run/strike rates of batsman and relative performance/economy rate for bowlers are available.

Other interesting functions include batting performance moving average, forecast and a function to check whether the batsman/bowler is in in-form or out-of-form.

The data for a particular player can be obtained with the getPlayerData() function from the package. To do this you will need to go to ESPN CricInfo Player and type in the name of the player for e.g Ricky Ponting, Sachin Tendulkar etc. This will bring up a page which have the profile number for the player e.g. for Sachin Tendulkar this would be http://www.espncricinfo.com/india/content/player/35320.html. Hence, Sachin’s profile is 35320. This can be used to get the data for Tendulkar as shown below

The cricketr package can be installed from GitHub with

library(devtools)
install_github("tvganesh/cricketr")
library(cricketr)
tendulkar <- getPlayerData(35320,dir="..",file="tendulkar.csv",type="batting",homeOrAway=c(1,2),
                           result=c(1,2,4))

Important Note This needs to be done only once for a player. This function stores the player’s data in a CSV file (for e.g. tendulkar.csv as above) which can then be reused for all other functions. Once we have the data for the players many analyses can be done. This post will use the stored CSV file obtained with a prior getPlayerData for all subsequent analyses

Sachin Tendulkar’s performance – Basic Analyses

The 3 plots below provide the following for Tendulkar

  1. Frequency percentage of runs in each run range over the whole career
  2. Mean Strike Rate for runs scored in the given range
  3. A histogram of runs frequency percentages in runs ranges
par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsmanRunsFreqPerf("./tendulkar.csv","Sachin Tendulkar")
batsmanMeanStrikeRate("./tendulkar.csv","Sachin Tendulkar")
batsmanRunsRanges("./tendulkar.csv","Sachin Tendulkar")

tendulkar-batting-1

dev.off()
## null device 
##           1

More analyses

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
batsman4s("./tendulkar.csv","Tendulkar")
batsman6s("./tendulkar.csv","Tendulkar")
batsmanDismissals("./tendulkar.csv","Tendulkar")

tendulkar-4s6sout-1

 

3D scatter plot and prediction plane

The plots below show the 3D scatter plot of Sachin’s Runs versus Balls Faced and Minutes at crease. A linear regression model is then fitted between Runs and Balls Faced + Minutes at crease

battingPerf3d("./tendulkar.csv","Sachin Tendulkar")

tendulkar-3d-1

Average runs at different venues

The plot below gives the average runs scored by Tendulkar at different grounds. The plot also displays the number of innings at each ground as a label at x-axis. It can be seen Tendulkar did great in Colombo (SSC), Melbourne ifor matches overseas and Mumbai, Mohali and Bangalore at home

batsmanAvgRunsGround("./tendulkar.csv","Sachin Tendulkar")
tendulkar-avggrd-1

Average runs against different opposing teams

This plot computes the average runs scored by Tendulkar against different countries. The x-axis also gives the number of innings against each team

batsmanAvgRunsOpposition("./tendulkar.csv","Tendulkar")
tendulkar-avgopn-1

Highest Runs Likelihood

The plot below shows the Runs Likelihood for a batsman. For this the performance of Sachin is plotted as a 3D scatter plot with Runs versus Balls Faced + Minutes at crease using. K-Means. The centroids of 3 clusters are computed and plotted. In this plot. Sachin Tendulkar’s highest tendencies are computed and plotted using K-Means

batsmanRunsLikelihood("./tendulkar.csv","Sachin Tendulkar")

tendulkar-kmeans-1

## Summary of  Sachin Tendulkar 's runs scoring likelihood
## **************************************************
## 
## There is a 16.51 % likelihood that Sachin Tendulkar  will make  139 Runs in  251 balls over 353  Minutes 
## There is a 58.41 % likelihood that Sachin Tendulkar  will make  16 Runs in  31 balls over  44  Minutes 
## There is a 25.08 % likelihood that Sachin Tendulkar  will make  66 Runs in  122 balls over 167  Minutes

A look at the Top 4 batsman – Tendulkar, Kallis, Ponting and Sangakkara

The batsmen with the most hundreds in test cricket are

  1. Sachin Tendulkar :Average:53.78,100’s – 51, 50’s – 68
  2. Jacques Kallis : Average: 55.47, 100’s – 45, 50’s – 58
  3. Ricky Ponting : Average: 51.85, 100’s – 41 , 50’s – 62
  4. Kumara Sangakarra: Average: 58.04 ,100’s – 38 , 50’s – 52

in that order.

The following plots take a closer at their performances. The box plots show the mean (red line) and median (blue line). The two ends of the boxplot display the 25th and 75th percentile.

Box Histogram Plot

This plot shows a combined boxplot of the Runs ranges and a histogram of the Runs Frequency. The calculated Mean differ from the stated means possibly because of data cleaning. Also not sure how the means were arrived at ESPN Cricinfo for e.g. when considering not out..

batsmanPerfBoxHist("./tendulkar.csv","Sachin Tendulkar")

tkps-boxhist-1

batsmanPerfBoxHist("./kallis.csv","Jacques Kallis")

tkps-boxhist-2

batsmanPerfBoxHist("./ponting.csv","Ricky Ponting")

tkps-boxhist-3

batsmanPerfBoxHist("./sangakkara.csv","K Sangakkara")

tkps-boxhist-4

Contribution to won and lost matches

The plot below shows the contribution of Tendulkar, Kallis, Ponting and Sangakarra in matches won and lost. The plots show the range of runs scored as a boxplot (25th & 75th percentile) and the mean scored. The total matches won and lost are also printed in the plot.

All the players have scored more in the matches they won than the matches they lost. Ricky Ponting is the only batsman who seems to have more matches won to his credit than others. This could also be because he was a member of strong Australian team

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanContributionWonLost("35320","Sachin Tendulkar")
batsmanContributionWonLost("45789","Jacques Kallis")
batsmanContributionWonLost("7133","Ricky Ponting")
batsmanContributionWonLost("50710","K Sangakarra")

tkps-wonlost-1

dev.off()
## null device 
##           1

Performance at home and overseas

From the plot below it can be seen

Tendulkar has more matches overseas than at home and his performance is consistent in all venues at home or abroad. Ponting has lesser innings than Tendulkar and has an equally good performance at home and overseas.Kallis and Sangakkara’s performance abroad is lower than the performance at home.

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanPerfHomeAway("35320","Tendulkar")
batsmanPerfHomeAway("45789","Kallis")
batsmanPerfHomeAway("7133","Ponting")
batsmanPerfHomeAway("50710","Sangakarra")
tkps-homeaway-1
dev.off()
## null device 
##           1
 

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 Range 0 – 50 Runs – Ponting leads followed by Tendulkar Range 50 -100 Runs – Ponting followed by Sangakkara Range 100 – 150 – Ponting and then Tendulkar

frames <- list("./tendulkar.csv","./kallis.csv","ponting.csv","sangakkara.csv")
names <- list("Tendulkar","Kallis","Ponting","Sangakkara")
relativeBatsmanSR(frames,names)

tkps-relSR-1

Relative Runs Frequency plot

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

Sangakkara leads followed by Ponting

frames <- list("./tendulkar.csv","./kallis.csv","ponting.csv","sangakkara.csv")
names <- list("Tendulkar","Kallis","Ponting","Sangakkara")
relativeRunsFreqPerf(frames,names)

tkps-relRunFreq-1

Moving Average of runs in career

Take a look at the Moving Average across the career of the Top 4. Clearly . Kallis and Sangakkara have a few more years of great batting ahead. They seem to average on 50. . Tendulkar and Ponting definitely show a slump in the later years

par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanMovingAverage("./tendulkar.csv","Sachin Tendulkar")
batsmanMovingAverage("./kallis.csv","Jacques Kallis")
batsmanMovingAverage("./ponting.csv","Ricky Ponting")
batsmanMovingAverage("./sangakkara.csv","K Sangakkara")

tkps-ma-1

dev.off()
## null device 
##           1

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.

  • Tendulkar’s forecasted performance seems to tally with his actual performance with an average of 50
  • Kallis the forecasted runs are higher than the actual runs he scored
  • Ponting seems to have a good run in the future
  • Sangakkara has a decent run in the future averaging 50 runs
par(mfrow=c(2,2))
par(mar=c(4,4,2,2))
batsmanPerfForecast("./tendulkar.csv","Sachin Tendulkar")
batsmanPerfForecast("./kallis.csv","Jacques Kallis")
batsmanPerfForecast("./ponting.csv","Ricky Ponting")
batsmanPerfForecast("./sangakkara.csv","K Sangakkara")

tkps-perffcst-1

dev.off()
## null device 
##           1

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("./tendulkar.csv","Sachin Tendulkar")
## *******************************************************************************************
## 
## Population size: 294  Mean of population: 50.48 
## Sample size: 33  Mean of sample: 32.42 SD of sample: 29.8 
## 
## Null hypothesis H0 : Sachin Tendulkar 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Sachin Tendulkar 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Sachin Tendulkar 's Form Status: Out-of-Form because the p value: 0.000713  is less than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./kallis.csv","Jacques Kallis")
## *******************************************************************************************
## 
## Population size: 240  Mean of population: 47.5 
## Sample size: 27  Mean of sample: 47.11 SD of sample: 59.19 
## 
## Null hypothesis H0 : Jacques Kallis 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Jacques Kallis 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Jacques Kallis 's Form Status: In-Form because the p value: 0.48647  is greater than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./ponting.csv","Ricky Ponting")
## *******************************************************************************************
## 
## Population size: 251  Mean of population: 47.5 
## Sample size: 28  Mean of sample: 36.25 SD of sample: 48.11 
## 
## Null hypothesis H0 : Ricky Ponting 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Ricky Ponting 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Ricky Ponting 's Form Status: In-Form because the p value: 0.113115  is greater than alpha=  0.05"
## *******************************************************************************************
checkBatsmanInForm("./sangakkara.csv","K Sangakkara")
## *******************************************************************************************
## 
## Population size: 193  Mean of population: 51.92 
## Sample size: 22  Mean of sample: 71.73 SD of sample: 82.87 
## 
## Null hypothesis H0 : K Sangakkara 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : K Sangakkara 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "K Sangakkara 's Form Status: In-Form because the p value: 0.862862  is greater than alpha=  0.05"
## *******************************************************************************************

3D plot of Runs vs Balls Faced and Minutes at Crease

The plot is a scatter plot of Runs vs Balls faced and Minutes at Crease. A prediction plane is fitted

par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./tendulkar.csv","Tendulkar")
battingPerf3d("./kallis.csv","Kallis")
plot-3-1par(mfrow=c(1,2))
par(mar=c(4,4,2,2))
battingPerf3d("./ponting.csv","Ponting")
battingPerf3d("./sangakkara.csv","Sangakkara")
plot-4-1dev.off()
## null device 
##           1

Predicting Runs given Balls Faced and Minutes at Crease

A multi-variate regression plane is fitted between Runs and Balls faced +Minutes at crease. A sample sequence of Balls Faced(BF) and Minutes at crease (Mins) is setup as shown below. The fitted model is used to predict the runs for these values

BF <- seq( 10, 400,length=15)
Mins <- seq(30,600,length=15)
newDF <- data.frame(BF,Mins)
tendulkar <- batsmanRunsPredict("./tendulkar.csv","Tendulkar",newdataframe=newDF)
kallis <- batsmanRunsPredict("./kallis.csv","Kallis",newdataframe=newDF)
ponting <- batsmanRunsPredict("./ponting.csv","Ponting",newdataframe=newDF)
sangakkara <- batsmanRunsPredict("./sangakkara.csv","Sangakkara",newdataframe=newDF)

The fitted model is then used to predict the runs that the batsmen will score for a given Balls faced and Minutes at crease. It can be seen Ponting has the will score the highest for a given Balls Faced and Minutes at crease.

Ponting is followed by Tendulkar who has Sangakkara close on his heels and finally we have Kallis. This is intuitive as we have already seen that Ponting has a highest strike rate.

batsmen <-cbind(round(tendulkar$Runs),round(kallis$Runs),round(ponting$Runs),round(sangakkara$Runs))
colnames(batsmen) <- c("Tendulkar","Kallis","Ponting","Sangakkara")
newDF <- data.frame(round(newDF$BF),round(newDF$Mins))
colnames(newDF) <- c("BallsFaced","MinsAtCrease")
predictedRuns <- cbind(newDF,batsmen)
predictedRuns
##    BallsFaced MinsAtCrease Tendulkar Kallis Ponting Sangakkara
## 1          10           30         7      6       9          2
## 2          38           71        23     20      25         18
## 3          66          111        39     34      42         34
## 4          94          152        54     48      59         50
## 5         121          193        70     62      76         66
## 6         149          234        86     76      93         82
## 7         177          274       102     90     110         98
## 8         205          315       118    104     127        114
## 9         233          356       134    118     144        130
## 10        261          396       150    132     161        146
## 11        289          437       165    146     178        162
## 12        316          478       181    159     194        178
## 13        344          519       197    173     211        194
## 14        372          559       213    187     228        210
## 15        400          600       229    201     245        226

Analysis of Top 3 wicket takers

The top 3 wicket takes in test history are
1. M Muralitharan:Wickets: 800, Average = 22.72, Economy Rate – 2.47
2. Shane Warne: Wickets: 708, Average = 25.41, Economy Rate – 2.65
3. Anil Kumble: Wickets: 619, Average = 29.65, Economy Rate – 2.69

How do Anil Kumble, Shane Warne and M Muralitharan compare with one another with respect to wickets taken and the Economy Rate. The next set of plots compute and plot precisely these analyses.

Wicket Frequency Plot

This plot below computes the percentage frequency of number of wickets taken for e.g 1 wicket x%, 2 wickets y% etc and plots them as a continuous line

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
bowlerWktsFreqPercent("./kumble.csv","Anil Kumble")
bowlerWktsFreqPercent("./warne.csv","Shane Warne")
bowlerWktsFreqPercent("./murali.csv","M Muralitharan")

relBowlFP-1

dev.off()
## null device 
##           1

Wickets Runs plot

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
bowlerWktsRunsPlot("./kumble.csv","Kumble")
bowlerWktsRunsPlot("./warne.csv","Warne")
bowlerWktsRunsPlot("./murali.csv","Muralitharan")
wktsrun-1
dev.off()
## null device 
##           1

Average wickets at different venues

The plot gives the average wickets taken by Muralitharan at different venues. Muralitharan has taken an average of 8 and 6 wickets at Oval & Wellington respectively in 2 different innings. His best performances are at Kandy and Colombo (SSC)

bowlerAvgWktsGround("./murali.csv","Muralitharan")
avgWktshrg-1

Average wickets against different opposition

The plot gives the average wickets taken by Muralitharan against different countries. The x-axis also includes the number of innings against each team

bowlerAvgWktsOpposition("./murali.csv","Muralitharan")
avgWktoppn-1

Relative Wickets Frequency Percentage

The Relative Wickets Percentage plot shows that M Muralitharan has a large percentage of wickets in the 3-8 wicket range

frames <- list("./kumble.csv","./murali.csv","warne.csv")
names <- list("Anil KUmble","M Muralitharan","Shane Warne")
relativeBowlingPerf(frames,names)

relBowlPerf-1

Relative Economy Rate against wickets taken

Clearly from the plot below it can be seen that Muralitharan has the best Economy Rate among the three

frames <- list("./kumble.csv","./murali.csv","warne.csv")
names <- list("Anil KUmble","M Muralitharan","Shane Warne")
relativeBowlingER(frames,names)

relBowlER-1

Wickets taken moving average

From th eplot below it can be see 1. Shane Warne’s performance at the time of his retirement was still at a peak of 3 wickets 2. M Muralitharan seems to have become ineffective over time with his peak years being 2004-2006 3. Anil Kumble also seems to slump down and become less effective.

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
bowlerMovingAverage("./kumble.csv","Anil Kumble")
bowlerMovingAverage("./warne.csv","Shane Warne")
bowlerMovingAverage("./murali.csv","M Muralitharan")

tkps-bowlma-1

dev.off()
## null device 
##           1

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 forecating 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

Take a look at the wickets forecasted for the bowlers below. – Shane Warne and Muralitharan have a fairly consistent forecast – Kumble forecast shows a small dip

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
bowlerPerfForecast("./kumble.csv","Anil Kumble")
bowlerPerfForecast("./warne.csv","Shane Warne")
bowlerPerfForecast("./murali.csv","M Muralitharan")

kwm-perffcst-1

dev.off()
## null device 
##           1

Contribution to matches won and lost

The plot below is extremely interesting
1. Kumble wickets range from 2 to 4 wickets in matches wons with a mean of 3
2. Warne wickets in won matches range from 1 to 4 with more matches won. Clearly there are other bowlers contributing to the wins, possibly the pacers
3. Muralitharan wickets range in winning matches is more than the other 2 and ranges ranges 3 to 5 and clearly had a hand (pun unintended) in Sri Lanka’s wins

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
bowlerContributionWonLost(30176,"Anil Kumble")
bowlerContributionWonLost(8166,"Shane Warne")
bowlerContributionWonLost(49636,"M Muralitharan")

kwm-wl-1

dev.off()
## null device 
##           1

Performance home and overseas

From the plot below it can be seen that Kumble & Warne have played more matches overseas than Muralitharan. Both Kumble and Warne show an average of 2 wickers overseas,  Murali on the other hand has an average of 2.5 wickets overseas but a slightly less number of matches than Kumble & Warne

par(mfrow=c(1,3))
par(mar=c(4,4,2,2))
bowlerPerfHomeAway(30176,"Kumble")
bowlerPerfHomeAway(8166,"Warne")
bowlerPerfHomeAway(49636,"Murali")

kwm-ha-1
dev.off()
## null device 
##           1
 

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 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

Note: The check for the form status of the bowlers indicate 1. That both Kumble and Muralitharan were out of form. This also shows in the moving average plot 2. Warne is still in great form and could have continued for a few more years. Too bad we didn’t see the magic later

checkBowlerInForm("./kumble.csv","Anil Kumble")
## *******************************************************************************************
## 
## Population size: 212  Mean of population: 2.69 
## Sample size: 24  Mean of sample: 2.04 SD of sample: 1.55 
## 
## Null hypothesis H0 : Anil Kumble 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Anil Kumble 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Anil Kumble 's Form Status: Out-of-Form because the p value: 0.02549  is less than alpha=  0.05"
## *******************************************************************************************
checkBowlerInForm("./warne.csv","Shane Warne")
## *******************************************************************************************
## 
## Population size: 240  Mean of population: 2.55 
## Sample size: 27  Mean of sample: 2.56 SD of sample: 1.8 
## 
## Null hypothesis H0 : Shane Warne 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : Shane Warne 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "Shane Warne 's Form Status: In-Form because the p value: 0.511409  is greater than alpha=  0.05"
## *******************************************************************************************
checkBowlerInForm("./murali.csv","M Muralitharan")
## *******************************************************************************************
## 
## Population size: 207  Mean of population: 3.55 
## Sample size: 23  Mean of sample: 2.87 SD of sample: 1.74 
## 
## Null hypothesis H0 : M Muralitharan 's sample average is within 95% confidence interval 
##         of population average
## Alternative hypothesis Ha : M Muralitharan 's sample average is below the 95% confidence
##         interval of population average
## 
## [1] "M Muralitharan 's Form Status: Out-of-Form because the p value: 0.036828  is less than alpha=  0.05"
## *******************************************************************************************
dev.off()
## null device 
##           1

Key Findings

The plots above capture some of the capabilities and features of my cricketr package. Feel free to install the package and try it out. Please do keep in mind ESPN Cricinfo’s Terms of Use.
Here are the main findings from the analysis above

Analysis of Top 4 batsman

The analysis of the Top 4 test batsman Tendulkar, Kallis, Ponting and Sangakkara show the folliwing

  1. Sangakkara has the highest average, followed by Tendulkar, Kallis and then Ponting.
  2. Ponting has the highest strike rate followed by Tendulkar,Sangakkara and then Kallis
  3. The predicted runs for a given Balls faced and Minutes at crease is highest for Ponting, followed by Tendulkar, Sangakkara and Kallis
  4. The moving average for Tendulkar and Ponting shows a downward trend while Kallis and Sangakkara retired too soon
  5. Tendulkar was out of form about the time of retirement while the rest were in-form. But this result has to be taken along with the moving average plot. Ponting was clearly on the way out.
  6. The home and overseas performance indicate that Tendulkar is the clear leader. He has the highest number of matches played overseas and his performance has been consistent. He is followed by Ponting, Kallis and finally Sangakkara

Analysis of Top 3 legs spinners

The analysis of Anil Kumble, Shane Warne and M Muralitharan show the following

  1. Muralitharan has the highest wickets and best economy rate followed by Warne and Kumble
  2. Muralitharan has higher wickets frequency percentage between 3 to 8 wickets
  3. Muralitharan has the best Economy Rate for wickets between 2 to 7
  4. The moving average plot shows that the time was up for Kumble and Muralitharan but Warne had a few years ahead
  5. The check for form status shows that Muralitharan and Kumble time was over while Warne still in great form
  6. Kumble’s has more matches abroad than the other 2, yet Kumble averages of 3 wickets at home and 2 wickets overseas liek Warne . Murali has played few matches but has an average of 4 wickets at home and 3 wickets overseas.

Final thoughts

Here are my final thoughts

Batting

Among the 4 batsman Tendulkar, Kallis, Ponting and Sangakkara the clear leader is Tendulkar for the following reasons

  1. Tendulkar has the highest test centuries and runs of all time.Tendulkar’s average is 2nd to Sangakkara, Tendulkar’s predicted runs for a given Balls faced and Minutes at Crease is 2nd and is behind Ponting. Also Tendulkar’s performance at home and overseas are consistent throughtout despite the fact that he has a highest number of overseas matches
  2. Ponting takes the 2nd spot with the 2nd highest number of centuries, 1st in Strike Rate and 2nd in home and away performance.
  3. The 3rd spot goes to Sangakkara, with the highest average, 3rd highest number of centuries, reasonable run frequency percentage in different run ranges. However he has a fewer number of matches overseas and his performance overseas is significantly lower than at home
  4. Kallis has the 2nd highest number of centuries but his performance overseas and strike rate are behind others
  5. Finally Kallis and Sangakkara had a few good years of batting still left in them (pity they retired!) while Tendulkar and Ponting’s time was up

Bowling

Muralitharan leads the way followed closely by Warne and finally Kumble. The reasons are

  1. Muralitharan has the highest number of test wickets with the best Wickets percentage and the best Economy Rate. Murali on average gas taken 4 wickets at home and 3 wickets overseas
  2. Warne follows Murali in the highest wickets taken, however Warne has less matches overseas than Murali and average 3 wickets home and 2 wickets overseas
  3. Kumble has the 3rd highest wickets, with 3 wickets on an average at home and 2 wickets overseas. However Kumble has played more matches overseas than the other two. In that respect his performance is great. Also Kumble has played less matches at home otherwise his numbers would have looked even better.
  4. Also while Kumble and Muralitharan’s career was on the decline , Warne was going great and had a couple of years ahead.

You can download this analysis at Introducing cricketr

Hope you have fun using the cricketr package as I had in developing it. Do take a look at  my follow up post Taking cricketr for a spin – Part 1

Also see
1. Analyzing cricket’s batting legends – Through the mirage with R
2. Masters of spin: Unraveling the web with R
3. Mirror,mirror …best batsman of them all

You may also like
1. A crime map of India in R: Crimes against women
2.  What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
3.  Bend it like Bluemix, MongoDB with autoscaling – Part 2
4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data
6. Deblurring with OpenCV:Weiner filter reloaded
7. Fun simulation of a Chain in Android

The common alphabet of programming languages


                                                                   a                                                                                    

                                    “All animals are equal, but some animals are more equal than other.”                                     “Four legs good, two legs bad.”

from Animal Farm by George Orwell

Note: This post is largely intended for those who are embarking on their journey into the world of programming. The article below highlights a set of constructs that recur in many imperative, dynamic and object-oriented languages.  While these constructs cannot be applied directly to functional programming languages like Lisp,Haskell or Clojure, it may help. To some extent the programming language domain has been intentionally oversimplified to show that languages are not as daunting as they seem. Clearly there are a  lot more subtle and complex differences among languages. Hope you have fun programming!

Introduction: Anybody who is about to venture into the deep waters of programming will be bewildered and awed by the almost limitless number of programming languages and the associated paradigms on which they are based on. It is easy to feel apprehensive of programming, when faced with this  this array of languages, not to mention the seemingly quirky syntax of each language.  Many opinions abound, about what is the best programming language. In my opinion each language is best suited for a particular class of problems and is usually clunky if used outside of this. As an aside here is an interesting link provided by reader AKS to Rosetta Code, which is stated to be a a programming chrestomathy (present solutions to the same task in as many different languages as possible, to demonstrate how languages are similar and different, and to aid a person with a grounding in one approach to a problem in learning another. Rosetta Code currently has 772 tasks, 165 draft tasks, and is aware of 582 languages)

You are likely to hear  “All programming languages are equal, but some languages are more equal than others” from seasoned programmers who have their own pet language. There may also be others who swear that “procedural languages good, object oriented languages bad” or maybe “object oriented languages good, aspect oriented languages bad”. Unity in diversity Regardless of the language this post discusses a thread that is common to all programming languages. In fact any programming language can be expressed as

Lx = C + Sx

Where Lx is any programming language ‘x’. All programming languages have a set of core, common constructs which I have denoted as ‘C’ and a set of Specialized constructs, unique to each language ‘x’ which I have denoted as Sx. I would like to look at these constructs that are common to most programming languages like C,C++,Perl, Python, Ruby, C#, R, Octave etc. In my opinion knowing these core, common constructs and a few of the more specialized constructs should allow you to get started off in the language of your choice. You can pick up the more unique constructs as you go along.   Here are the common constructs (C mentioned above) that you must familiarize yourself with when embarking on a new language

  1. Reading user input and printing to screen
  2. Reading and writing from a file
  3. Conditional statement if-then-else if-else
  4. Loops – For, while, repeat, do while etc.

Knowing these constructs and some of the basic concepts unique to each language for e.g.
– Structure, Pointers in C,
– Classes, inheritance in C++
– Subsetting in Octave, R
– car, cdr in Lisp will enable you to get started off in your chosen language.
I show the examples of these core constructs in many languages. Note the similarity between these constructs
1. C
Read from and write to console

scanf(x,”%d); printf(“The value of x is %d”, x);
Read from and write to file
fread(buffer, strlen(c)+1, 1, fp);
fwrite(c, strlen(c) + 1, 1, fp);

Conditional
if(x > 5) {
printf(“x is greater than 5”);
}
else if (x < 5)
{ printf(“x is less than 5”);
}
else{ printf(“x is equal to 5”);
}

Loops I will only consider for loops, though one could use while, repeat etC.
for(i =0; i <100; i++)
{ money = money++)
}

2. C++
Read from and write to console
cin >> age;
Cout << “The value is “ << value

Read from and write to a file // open a file in read mode.
ifstream infile;
infile.open("afile.dat");
cout << "Reading from the file" <<
endl;
infile >> data;
ofstream outfile;
outfile.open("afile.dat");
// write inputted data into the file.
outfile << data <<
endl;

Conditional same as C
if(x > 5) {
printf(“x is greater than 5”);
}

else if (x < 5) {
printf(“x is less than 5”);
}
else{ printf(“x is equal to 5”);
}

Loops
for(i =0; i <100; i++)
{ money = money++)

}

2. C++ Read from and write to console
cin >> age;
Cout << “The value is “ << value
Read from and write to a file // open a file in read mode.
ifstream infile;
infile.open("afile.dat");
cout << "Reading from the file" << endl;
infile >> data; ofstream outfile;
outfile.open("afile.dat");
// write inputted data into the file.
outfile << data << endl;
Conditional same as C
if(x > 5) {
printf(“x is greater than 5”);
}
else if (x < 5) {
printf(“x is less than 5”);
}
else{ printf(“x is equal to 5”);
}
Loops
for(i =0; i <100; i++){
money = money++)
}
3. Java
Reading from  and writing to standard input
Console c = System.console();
int val = c.readLine("Enter a value: ");
System.out.println("Value is "+ val);
Reading and writing from file
try {
in = new FileInputStream("input.txt");
out = new FileOutputStream("output.txt");
int c;
while ((c = in.read()) != -1) {
out.write(c); } } ...
Conditional (same as C)
if(x > 5) {
printf(“x is greater than 5”);
}
else if (x < 5) {
printf(“x is less than 5”);
}
else{ printf(“x is equal to 5”); }
Loops (same as C)
for(i =0; i <100; i++){
money = money++)
}

4. Perl Read from console
#!/usr/bin/perl
$userinput =  ;
chomp ($userinput);
Write to console
print "User typed $userinput\n";
Reading and write to a file
open(IN,"infile") || die "cannot open input file";
open(OUT,"outfile") || die "cannot open output file";
while() {
print OUT $_;
# echo line read
}
close(IN);
close(OUT)
Conditional
if( $a  ==  20 ){
# if condition is true then print the following
printf "a has a value which is 20\n";
}
elsif( $a ==  30 ){
# if condition is true then print the following
printf "a has a value which is 30\n";
}else{
# if none of the above conditions is true
printf "a has a value which is $a\n";
}
Loops
for (my $i=0; $i <= 9; $i++) {
print "$i\n";
}

5. Lisp
The syntax for Lisp will be different from the others as it is a functional language. You need to familiarize yourself with these constructs to move ahead
Read and write to console
To read from standard input use
(let ((temp 0))
(print ‘(Enter temp))
(setf temp (read))
(print (append ‘(the temp is) (list temp))))
Read from and write to file
(with-open-file (stream “C:\\acl82express\\lisp\\count.cl”)
(do ((line (read-line stream nil) (read-line stream nil)))
(with-open-file (stream “C:\\acl82express\\lisp\\test.txt” :direction :output :if-exists :supersede)
(write-line “test” stream) nil)
Conditional
$ (cond ((< x 5)
(setf x (+ x 8))
(setf y (* 2 y)))
((= x 10) (setf x (* x 2)))
(t (setf x 8)))
Loops
$  (setf x 5)
$ (let ((i 0))
(loop (setf y (* x i))
(when (> i 10) (return))
(print i) (prin1 y) (incf i )))

6. Python
Reading and writing from console
var = raw_input("Please enter something: ")
print “You entered: ”  value
Reading and writing from files
f = open(filename, 'r')
a = f.readline().strip()
target = open(filename, 'w')
target.write(line1)
Conditionals
if x > 5:
print "x is greater than 5”
elif
x < 5:
print "x is less than 5"
else:
print "x is equal to 5"
Loops
for i in range(0, 6):
print "Value is :" % i 7.

R
x=5
paste('The value of x is =',x)
Reading and writing to a file
infile = read.csv(“file”)
write(x, file = "data", sep = " ")
Conditional
if(x > 5){
print(“x is greater than 5”) 
}else if(x < 5){
print(“x is less than 5”) 
}else {
print(“x is equal to 5”)
}
Loops
for (i in 1:10) print(i)

Conclusion
As can be seen the core constructs are very similar in different languages save for some minor variations. It is generally useful to get started with just knowing these constructs and few other important other features  of the language that you are trying to learn. It is possible to code most programs with these Core constructs and a few of the Specialized constructs in the language. These Core constructs are the glue that hold your code together.

You can learn more compact and more powerful features of the language as you go along The above core constructs are like the letters of the programming language alphabet. You need to construct words by stringing together these constructs and form sensible sentences which will be your program. Good luck with your adventure in your next new programming language!!!

Also see
1.Programming languages in layman’s language
2. The mind of the programmer
3. How to program – Some essential tips
4. Programming Zen and now – Some essential tips -2 

You may also like
1. A crime map of India in R: Crimes against women
2.  What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
3.  Bend it like Bluemix, MongoDB with autoscaling – Part 2
4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data
6. Deblurring with OpenCV:Weiner filter reloaded

TWS-5: Google’s Page Rank: Predicting the movements of a random web walker


Internet history can be divided into 2 epochs. The epoch before the Google search and that after. Prior to Google there were many unsuccessful attempts to organize the Web, which  a miniscule fraction of what we have today, through Web portals. So we had Yahoo, Excite, Alta-vista, Lycos etc. trying to categorize the pages of the Web into News, Sports, and Finance etc. Navigating through them was an exercise an frustration but one had to live with this for quite some time. ( The material for this post is taken from Mining Massive Datasets lecture from Coursera – Lecture by Prof. Jure Leskovec, Stanford University)

The Google Search powered by the Page Rank algorithm arrived at a time when the internet was exploding. This was precisely what ‘the doctor ordered’ as navigating the web became synonymous with the Web search. This post takes a look at the Page Rank algorithm behind Google Search.

The Web can be viewed as a large directed graph with out-links from Web pages to other pages (links from a page to external Web pages) and in-links into Web pages from other pages.

For the Google search, Google uses Web crawlers to index the pages of the Web and probably creates an inverted index of keywords to documents that contain them. It then uses the Page Rank algorithm to determine the relevance and importance of the Web page

How does Google identify the importance of a Web page?

The importance of a Web page is determined by the number of in-links to the page. Each in-link is considered a vote for this page. Also the in-link from an important page is higher than another in-link from a less important page. So for example an in-link from New York Times will be much larger than an in-link from the National Enquirer for example

1

In the figure above it can B has a highest Page Rank because it has the highest number of in-links. In addition the out-link from B to C increases the Page Rank of C.

A) Flow formulation: The Flow formulation for Page Rank is based on the following

  • Each Web page’s vote (in-link) is proportional to the importance of the source page
  • If a page ‘j’ with page rank rj has n out-links each link gets rj/n votes
  • Page ‘j’s own importance is the sum of all the votes on its in-links

2

Where rj = ri/3 + rk/4 as seen from the above figure

According to the Flow equation for Page rank, the rank rj for a page j is
rj = ∑ ri/d
I -> j

In other words the rank rj is the sum of the the in-links from all pages ri divided by its out-degree.

3

The flow equations for the above simple view of a Web links can be expressed as based on the rank ri of each node divided by its out-degree. So ry and ra have an out-degree of 2 and hence they are ry/2 and ra/2 per out-link

ry = ry/2 + ra/2
ra = rm + ry/2
rm = ra/2

B) The Matrix formulation

In the Matirx formulation for Page Rank an Adjacent matrix Mji is defined as follows
If a page I has di out-links
If page I has an out-link to page j then
I -> j                   Mji = 1/di else Mji =0

The Rank vector ri is the importance of page i
It is also assumed that  ∑ri = 1

3

The Flow formulation for the above was shown to be
ry = ry/2 + ra/2
ra = rm + ry/2
rm = ra/2

The Matrix formulation is

4

However when we a billions of Web pages with several hundred thousand in-links and out-links the Page rank is iteratively calculated

If we start with

5

To start the page rank of ra=ry=rm = 1/3 so that the sum ∑ri =1
This is then iterated
Using the

r = M x r to arrive at values that converge
ry            ½     ½     0                             1/3
ra    =     ½     0      1          x                   1/3
r m         0     ½      0                               1/3

This will eventually converge at ry=2/5 ra=2/5 and rm =1/5

The ability to rank Web pages on the order of importance was a real breakthrough for Google

The Page Rank also implies the probability that a Web surfer who randomly clicks the ou-links of a the Web pages will land on after some time. It is the probability of a random walk of the Web when clicking the Web links on pages at random.

While Google does a great job in crawling and serving pages it is rumored that more than 75% of the Web is inaccessible to Web search engines. This is known as the “Dark Net‘ or “Dark Web” much like the dark matter of the universe

Also see
1. A crime map of India in R: Crimes against women
2.  What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
3.  Bend it like Bluemix, MongoDB with autoscaling – Part 2
4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data
6. Deblurring with OpenCV:Weiner filter reloaded

Into the Telecom vortex


“Ten little Indian boys went out to dine,
One choked his little self and then there were nine
Nine little Indian boys sat up very late;
One overslept himself and then there were eight…”

From the poem “Ten Little Indians”

a

You don’t need to be particularly observant to notice that the telecom landscape over the last decade and a half is full of dead organizations, bloodshed and gore. Organizations have been slain by ruthless times and bigger ones have devoured the weaker, fallen ones. Telecom titans have vanished, giants have been reduced to dwarfs.

Some telecom companies have merged in a deadly embrace trying to beat the market forces only to capitulate to its inexorable death march.

The period from the early 1980s to the late 1990’s were the glorious periods for telecommunication. Digital switches (1972-1982), ISDN (1988), international calling, trunk protocols, mobile (~1991), 2G, 2.5G, and 3G moved in succession, one after another.

Advancement came after advancement. The future had never looked so bright for telecom companies.

The late 1990’s were heady years, not just for telecom companies, but to all technology companies. Stock prices soared. Many stocks were over-valued.  This was mainly due to what was described as the ‘irrational exuberance’ of the stock market.

Lucent, Alcatel, Ericsson, Nortel Networks, Nokia, Siemens, Telecordia all ruled supreme.

1997-2000. then the inevitable happened. There was the infamous dot-com bust of the 2000 which sent reduced many technology stocks to penny stocks. Telecom company stocks went into a major tail spin.  Stock prices of telecom organizations plummeted. This situation, many felt, was further exacerbated by the fact that nothing important or earth shattering was forth-coming from the telecom. In other words, there was no ‘killer app’ from the telecommunication domain.

From 2000 onwards 3G, HSDPA, LTE etc. have all come and gone by. But the markets were largely unimpressed. This was also the period of the downward slide for telecom. The last decade and a half has been extra-ordinarily violent. Technology units of dying organizations have been cannibalized by the more successful ones.

Stellar organizations collapsed, others transformed into ‘white dwarfs’, still others shattered with the ferocity of a super nova.

Here is a short recap of the major events.

  • 2006 – After a couple of unsuccessful attempts Alcatel and Lucent finally decide to merge
  • 2006 – Nokia marries Siemens in a 20 billion Euro deal. N
  • 2009-10 – Ericsson purchases Nortel’s CDMA and LTE business for $1.13 billion
  • 2009-10 – Nortel implodes
  • 2010 – Motorola sells networking unit to Nokia for $1.2 Billion
  • 2011 – Internet giant Google mops up Motorola’s handset division for $12.5 billion, largely for the patents
  • 2012 – Ericsson closes a deal with Telcordia for $1.15 billion
  • 2013 – Nokia sells its handset division to Microsoft after facing a serious beating from smartphones
  • 2015 – Nokia agrees to a $16.6 billion takeover of Alcatel Lucent

And so the story continues like the rhyme in Agatha Christie’s mystery novel

And then there were none

Ten little Indian boys went out to dine,                                                                                                                
One choked his little self and then there were nine…”

The Telecom companies continue their search for the elusive ‘killer app’ as progress comes in small increments – 3G, 3.5G, 3.75G, 4G, and 5G etc.

Personally I think the future of Telecom companies, lies in its ability to embrace the latest technologies of Cloud Computing, Big Data, Software Defined Networks, and Software Defined Datacenters and re-invent themselves. Rather than looking for some elusive ‘killer app’ they have to re-enter the technology scene with a Big Bang

As I referred to in one of my earlier posts “Architecting a cloud Based IP Multimedia System” the proverbial pot at the end of the rainbow may be in

  1. Virtualizing IP Multimedia Switches (IMS) namely the CSCFs (P-CSCF, S-CSCF, I-CSCF etc.),
  2. Using the features of the cloud like Software Defined Storage (SDS) , Load balancers and auto-scaling to elastically scale-up or scale down the CSCF instances to handle varying ‘call traffic’
  3. Having equipment manufacturers (Nokia, Ericsson, and Huawei) will have to use innovating pricing models with the carriers like AT&T, MCI, Airtel or Vodafone. Instead of a one-time cost for hardware and software, the equipment manufacturers will need to charge based on usage or call traffic (utility charging). This will be a win-win for both the equipment manufacturer and carrier
  4. Using SDN to provide the necessary virtualized pipes between users with the necessary policies for advanced services like video-chat, white-boarding, real-time gaming etc.
  5. Using Big Data and Hadoop to analyze Call Detail Records (CDRs) and provide advanced services to customers like differential rates for calls etc

Clearly there will be challenges in this virtualized view of things. Telecom equipment is renowned for its 5 9’s availability. The challenge will be achieving this resiliency, high availability and fault-tolerance with cloud servers. How can WAN latencies be mitigated? How to can SDN provide the QoS required for voice, video and data traffic in IMS?

IMS has many interesting services where video calls from laptops can be transferred as data calls to mobile phones and vice versa, from mobile networks to WiFi  and so on.

Many hurdles will have to be crossed. But this is, in my opinion, will be the path forward.

While the last decade and a half have been bad for the telecom industry, I personally feel we are on the verge on the next big breakthrough in telecom in the next year or two. Telecom will rise like the phoenix from its ashes in the next couple of years

Also see
1. A crime map of India in R: Crimes against women
2.  What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
3.  Bend it like Bluemix, MongoDB with autoscaling – Part 2
4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data
6. Deblurring with OpenCV:Weiner filter reloaded

TWS-4: Gossip protocol: Epidemics and rumors to the rescue


Having successfully completed a grueling yet enjoyable ‘Cloud Computing Concepts’ course at Coursera, from the University of Illinois at  Urbana-Champaign,  by Prof Indranil Gupta, I continue on my “Thinking Web Scale (TWS)” series of posts. In this post, I would like to dwell on Gossip Protocol.

Gossip protocol finds its way into distributed system from Epidemiology, a branch of science, which studies and models how diseases, rumors spread through society.   The gossip protocol disseminates information –  the way diseases, rumors spread in society or the way a computer virus is able to infect large networks very rapidly

Gossip protocol is particularly relevant in large distributed systems with hundreds and hundreds of servers spread across multiple data centers for e.g.  Social networks like Facebook, Google or Twitter etc.. The servers that power Google’s search, or the Facebook or Twitter engine is made of hundreds of commercial off the shelf (COTS) computers. This is another way of saying that the designers of these systems should fold extremely high failure rates of the servers into their design. In other words “failures will be the norm and not the exception”

As mentioned in my earlier post, in these large distributed systems  servers will be fail and new servers will be continuously joining the system. The distributed system must be able to accommodate servers joining or leaving the system. There is no global clock and each server has its own clock. To handle server failures data is replicated over many servers which obviously leads to issues of maintaining data consistency between the replicas.

A well-designed distributed system must include in its design key properties of

  1. Availability – Data should be available when you want it
  2. Consistency – Data should consistent across multiple copes
  3. Should be fault tolerant
  4. Should be scalable
  5. Handle servers joining or leaving the systems transparently

One interesting aspect of Distributed Systems much like Operating System (OS) is the fact that a lot of the design choices are based on engineering judgments. The design choices are usually a trade-off of slightly different performance characteristics. Some of them are obvious and some not so obvious.

Why Gossip protocol? What makes it attractive?

Here are some approaches

  1. Centralized Server:

Let us assume that in a network of servers we have a server (Server A) has some piece of information which it needs to spread to other servers. One way is to have this server send the message to all the servers. While this would work there are 2 obvious deficiencies with this approach

  1. The Server A will hog the bandwidth in transmitting the information to all other servers
  2. Server A will be a hot spot besides also being a Single Point of Failure

Cons: In other words if we have a central server always disseminating information then we run into the issue of ‘Single point of Failure’ of this central  server.

  1. Directed Graph

Assuming that we construct a directed overlay graph over the network of servers, we could transmit the message from server A to all other servers. While this approach, has the advantage of lesser traffic as  each server node will typically have around a 1 -3 children. This will result in lesser bandwidth utilization. However the disadvantage to this approach, will be that , when an intermediate non-leaf node fails then information will not reach all children of the failed nodes.

 Cons: Does not handle failures of non-leaf nodes well

  1. Ring Architecture

In this architecture we could have Server A, pass the message round the ring till it gets to the desired server. Clearly each node has one predecessor and one successor. Like the previous example this has the drawback that if one or more servers of the ring fail then the message does not get to its destination.

Cons: Does not handle failures of nodes in the ring well

Note: We should note that these engineering choices only make sense in certain circumstances. So for e.g. the directed graph or the ring structure discussed below have deficiencies for the distributed system case, however  these are accepted design patterns in computer networking for e.g. the Token Ring IEEE 802.5 and graph of nodes in a network. Hierarchical trees are the norm in telecom networks where international calls reach the main trunk exchange, then the central office and finally to the local office in a route that is a root-non-leaf-leaf route.

  1. Gossip protocol

Enter the Gossip protocol (here is a good summary on gossip protocol). In the gossip protocol each server sends the message to ‘b’ random peers. The value ‘b’ typically a small number is called the fan-out.  The server A which has the data is assumed to be ‘infected’. In the beginning only server A is infected while all other servers are ‘susceptible’.  Each server receiving the message is now considered to be infected. Each infected server transmits to ‘b’ other servers. It is likely that the receiving sever is already infected in which case it will drop the message.

In many ways this is similar to the spread of a disease is through a virus. The disease spreads when an infected person comes in contact with another person.

The nice part about the gossip protocol is that is light weight and it can infect the entire set of servers in the order of O (log N)

This is fairly obvious as each round the ‘b’ infected servers will infect ‘b*n’ other servers where ‘n’ is the fan-out.
The computation is as follows

Let x0 = n (Initial state, all un-infected) and y0 =1 (1 infected server) at time t = 0
With x0 + y= n + 1 at all times

Let β be the contact rate between the ‘susceptible’ and ‘infected’  (x*y), then the rate of infection can be represents as
dx/dt= -βxy

The negative sign indicates that the number of ‘non-infected’ servers will decrease over time
(It is amazing how we can capture the entire essence of the spread of disease through a simple, compact equation)

The solution for the above equation (which I have taken in good faith, as my knowledge in differential equations is a faint memory. Hope to refresh my memory when I get the chance, though!)
x=n(n+1)/(n+e^β(n+1)t )  – 1
y=(n+1)/(1+ne^(-β(n+1)t)) – 2

The solution (1)  clearly shows that the number ‘x’ of un-infected servers  at time‘t’ rapidly to 0 as the denominator becomes too large. The number of infected units ‘y’  as t increases tends to n+1, or in other words all servers get infected

This method where infected server sends a message to ‘b’ servers is known as the ‘push’ approach.

Pros: The Gossip protocol clearly is more resilient to servers failing as the gossip message is sent a ‘b’ random targets and can handle failures better.
Cons: There is a possibility that the ‘b’ random targets selected for infection are already infected, in which case the infection can die rapidly if these infected servers fail. 

The solution for the above is to have a ‘pull’ approach where after a time ‘t’ the un-infected servers pull the data from random servers. This way the un-infected servers will also get infected if they pull the data from already infected servers

A third approach is to have a combination of a push-pull approach.
Gossip has been used extensively in Facebook’s and Apache’s Cassandra NoSQL database. Amazon’s Dynamo DB and Riak NoSQL DB also use forms of Gossip Protocol

Failure detection: Gossip protocol has been used extensively in detecting failures. The failed servers are removed from the membership list and this is list is gossiped so that all servers have a uniform view of the set of live servers. However, as with any approach this is prone to high rate  false-positives,  where servers are assumed to have failed even though this may have been  marked as ‘failed’ because of a temporary network failure.   Moreover the network load on epidemic style membership lists are also high.

Some methods to handle false positives is to initially place failed servers under a ‘suspicion’.  When the number of messages attributing failure to this server increases above a threshold ‘t’, then the server is assumed to have failed and removed from the membership list.

Cassandra uses a failure ‘accrual’ mechanism to detect failures in the distributed NoSQL datanase

Epidemic protocols, like the gossip protocol are particularly useful in large scale distributed systems where servers leave and join the system.

One interesting application of the epidemic protocol is to simply to collect the overall state of the system.  If we consider an information exchange where all nodes have set an internal value xi = 0 except node 1 which has x1=1 (infected)  (from the book Distributed Systems: Principles & paradigms by Andrew Tannenbaum and Maarten Van Steen)

where xi = 1 if i =1, or 0 if i > 1
If the nodes gossip this value and compute the average (xi + xj) /2, then after a period of time this value will tend towards 1/N where N is the total number of nodes in the system. Hence all the servers in the system will become aware of the total size of the system.

Conclusion: Gossip protocol has widespread application in distributed systems of today, from spreading information, membership, failure detection, monitoring and alarming. It is really interesting to note that the theory of epidemics or disease spread from a branch of sociology become so important in a field of computer science.

Also see
1. A crime map of India in R: Crimes against women
2.  What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
3.  Bend it like Bluemix, MongoDB with autoscaling – Part 2
4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid
5. Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data

Thinking Web Scale (TWS-3): Map-Reduce – Bring compute to data


In the last decade and a half, there has arisen a class of problem that are becoming very critical in the computing domain. These problems deal with computing in a highly distributed environments. A key characteristic of this domain is the need to grow elastically with increasing workloads while tolerating failures without missing a beat.  In short I would like to refer to this as ‘Web Scale Computing’ where the number of servers exceeds several 100’s and the data size is of the order of few hundred terabytes to several Exabytes.

There are several features that are unique to large scale distributed systems

  1. The servers used are not specialized machines but regular commodity, off-the-shelf servers
  2. Failures are not the exception but the norm. The design must be resilient to failures
  3. There is no global clock. Each individual server has its own internal clock with its own skew and drift rates. Algorithms exist that can create a notion of a global clock
  4. Operations happen at these machines concurrently. The order of the operations, things like causality and concurrency, can be evaluated through special algorithms like Lamport or Vector clocks
  5. The distributed system must be able to handle failures where servers crash, disk fails or there is a network problem. For this reason data is replicated across servers, so that if one server fails the data can still be obtained from copies residing on other servers.
  6. Since data is replicated there are associated issues of consistency. Algorithms exist that ensure that the replicated data is either ‘strongly’ consistent or ‘eventually’ consistent. Trade-offs are often considered when choosing one of the consistency mechanisms
  7. Leaders are elected democratically.  Then there are dictators who get elected through ‘bully’ing.

In some ways distributed systems behave like a murmuration of starlings (or a school of fish),  where a leader is elected on the fly (pun unintended) and the starlings or fishes change direction based on a few (typically 6) closest neighbors.

This series of posts, Thinking Web Scale (TWS) ,  will be about Web Scale problems and the algorithms designed to address this.  I would like to keep these posts more essay-like and less pedantic.

In the early days,  computing used to be done in a single monolithic machines with its own CPU, RAM and a disk., This situation was fine for a long time,  as technology promptly kept its date with Moore’s Law which stated that the “ computing power  and memory capacity’ will  double every 18 months. However this situation changed drastically as the data generated from machines grew exponentially – whether it was the call detail records, records from retail stores, click streams, tweets, and status updates of social networks of today

These massive amounts of data cannot be handled by a single machine. We need to ‘divide’ and ‘conquer this data for processing. Hence there is a need for a hundreds of servers each handling a slice of the data.

The first post is about the fairly recent computing paradigm “Map-Reduce”.  Map- Reduce is a product of Google Research and was developed to solve their need to calculate create an Inverted Index of Web pages, to compute the Page Rank etc. The algorithm was initially described in a white paper published by Google on the Map-Reduce algorithm. The Page Rank algorithm now powers Google’s search which now almost indispensable in our daily lives.

The Map-Reduce assumes that these servers are not perfect, failure-proof machines. Rather Map-Reduce folds into its design the assumption that the servers are regular, commodity servers performing a part of the task. The hundreds of terabytes of data is split into 16MB to 64MB chunks and distributed into a file system known as ‘Distributed File System (DFS)’.  There are several implementations of the Distributed File System. Each chunk is replicated across servers. One of the servers is designated as the “Master’. This “Master’ allocates tasks to ‘worker’ nodes. A Master Node also keeps track of the location of the chunks and their replicas.

When the Map or Reduce has to process data, the process is started on the server in which the chunk of data resides.

The data is not transferred to the application from another server. The Compute is brought to the data and not the other way around. In other words the process is started on the server where the data, intermediate results reside

The reason for this is that it is more expensive to transmit data. Besides the latencies associated with data transfer can become significant with increasing distances

Map-Reduce had its genesis from a Lisp Construct of the same name

Where one could apply a common operation over a list of elements and then reduce the resulting list of elements with a reduce operation

The Map-Reduce was originally created by Google solve Page Rank problem Now Map-Reduce is used across a wide variety of problems.

The main components of Map-Reduce are the following

  1. Mapper: Convert all d ∈ D to (key (d), value (d))
  2. Shuffle: Moves all (k, v) and (k’, v’) with k = k’ to same machine.
  3. Reducer: Transforms {(k, v1), (k, v2) . . .} to an output D’ k = f(v1, v2, . . .). …
  4. Combiner: If one machine has multiple (k, v1), (k, v2) with same k then it can perform part of Reduce before Shuffle

A schematic of the Map-Reduce is included below\

2

Map Reduce is usually a perfect fit for problems that have an inherent property of parallelism. To these class of problems the map-reduce paradigm can be applied in simultaneously to a large sets of data.  The “Hello World” equivalent of Map-Reduce is the Word count problem. Here we simultaneously count the occurrences of words in millions of documents

The map operation scans the documents in parallel and outputs a key-value pair. The key is the word and the value is the number of occurrences of the word. E.g. In this case ‘map’ will scan each word and emit the word and the value 1 for the key-value pair

So, if the document contained

“All men are equal. Some men are more equal than others”

Map would output

(all,1),  (men,1), (are,1), (equal,1), (some,1), (men,1), (are,1),  (equal,1), (than,1), (others,1)

The Reduce phase will take the above output and give sum all key value pairs with the same key

(all,1),  (men,2), (are,2),(equal,2), (than,1), (others,1)

So we get to count all the words in the document

In the Map-Reduce the Master node assigns tasks to Worker nodes which process the data on the individual chunks

3

Map-Reduce also makes short work of dealing with large matrices and can crunch matrix operations like matrix addition, subtraction, multiplication etc.

Matrix-Vector multiplication

As an example if we consider a Matrix-Vector multiplication (taken from the book Mining Massive Data Sets by Jure Leskovec, Anand Rajaraman et al

For a n x n matrix if we have M with the value mij in the ith row and jth column. If we need to multiply this with a vector vj, then the matrix-vector product of M x vj is given by xi

1

Here the product of mij x vj   can be performed by the map function and the summation can be performed by a reduce operation. The obvious question is, what if the vector vj or the matrix mij did not fit into memory. In such a situation the vector and matrix are divided into equal sized slices and performed acorss machines. The application would have to work on the data to consolidate the partial results.

Fortunately, several problems in Machine Learning, Computer Vision, Regression and Analytics which require large matrix operations. Map-Reduce can be used very effectively in matrix manipulation operations. Computation of Page Rank itself involves such matrix operations which was one of the triggers for the Map-Reduce paradigm.

Handling failures:  As mentioned earlier the Map-Reduce implementation must be resilient to failures where failures are the norm and not the exception. To handle this the ‘master’ node periodically checks the health of the ‘worker’ nodes by pinging them. If the ping response does not arrive, the master marks the worker as ‘failed’ and restarts the task allocated to worker to generate the output on a server that is accessible.

Stragglers: Executing a job in parallel brings forth the famous saying ‘A chain is as strong as the weakest link’. So if there is one node which is straggler and is delayed in computation due to disk errors, the Master Node starts a backup worker and monitors the progress. When either the straggler or the backup complete, the master kills the other process.

Mining Social Networks, Sentiment Analysis of Twitterverse also utilize Map-Reduce.

However, Map-Reduce is not a panacea for all of the industry’s computing problems (see To Hadoop, or not to Hadoop)

But the Map-Reduce is a very critical paradigm in the distributed computing domain as it is able to handle mountains of data, can handle multiple simultaneous failures, and is blazingly fast.

Also see
1. A crime map of India in R: Crimes against women
2.  What’s up Watson? Using IBM Watson’s QAAPI with Bluemix, NodeExpress – Part 1
3.  Bend it like Bluemix, MongoDB with autoscaling – Part 2
4. Informed choices through Machine Learning : Analyzing Kohli, Tendulkar and Dravid

To see all posts click ‘Index of Posts