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Introduction

• Cricket, the second most popular sport in the world has always been one among the most evolving sports. Loved by people in England, India, Australia, Pakistan, South Africa etc this sport has given the world many heroes.
• What began in England as a 5 day game now has three formats i.e., Test, ODI and T20.
• As a game of physicality and strategy there are a couple of other factor that are beyond human control that affect the outcome of each game. Especially in the T20 format where each team plays only 20 overs, winning the toss and being familiar with the ground you play on seem to give a head start to the team.
• In our investigation we have taken a data set that has the data of the best T20 league in the world, the Indian Premier League. with over 900 matches played this data set will is rich with the evidences we need for our analysis.
• The main terms to be kept in mind that exist in the data set are ‘TossWinner’- team thet wins the toss,‘WinningTeam’- match winning team,‘Team1’- home team,‘Team2’- away team,‘TossDecision’- decision taken by the winning team at the toss(batting or fielding) and ‘Season’- Year this game was played.
• For our analysis we have renames ‘Season’ to ‘Year’ and created another feature ‘Season’ which is a number associated to the season in ascending order. We have created features like ‘Toss_analysis’ and ‘Home_analysis’ which we will explain as we create it.

Problem Statement

• Considering factors that cannot be controlled by players like toss and the ground on which they play. Will these factors actually affect the game ?
• If there is an advantage in winning the toss will home ground advantage nullify it?

Data

• Cricket is a well-liked sport in which two teams of eleven players each compete.
• Although it is played all over the world, it is most frequently linked with nations like India, England, Australia, Pakistan, South Africa, and the West Indies.
• The most popular formats for cricket matches are Test matches, ODIs, and T20 Internationals.
• IPL is among the most famous cricket league with players coming from worldwide.
• The IPL data set selected for analysis is taken from Kaggle contains all details of the match: Venue of the match, Toss Decision, Match Winner, Man of the Match, Squads, etc.
• The selected data set consists of 20 variables. Out of 20 variables we are mainly focusing on Toss Winner, Toss Decision, Winning Team, Venue for out analysis.
• Out of the 2 playing teams there is 50% probability of each team winning a toss.Toss Winning team can only have 2 options either choosing bat first or field , here also the probability is considered as 50%.
• Certain variables in selected data set are not important, hence working on a subset with required variables is preferably a good choice.

Descriptive Statistics and Visualisation

• The original selected data does not have missing values.No outliers found in data.
• After selecting the required variables we have created two new variables (Toss Analysis & Home Ground Analysis). While creating Toss Analysis, we have assigned -1 to all rows.
• Toss Analysis :If a team wins the toss & the match, we have assigned 1 else 0.
• Rows with Toss Analysis as -1 indicates matches with no results, hence we have removed them from our analysis.
• Home Analysis :If a team wins a match in its home ground, we have assigned 1 else 0 (Team1 represents the team that are playing in home ground).

df <- read_csv("IPL_Matches_2008_2022.csv")
data <- df[,c('TossWinner','WinningTeam','Team1','Team2','TossDecision','Season')]
data$tossanalysis <- -1
data$tossanalysis[data$TossWinner == data$WinningTeam] <- 1
data$tossanalysis[!data$TossWinner == data$WinningTeam] <- 0
data <- data[(data$tossanalysis==1 | data$tossanalysis==0),]
data$homeanalysis <- -1
data$homeanalysis[data$Team1 == data$WinningTeam] <- 1
data$homeanalysis[data$Team2 == data$WinningTeam] <- 0

Decsriptive Statistics Cont 1.

knitr::kable((head(data)))

Decsriptive Statistics Cont 2.

• To analyse the effect of toss on a match , we need to look at each season. This is done using table() function and modified it to create a clean data frame as below.

Season<- 1:15
grouped_df <- data[,c("tossanalysis","Season")]
tdf <- table(grouped_df  )
tdf <- as.data.frame(tdf)
toss_winner_won <- tdf$Freq[tdf$tossanalysis==1]
toss_winner_lost <- tdf$Freq[tdf$tossanalysis==0]
Year <- unique(tdf$Season)
hgrouped_df <- data[,c("homeanalysis","Season")]
hdf <- table(hgrouped_df)
hdf <- as.data.frame(hdf)
home_team_won <- hdf$Freq[hdf$homeanalysis==1]
away_team_won <- hdf$Freq[hdf$homeanalysis==0]
ddf <- data.frame(Season,Year,toss_winner_won, toss_winner_lost,home_team_won ,away_team_won)
knitr::kable(head(ddf))

Decsriptive Statistics Cont 3.

• Graphical representation of season wise Toss Analysis.

plot(Season, ddf$toss_winner_lost, type = "o", col = "red", xlab = "Seasons", ylab = "Number of Matches", main = "Toss Analysis",ylim= c(20,50))
lines(Season, ddf$toss_winner_won, col = "green", type="o")
legend("topright", legend = c("Loss", "Win"), col = c("red", "green"), lty = 1 )

- From the above graph we can see the trend of toss impacting match result.

Decsriptive Statistics Cont 4.

• Graphical representation of season wise Home Ground Analysis.

plot(Season, ddf$away_team_won, type = "o", col = "red", xlab = "Seasons", ylab = "Number of Matches", main = "Home Ground Analysis", ylim= c(20,60))
lines(Season, ddf$home_team_won, col = "green", type="o")
legend("topright", legend = c("Away team won", "Home team won"), col = c("red", "green"), lty = 1 )

-From the above graph we can see the trend of home ground impacting match result.

Decsriptive Statistics Cont 5.

• Summarizing the toss’ impact on match result as below.

ddf%>%summarise(Min = min(ddf$toss_winner_won,na.rm = TRUE),
          Q1 = quantile(ddf$toss_winner_won,probs = .25,na.rm = TRUE),
          Median = median(ddf$toss_winner_won, na.rm = TRUE),
          Q3 = quantile(ddf$toss_winner_won,probs = .75,na.rm = TRUE),
          Max = max(ddf$toss_winner_won,na.rm = TRUE),
          Mean = mean(ddf$toss_winner_won, na.rm = TRUE),
          SD = sd(ddf$toss_winner_won, na.rm = TRUE)) -> table1
knitr::kable(table1)

ddf%>%summarise(Min = min(ddf$toss_winner_lost,na.rm = TRUE),
          Q1 = quantile(ddf$toss_winner_lost,probs = .25,na.rm = TRUE),
          Median = median(ddf$toss_winner_lost, na.rm = TRUE),
          Q3 = quantile(ddf$toss_winner_lost,probs = .75,na.rm = TRUE),
          Max = max(ddf$toss_winner_lost,na.rm = TRUE),
          Mean = mean(ddf$toss_winner_lost, na.rm = TRUE),
          SD = sd(ddf$toss_winner_lost, na.rm = TRUE))-> table2
knitr::kable(table2)

Hypothesis Testing-1

• We are interested in finding the impact of toss in a game.
• NULL HYPOTHESIS(H0): There is no significant impact i.e., mean(toss_winner_lost) = mean(toss_winner_won)
• ALTERNATE HYPOTHESIS(H1): There is a significant impact i.e., mean(toss_winner_lost) != mean(toss_winner_won)

pttest <- t.test(ddf$toss_winner_won, ddf$toss_winner_lost ,
                 paired = TRUE,
                 alternative = "two.sided",
                 conf.level = .95)
pttest

## 
##  Paired t-test
## 
## data:  ddf$toss_winner_won and ddf$toss_winner_lost
## t = 1.211, df = 14, p-value = 0.246
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -1.645080  5.911746
## sample estimates:
## mean difference 
##        2.133333

Discussion on Hypothesis Testing-1

• From the two sample t test we can find that the p-value(0.246) is greater than 0.05.
• This indicates that we cannot reject the null hypothesis.
• The toss does not seem to have a significant impact on the game.

Hypothesis Testing-2

• We are interested in finding the association between toss and home ground.
• NULL HYPOTHESIS(H0): There is no association between toss and home ground.
• ALTERNATE HYPOTHESIS(H1): There is an association between toss and home ground .

par(mfrow = c(1, 1))
#home team won the toss and the match
htw<-nrow(data[(data$WinningTeam==data$Team1 & data$TossWinner==data$Team1),]) #203 
#home team lost the toss and won the match
hlw<-nrow(data[(data$WinningTeam==data$Team1 & data$TossWinner==data$Team2),]) #277
#away team won the toss and the match
aww<-nrow(data[(data$WinningTeam==data$Team2 & data$TossWinner==data$Team2),]) #286
#away team lost the toss and won the match
alw<-nrow(data[(data$WinningTeam==data$Team2 & data$TossWinner==data$Team1),]) #180
table <- matrix(c(htw, hlw, aww, alw), nrow = 2)
table2<- table %>% prop.table(margin = 2)
barplot(table2,main = "Home Team Wins vs Away Team Wins",ylab="Matches won",
ylim=c(0,0.7),legend=rownames(table2),beside=TRUE,args.legend=c(x = "topleft",horiz=TRUE,title="Stumble Direction"),xlab="Team 1 vs Team 2",col=c("green","red"))
legend("topright", legend = c("Won Toss","Lost Toss"), fill = c("green","red"), title = "Legend")

- In the above bar plot we can see the impact of toss on the result, when played on home team & away team.

Hypothesis Testing-2 Cont.

result <- chisq.test(table)
result

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  table
## X-squared = 33.717, df = 1, p-value = 6.374e-09

Discussion on Hypothesis Testing-2

• From the chi squared test we can find that the p value(6.374e-09) is lesser than 0.05.
• This indicates that we reject the null hypothesis.
• There is significant association between toss and home ground

Hypothesis Testing-3

• Since there is association between Toss and Home ground. We will have to investigate the effects of the toss on the home ground and away ground
• For this we need two sample t test on the games won by the toss winner in home and away conditions
• NULL HYPOTHESIS(H0): There is no significant impact if you win the toss
• ALTERNATE HYPOTHESIS(H1): mean of sample that has teams winning the toss and match in home ground is lesser than the mean of sample that has away teams winning the toss and match

ggrouped_df <- data[,c("tossanalysis","homeanalysis","Season")]
ddf <- table(ggrouped_df  )
ddf <- as.data.frame(ddf)
#won toss and match on home ground
hww <- ddf$Freq[(ddf$homeanalysis==1 & ddf$tossanalysis==1)]
#won toss and match on away ground
aww<- ddf$Freq[(ddf$homeanalysis==0 & ddf$tossanalysis==1)]
pttest <- t.test(hww, aww ,
                 paired = FALSE,
                 alternative = "less",
                 conf.level = .95)
pttest 

## 
##  Welch Two Sample t-test
## 
## data:  hww and aww
## t = -2.3932, df = 27.645, p-value = 0.01187
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##       -Inf -1.598338
## sample estimates:
## mean of x mean of y 
##  13.53333  19.06667

Discussion on Hypothesis Testing-3

• From the two sample t test we can find that the p-value(0.01187) is lesser than 0.05.
• This indicates that we should reject the null hypothesis.
• The winners of toss in away matches seems to win the match.
• The toss on the home ground does seem to have a significant impact on the game. Thus home ground cannot nullify the toss advantage.

References

• https://www.kaggle.com/datasets/vora1011/ipl-2008-to-2021-all-match-dataset?select=IPL_Matches_2008_2022.csv
• https://cricsheet.org/