With the advent of statistical modeling in sports, predicting the outcome of a game has been established as a fundamental problem. Cricket is one of the most popular team games in the world. With this article, we embark on predicting the outcome of a One Day International (ODI) cricket match using a supervised learning approach from a team composition perspective. Our work suggests that the relative team strength between the competing teams forms a distinctive feature for predicting the winner. Modeling the team strength boils down to modeling individual player's batting and bowling performances, forming the basis of our approach. We use career statistics as well as the recent performances of a player to model him. Player independent factors have also been considered in order to predict the outcome of a match. We show that the k-Nearest Neighbor (kNN) algorithm yields better results as compared to other classi ers.
Statistical modeling has been used in sports since decades and has contributed signi cantly to the success on eld. Cricket is one of the most popular sports in the world, second only to soccer. Various natural factors a ecting the game, enormous media coverage, and a huge betting market have given strong incentives to model the game from various perspectives. However, the complex rules governing the game, the ability of players and their performances on a given day, and various other natural parameters play an integral role in a ecting the nal outcome of a cricket match. This presents signi cant challenges in predicting the accurate results of a game.
The game of cricket is played in three formats - Test Matches, ODIs and T20s. We focus our research on ODIs, the most popular format of the game. To predict the outcome of ODI cricket matches, we propose an approach where we rst estimate the batting and bowling potentials of the 22 players playing the match using their career statistics and active participation in recent games. We use these player potentials to render the relative dominance one team has over the other. Taking two other base features into account, namely, toss decision and the venue of the match, along with the relative team strength, we adopt supervised learning algorithms to predict the winner of the match.
The major contributions of our paper are as follows: { We propose novel methods to model batsmen, bowlers and teams, using various career statistics and recent performances of the players. { To predict the winner of ODI cricket matches, we propose a novel dynamic approach to re ect the changes in player combinations. 2
In literature, Duckworth and Lewis proposed a solution, called the D/L method
[
In this paper, we embark upon a very critical aspect that the team composition changes over time, which has not been studied yet. A team is comprised of 11 players, and these 11 players are replaced over time. A team changes its composition depending upon the match conditions, venue, opponent team, etc. There could be various other reasons for the same, such as a player getting injured, or getting dropped from the team for his poor performance, or taking retirement from the sport itself. Figure 1 shows that on average at least 2 players change per match for each team. Therefore, relying completely on the historical data is not only insu cient, but also fallacious since it does not portray the current competence of a team. Taking such obsolete factors into account might lead us to incorrect conclusions. 3.0 In this section, we explain our approach to the problem in detail, including the de nitions and the mechanics of various algorithms used to model the batsmen, bowlers and the teams.
Notations: We use A and B as the two teams competing in a match m, P (T ,m)
as the set of all the players in team T playing in match m, and (p) as the set
of the career statistics of the player p throughout the paper. The major career
statistics of a player p (as used by [
Bowling Economy Average #runs conceded by the player per over bowled Modeling Batsmen: The batting ability of a player has a signi cant contribution in shaping the outcome of a match. A team usually comprises of a set of 6-7 specialist batsmen out of the 11 players. To model a batsman's aptitude, we have two types of statistics to get necessary insights into a player's characteristics. First, we examine his career performances to determine his potency as a contender. Second, we consider his recent match scores to analyze his prevailing form: where form of a batsman determines his contribution to the team in recent matches, which in turn re ects his con dence levels.
Algorithm 1 Modeling Batsmen
Input: Players p 2 fP (A; m) [ P (B; m)g, Career Statistics of player p: (p) Output: Batsmen Score of all the players: Batsman Score 1: for all players p 2 fP (A; m) [ P (B; m)g do 2: (p)
q 3: 4: 5: 6: u v w
Bat Inngs
Matches P layed 20 Num Centuries + 5 0:3 v + 0:7 Bat Avg
Career Score u w 7: M Last 4 matches played by p 8: Recent Score mean(MRpuns) 9: end for 10: for all players p 2 fP (A; m) [ P (B; m)g do 11: Career Score maxC(aCreaerreeSrcSorceore) 12: Recent Score maxR(eRceencetnStcSorceore) 13: Batsmen Score = 0:35 Career Score + 0:65 14: end for
Num F ifties
Recent Score
The pseudo code of the algorithm to model the batsmen for a given match is
given in Algorithm 1. Lines 2-6 calculate a player's Career Score using his overall
career statistics. Variable u (line 3) is the ratio of the number of matches in
which the batsman batted to the total number of matches he played. It captures
whether the player is a full-time specialist batsman or not. Higher values of u
indicate that the player often bats at the top of the batting order and hence he
gets to bat in almost every match. On the other hand, lower values of u tell us
that the player bats lower down the batting order and his chances of batting in
the next match is also comparatively low. Variable Career Score (line 6) takes all
the career statistics into account, and therefore signi es the Career Score of the
batsman. Similarly, lines 7-8 calculate the Recent Score of a batsman. Variable
M (line 7) holds the recent matches played by the player. Variable Recent Score
(line 8) captures the Recent Score of a batsman, which is the average number
of runs scored by the player in his recent games. Since the Career Score and
the Recent Score of players have di erent ranges, we have normalized them
(lines 11-12) to lie in a common range of [
Modeling Bowlers: Even though, cricket is called a batsman's game, one cannot undermine the importance of specialist bowlers in a team. A team usually comprises of a set of 4-5 specialist bowlers out of the 11 players. To model a bowler, we are examining his career performances to estimate his potential for the next match. u v w
7: end for 10
Bowl Inngs Matches P layed
Bowl Avg Bowl Eco u v w Algorithm 2 Modeling Bowlers
Input: Players p 2 fP (A; m) [ P (B; m)g, Career Statistics of player p: (p) Output: Bowler Score of all the players: Bowler Score 1: for all players p 2 fP (A; m) [ P (B; m)g do 2: (p) q
W kts T aken
The pseudo code of the algorithm to model bowlers for a given match is given in Algorithm 2. Variable u (line 3) is the ratio of the number of matches in which the bowler bowled to the total number of matches he played. It captures whether the player is a full-time specialist bowler or not. Higher values of u indicate that the player often bowls at the top of the bowling order and hence, he gets to bowl in almost every match. On the other hand, lower values of u tell us that the player is a part-time bowler who doesn't bowl in every match he plays and his chances of bowling in the next match are also comparatively low. Variables v and w (lines 4-5) consider other statistically signi cant features of a bowler. Finally, variable Bowler Score (line 6) takes everything into account, and therefore signi es the Bowler Score of the player.
Notice that unlike batsmen, we haven't considered the recent performances of a bowler in calculating his Bowler Score. This is due to the lack of data, as we do not have match-wise individual performances of every bowler. Modeling Teams: The batsmen and the bowlers are the fundamental units of a team. Therefore, using the modeled batsmen and bowlers, we intend to de ne an overall score of a team with respect to the other. We de ne the batting score of a team as the summation of the batting scores of all its players. Similarly, the bowling score of a team is de ned as the summation of the bowling scores of all its players. We have directly used the scores of all the players in the team score, as the variable u in the Algorithms 1 and 2 already takes care of the weighted contribution of individual players to the team score.
Our algorithm to nd the relative strength between two teams, A and B,
competing against one another in a match m is shown in Algorithm 3. Since the
Batsman Scores and the Bowler Scores have di erent ranges, we rst normalize
them to lie in the same range of [
Input: Players p 2 fP (A; m) [ P (B; m)g,
Batsman Score: pBatsman Score, Bowler Score: pBowler Score
Output: Strength of Team A against Team B: SA=B 1: for all players p 2 fP (A; m) [ P (B; m)g do 2: Batsman Score maxB(aBtsamtsamnanScSorceore)
Bowler Score max( Bowler Score) 3: Bowler Score 4: end for 5: Bat StrengthA 6: Bowl StrengthA 7: Bat StrengthB 8: Bowl StrengthB ! ! ! ! 9: SA=B = BBoawtl SSttrreennggtthhAB
Bat StrengthB
Bowl StrengthA Feature Construction: To predict the winner of an ODI cricket match, we choose the venue of the match and the outcome of the toss as two other important features, along with the relative strength of one team against the other. Therefore, every match played between team A and team B in our dataset has three features: Toss, Venue, and StengthA=B. The value of Toss is 1 if team A is batting rst, or 0 otherwise. The value of Venue is 1 if the match is being played at a home ground of team A, 0 if it is played at a home ground of Team B, and 2 otherwise. The value of StengthA=B is the relative strength of team A against team B, as calculated in the Algorithm 3. The target variable Winner de nes the winner of a match. It is a binary variable. The value of Winner is 1 if the winner of the match is team A, and 0 if the winner is team B. Using these three features, we apply machine learning algorithms to predict the winner of a match.
Note that out of the two competing teams, any one of them could be considered as team A and all the feature values and the target value would update accordingly. 4
Dataset: To retrieve all the required statistics, the entire dataset has been
scraped from the cricinfo website [
We have restricted our study to only top 9 ODI-playing teams, namely, Australia, South Africa, India, England, Sri Lanka, Pakistan, New Zealand, Bangladesh and West Indies. Since the impact of the nature on the game cannot be foreseen, a total of 109 matches which were either interrupted by rain or ended up in a draw/tie, have been removed from the dataset. Finally, we divided the dataset into two parts, namely, the test data and the training data. The training dataset contains all the matches played during the years 2010 to 2013, and the test dataset contains all the matches played in the year 2014. There are a total of 299 matches in training dataset and 67 matches in test dataset. Learning Weights: To assign the weights to various features in the Algorithms 1 and 2, we have used the 5-match ODI series played between India and Sri Lanka in July, 2012. A series of consecutive matches was deliberately chosen to study the impact of the recent scores of a batsman on his upcoming performances. The estimated scores of the players are compared against their actual performances. After exhaustive experimentation, the nal weights are chosen such that the top 6 performing batsmen and bowlers (in terms of runs scored and wickets taken, respectively) from both the teams match with the top 6 batsmen and bowlers estimated by our algorithms.
Binary Classi ers: Using various binary and numeric features and the
outcome of the match as the label, we evaluated a large number of binary classi ers
using their scikit-learn implementations [
The only obstacle we faced while evaluating our approach is the inability to
compare against previous models like [
Although we cannot directly compare these results with the prior
state-ofthe-art approaches due to di erences in the dataset, it is noteworthy that the
best accuracy in predicting the outcome of ODI cricket matches reported so far
in the literature is between 0.68 and 0.70 ( [
Country The paper addresses the problem of predicting the outcome of an ODI cricket match using the statistics of 366 matches. The novelty of our approach lies in addressing the problem as a dynamic one, and using the participating players as the key feature in predicting the winner of the match. We observe that simple features can yield very promising results.