Predicting the outcome of a match has always been at the center of sports analytics. Indian Premier League (IPL), a professional Twenty20 (T20) cricket league in India, has established itself as one of the biggest tournaments in cricket history. In this paper, we propose a model to predict the winner at the end of each over in the second innings of an IPL cricket match. Our methodology not only incorporates the dynamically updating game context as the game progresses, but also includes the relative strength between the two teams playing the match. Estimating the relative strength between two teams involves modeling the individual participating players' potentials. To model a player, we use his career as well as recent performance statistics. Using the various dynamic features, we evaluate several supervised learning algorithms to predict the winner of the match. Finally, using the Random Forest Classi er (RFC), we have achieved an accuracy of 65:79% - 84:15% over the course of second innings, with an overall accuracy of 75:68%.
The use of statistical analysis in sports has been growing rapidly since the past decade. It has not only changed the way game strategies are formed or the players are evaluated, but also has impacted the way sports is viewed by the audience. Cricket is one of the most followed team games in the world with billions of fans all across the globe. The complex rules governing the game along with many other player-dependent and natural parameters provide ample opportunities to model the game from various perspectives.
Cricket has evolved over time. Today, it is played in three major formats { Test Matches, One Day Internationals (ODIs) and the T20 cricket. T20 cricket ? This work was done when the author was a student at IIIT-Hyderabad. is the latest and the most exciting format of the game. Ever since its inception in 2007, IPL has been a huge success and has generated a billion-dollar industry. It is played during April and May of every year by teams representing Indian cities and has already completed 10 successful seasons. Therefore, in this paper, we focus our study on the IPL cricket matches. We propose a dynamic model to predict the winner of a match at the end of each over in the second innings of the match. Apart from various game dependent features such as the number of balls remaining, the number of runs to be scored remaining, and the number of wickets remaining, we have used the relative team strength between the competing teams as a distinctive feature in predicting the winner of the match. A team is composed of players, hence, estimating the relative team strength between two competing teams requires us to estimate the potential of the players. Therefore, using the recent and career performance statistics of a player we de ne novel methods to render his batting and bowling capabilities, the two major roles of a player in the game of cricket. Using these features, we have evaluated various supervised learning algorithms to predict the winner of the match at the end of each over as the match progresses. 2
Over the last decade, the application of statistical methods in cricket analysis
has manifolded, particularly in the context of winner prediction. The application
of supervised learning techniques { Support Vector Machines (SVM) and
NaiveBayes Classi cation towards predictive analysis, considering various factors such
as coin toss outcome, competing teams, home venue etc., in ODI matches is
presented in Khan, Mehvish, Riddhi Shah [
However, the problem of winner prediction, while the game is in progress,
has not been studied in detail. Shankarnarayanan et al. [
In the T20 format of cricket, each of the two playing teams bats for a maximum of 120 deliveries and bowls for a maximum of 120 deliveries. The team that scores the maximum amount of runs in the 120 deliveries or before they lose their 10 wickets, wins the match
Over: A sequence of six balls bowled by a bowler from one end of the pitch is called an over in cricket terminology.
Innings: An innings is one of the divisions of a cricket match during which one team takes its turn to bat. There are two innings in a game of cricket. In this paper, we restrict our study to the second innings of a match.
State: In our study, we de ne state to represent the di erent stages in the match at which we make the predictions using our model. We consider 21 states for each match; 1 at the beginning of the second innings and 20 at the end of each over of the second innings. It is to be noted here that the number of states considered to make predictions can be changed. 3.2
In this section, we introduce the notation to be used throughout this paper. We use m to represent a match, innings1 and innings2 to denote the rst and second innings respectively. We use T eamA to represent the team batting in innings1 and T eamB to represent the team batting in innings2. ScoreA denotes the runs scored by T eamA in innings1. T arget denotes the number of runs that T eamB needs to score to win the match, T arget = ScoreA + 1. Si, 0 i 20 represents the states in a m. S0 corresponds to the state at the end of innings1 and the remaining states 1 i 20 each correspond to the state at the end of over i in innings2. S20 has been considered for training examples so as to make sure that the model learns which team has won the game. S20 has been used in the testing set as well and it serves as a con rmation that the model is working as expected. P lAm denotes the set of 11 players in T eamA playing in m and P lBm denotes the set of 11 players in T eamB playing in m.
C(p) denotes the set of career statistics of a player p and F (p) denotes the set of recent statistics (recent 4 games) or form of a player p. The career statistics are shown in Table 1 and recent statistics are similar to career statistics, replacing C with F .
At each state, there are 3 parameters along with the relative team scores that we use in our model to make predictions.
{ Rriuns remaining denotes the number of runs T eamB needs to get to win the runs scored by T eamB at state i m at state i. Rriuns remaining = T arget { Rwiickets remaining denotes the number of wickets T eamB has in hand at wickets lost by T eamB at state i state i. Rwiickets remaining = 10 { Rbiall remaining denotes the number of balls T eamB is yet to play at state i.
Rbialls remaining = 120 balls played by T eamB at state i
Calculation of Batting Average: Batting Average is de ned as the average number of runs scored by the batsman before he gets out. Batting average for the career statistics is calculated in the following way
BaC =
RSC
N OC
; BaSRC =
RSC (OBC 6) 100 Calculation of Batting Strike Rate: Batting Strike Rate is de ned as the average number of runs scored by the batsman before per 100 balls faced. Batting strike rate for the career statistics is calculated in the following way (1) (2)
The batting average and strike rate for the recent statistics is calculated similar to equations 1 and 2.
Calculation of Batsman Score The quality of the batsmen a team possesses
can greatly a ect the outcome of a game. Consistency and fast run-scoring ability
are two traits common to all the good batsmen. Batting average and is a measure
of the consistency of the batsman and batting strike rate is a measure of his fast
run-scoring ability. As illustrated in [
p career batting score = p recent batting score = r BaIC
M PC r BaIF n
BaC
The nal batting score fpinal batting score of a player considering his career and recent statistics is given by the equation 5 p final batting score = p career batting score + (1 ) p recent batting score (5) where n represents the number of recent matches considered and represents the weight assigned to the career score in calculating the nal batting score of a player. (3) (4) (6) (7) (8) 4.2
Calculation of Bowling Average: Bowling Economy is de ned as the average number of runs conceded by the bowler per over he bowls. Bowler average for the career statistics is calculated in the following way
BEC =
RCC
OBC BoSRC = (OBC
6) W TC
average number of balls bowled by the bowler per wicket taken. Bowling strike rate for the career statistics is calculated in the following way p career bowling score = r BoIC
Calculation of Bowler Score The quality of the bowlers a team possesses
also has signi cant impact on the game's outcome. Economical bowling and
high wicket-taking ability are two traits common to all the good bowlers.
Bowling economy and bowling strike rate is a measure of the economical bowling
while bowling strike rate is a measure of the bowler's high wicket-taking
ability.As illustrated in [
r BoIF
n rpecent bowling score = ( BEF ) (9) The nal bowling score fpinal bowling score of a player considering his career and recent statistics is given by the equation 10 1 BoSRF p final bowling score = p career bowling score + (1 ) p recent bowling score (10) where n represents the number of recent matches considered and represents the weight assigned to the career score in calculating the nal batting score of a player, and are same as the ones introduced in Equations 4 and 5, respectively. 4.3
A team's batting and bowling strength will be a consolidated measure of the batting and bowling strengths of the 11 players playing in that match. Algorithm 1 illustrates the computation of Relative strengthT eamB=T eamA . Lines 1- 4 normalize the bpatting score and bpowling score for all the players. As the match progresses through the innings2, there is every possibility of some batsmen getting out and some the bowlers using up their quota of deliveries (24 balls). Thus, we compute the bTaetatimng score and bTaetatimng score of a team as a weighted sum of players (batsmen) who are not yet out and the players (bowlers) who still retain their quota of deliveries respectively, Lines 5- 8. This introduces dynamism in the team scores by removing players, who cannot contribute to the game any longer (in terms of batting and bowling), from the respective batting and bowling scores of the team. Line 9 computes the Relative strengthT eamB=T eamA . We only calculate Relative strength with respect to T eamB because T eamB bats in innings2 according to our notation and we make predictions only for innings2 in our model. T eamA bowling score has a negative impact on T eamB batting score and vice-versa in the formula in line 9. 4.4
To predict the outcome of an ongoing T20 (IPL) match we rst split the innings2 into 21 states. S0 at the end of innings1 and Si(1 i 20) at the end of i overs. At a state Si we use the following dynamic features to make the prediction: { Runs remaining to be scored to win the match Rriuns remaining { Wickets that T eamB still has in hand Rwiickets remaining { Balls remaining to be played by T eamB in the innings Rbiall remaining { Relative strengthT eamB=T eamA ; serving as a dynamic metric of team strengths to better forecast predictions.
The aforementioned features capture the state of the match at any given instance while the match is in progress and these features change as the match progresses towards completion. All these features are parsed to a classi er along with the label (1 if T eamB wins, 0 otherwise) to forecast predictions for the match winner. Venue or home advantage is not used as a feature because most of the pitches in IPL are somewhat similar and the crowd support is even. Also, the shorter format of the game makes this feature negligible.
Modeling Teams at the beginning of an over T eamA batting score bToewalminBg score 5
5.1
The dataset can be broadly divided into two categories { historical data:
pertaining to the career statistics of players, and ball by ball data: pertaining to
various states of a match. The dataset for career statistics has been scraped
from the cricinf o website [
To learn the values of the parameters n and , used in Equations 4, 5, 9 and 10, we used all the matches played in seasons 3-8. We did a grid search over the values of n and . For each combination of n and , we ranked the players in the order of their estimated batting scores and estimated bowling scores, which are compared against the actual ranked batting and bowling score lists in the last n matches. Finally, n = 4 and = 0:8 yielded the least squared error in terms of the rank di erence between estimated and the actual lists.
Decision
Tree
KNN
Gradient SVM
Boost
Logistic Random
Regression Forest
Accuracy after each over in innings2
Accuracy % 5.3
Results 100 95 90 % 85 y c ra 80 u c cA 75 70 65 60 76 75 74 73 72 71
Accuracy of di erent classi ers
Using the features described and match outcome as the label, we evaluated
various binary classi ers such as SVM, Random Forests, k Nearest Neighbors
(kNN), Logistic Regression and Decision Trees using their scikit-learn [
From the plot in Figure 5.3, we observe an increasing trend in prediction accuracies after each over as the match progresses until completion. This proves the ability of our classi er to predict the winner with increasing con dence after each over. This also agrees with common intuition, that as the game nears its end, it is easier to predict the winner based on a given match state. While we examine the increasing trend of prediction accuracies in Figure 5.3, some uctuations are observed around the middle overs. This is because a game need not necessarily progress with increasing chances of one team's victory. Most of the times, the game uctuates between both the team based on their very recent (last few overs) performance in the match. However, when generalized over a set of matches, the probability of accurately predicting the winner increases as the game progresses towards its end.
The overall prediction accuracy obtained regardless of the match state is 75:68%, with an accuracy of 65:79% at the beginning of the second innings which increases to 84:15% at the end of the 19th over.
There have been several works such as [