A team recommendation system and outcome prediction for the game of cricket

1Introduction

Cricket is the most popular game in Asian countries, a lot of series are played across the set of different countries during a year and World Cup is played once in four years across all the cricket playing nations. Cricket is played in different formats like one day international (ODI), T20 and Test matches. Apart from this many league matches at club level and national level are played within the country. For any such tournaments, series or World Cup a suitable team of playing 11 and 4 extra players needs to be selected to form a team. Cricket team consists of a set of batsmen and bowlers with one wicket keeper who can also bat or bowl. The selectors and team captain has to select batsman and bowlers in the team with a wicket keeper. Each batsman in the team will be specialized to bat at a different position in the playing eleven and there are varieties of bowlers like spin, fast and medium fast in the team. Team members need to be selected from a pool of players depending on the opponent team against which the team is playing. The team selected may also be analyzed on their strength to chase or target setting against the team which they play. So selecting such a team by coaches and captain is biased and error prone, this decision depends on the experience and analytic skills of the individual by using the performance measures and statistics of the players. So automating the selection process by considering the performance measures and forecasting the match outcome helps coaches and captains to select the most efficient team which have higher chances of winning the game. The other challenge which might occur during selection is the lack of or few number statistics of the new player who have not played many international series. In this scenario, it becomes very important to correlate the new player with the existing player database with the statistics of club level and few international level games he had played. To automate such process, we propose a team selection and predicting the outcome of a game with player profiling facility to assign the performance measure to the new player.

Many people have worked on team selection, optimal ordering of the team and win prediction of the cricket game. A genetic algorithm is used to automate the cricket team selection of 15 members (11 playing and 4 extra players). This algorithm represents the team as a string by considering each player as a bit in a sting. Later these strings are evaluated using objective function and is converted into fitness. This is genetically evolved using the cross over, mutation and replacement techniques to select the Indian squad for the World Cup. To bid players for a league match IPL (Indian Premier League) played in India with a budget constraint, franchises considered both budget constrains and the player performance while selecting the team. With these multiple constraints an optimal team was selected with the best bowling and batsman using a nondominant sorting genetic algorithm (NSGA II) by solving the multi-objective optimization problem Ahmed et al. (2011); Omkar and Verma, (2003). A team selection is done using a short cricket series by using linear integer programming. Various measures used in the literature are discussed in detail and the measure is proposed which is derived by comparing the individual performance with the team performance in the series. Lemmer (2013). After or while the team is selected, optimal ordering of the batsmen and predicting the match outcomes are performed to forecast the success of the team selected. An optimal team line up is found from the huge combinatorial space using simulated annealing algorithm by considering the batting and bowling characteristics of the selected players. Parameters like Batting average (BA), Batting strike rate (SR), Bowling average (BA), Bowling economy rate (ER) is used Perera et al. (2016); Swartz et al. (2006). The combination of a supervised and unsupervised algorithm is used to predict the outcome of the one-day international match by using linear regression and nearest neighbor clustering methods. Using these methods, a total number of runs to be scored in the match is forecasted which is one of the important components in predicting the outcome of the match. Historic features extracted from the previous matches is combined with the ongoing match features like a number of wickets and runs scored are used in prediction Sankaranarayanan et al. (2014). The logistic regression model is used to extract features from the one-day cricket as the match is in progress, which reduces the parameters dramatically. Cross-validation method is used to decide the parameters which need to be used for the model Asif and McHale (2016). A software tool crickAI is developed using the machine learning technique bayesian classifier to predict the outcome of the one-day match. Factors like scoring, both the team strengths, toss, day-night match effect, home ground advantage are factors used for analysis Kaluarachchi and Aparna (2010). The score made by each team and difference between the scores of both the teams are approximated to the normal distribution, which facilitates the use of multiple linear regression to predict a score of the team batting first and victory margin in ODI Bailey and Clarke (2006). Multinomial logistic regression is used to predict the outcome of the test match as a multinominal response (win, draw, loss) using the match position at the session start and pre-match team strength and other features of test cricket Akhtar and Scarf (2012).

In this research, we propose a framework which predicts the outcome of the matches and performs team analysis and recommends the player role by extracting the statistics about the cricket game and players from various websites. The contributions of the proposed frame work are as follows:

2Proposed framework

The proposed framework for match win prediction, team analysis and player recommendation comprised of four phases: Player specific data collection, player performance quantification, model for win prediction and team structure analysis and player preferred role recommendation system as shown in the Fig. 1. In the first phase, the unstructured match data is pre-processed and stored in the data store. This data is input to next phase viz. player performance quantification, this phase uses the statistics of the players stored in the database to quantify and rank the players. This player statistics and player quantification details are used in later two phases. In win prediction and team structure analysis phase, the player quantification and historic match win or lose data is used to train the SVM for predicting the win or loss percentage. In the final phase, the clustering and k-nearest neighbor methods are used to recommend the preferred role for given player.

Fig.1

Proposed framework.

3Match outcome prediction and team structure analysis

To predict the match outcome, we use a support vector machine (SVM). SVM is a supervised classification technique which creates a separation plane between the positive and negative samples. We have used the SVM with linear and nonlinear techniques to predict the outcome of the match as a binary class problem. The prediction classes are the win (W) and loss (L) by a team in a match. The SVM does this by creating the feature vector with finite-dimension where each dimension represents the feature extracted from the historic match. This feature vector of known objects is used by SVM to train a model which assigns the class to a match as either win (W) or loss (L).

We train the SVM using a ranking index of batsman and bowlers, which is calculated using the measures evaluated in Section  2.2. The feature vector is generated by dividing the whole team into six divisions four for batting and two for bowling. These divisions are opening, top middle order, low middle order, tail-enders, pacers (both medium fast and fast bowlers) and spin. This is done for both the teams and for each division a feature is calculated by subtracting the average ranking of players in each division with the opponent team. Our system allows captain or the coach of the team to select the players in the order of their batting and bowling from both the teams and the prediction is made whether they win or lose with the specific opponent. This also helps them to see the strength and weakness of the team at particular division against particular team. So we also project the strength and weakness of the team at different levels of the team. so the feature vector X = {x_op, x_tm, x_lm, x_te, x_fb, x_sb} which represents the value calculated for each division and the outcome of the prediction y = {W, L} where W represents win and L represents the loss. These feature vector X is used to train the classifier with linear and nonlinear SVM.

3.2Nonlinear SVM

Nonlinear SVM is applied on the data sets that have nonlinear decision boundary. This uses a trick which transforms the data from the original coordinate space in X into a new feature space φ (X) and uses the linear decision boundary to separate the instances in transformed space. The learning task for nonlinear SVM can be given as the following optimization problem.

min||w||22

subject to y_i(w. φ(X_i) + b ≥ 1, i=1,2,....,N, the difference between linear and nonlinear kernel is that instead of using original attributes of X, the learning task is performed on the transformed attributes φ (X). SVM with poly kernel is a nonlinear kernel which deals with all non-linearly separable data set. This represents the values of the feature vector X of our training samples into polynomials in the feature space. This is represented by the equation K (X, Y) = (X^TY + c) ^p for the polynomial of degree p. where X and Y represent the feature vector in the input space and c represents the parameter which makes a trade-off between higher order and lower order term.

SVM with RBF kernal: This also deals with non-linearly separable dataset. It uses a Gaussian function to establish separating hyperplane in support vector. It works basically on the density of points in support vector. Which will build as many as virtual clusters dependent on the density of points this makes classifier produce very accurate results. Equation that decides decision boundary is as follows: Exp(12σ2||X-Xi||2) .

The Application for match outcome prediction and players contribution at different levels for the win is performed using the graphical user interface (GUI) shown in the Fig. 2a. It provides an option to the user to select the players for both the teams in the order of batting. This input is taken and the feature vectors X for the test data is generated using the player ranking average in each section and subtracting the corresponding section player average of the opposite team. This feature vector is fed as input to the model which is trained using SVM. The outcome of the match is predicted and displayed as shown in the Fig. 2b. Evaluated values of feature vector at each section is used to find the slot contributing to win and withholding the win and are displayed as shown in the Fig. 3. Match outcome prediction using SVM is further explained in Appendix 1.

Fig.2

Application showing match prediction and results

Fig.3

Contribution of different sections made in the team.

4Player preferred role recommendation system

To suggest the player and position which he is suitable to play, we have proposed the player preferred role recommendation system. This system is capable of suggesting the player to the team, who had not played in the tournament or he had only played in club level matches. To achieve the same, we find five players similar to the given player and suggest the position in which he needs to play. For this purpose, we have used the statistics and performance measures found in the Section 2.2. These data set of all the players are clustered using k-means clustering by applying cosine similarity measure between the data points. After the clustering, k-nearest neighbor method is used to find five players similar to the given player. Using the information about these players, the new player is recommended for the team and his role in the team is specified. Five players and the percentage of player similarities are shown in Fig. 4. Player recommendation system is explained further in Appendix 2.

Fig.4

Player profiling showing five similar players for the given player.

5Experimental results

To validate the prediction of cricket game outcome using SVM, we have used the 2011 World Cup matches excluding the matches abounded due to rain and draw. We have collected data of 48 matches and by considering both target setting and chasing innings of a match, our data set contains historical data of 96 matches. From this data set, a player ranking is used and feature vectors set X and Y for all the matches are created as mentioned in the Section 3. This feature set is used to train and test the SVM model with linear, poly and RBF kernels. The experiments are conducted by training the SVM by selecting random 48 matches and the model is tested using remaining 48 matches, to find accuracy, precision, and recall. The formulas for all the three measures are given in the following equations and the results are shown in the Table 1.

The results in the table show that the RBF kernel outperforms in two measures compared to the linear and poly kernel. This shows that the data points are linearly non-separable. To visualize the n-dimensional data points, the dimensions of the feature vector is reduced by using principal component analysis (PCA) method. PCA transforms the variables in the feature vector to a new set of variables known as principal components. Using these values, two dimensions plot for linear, poly and RBF kernel is plotted and is given in the Figs. 5a, 5b and 5c respectively.

Fig.5

Liner, Poly and RBF SVM plots.

6Conclusions

In this paper, we have proposed a model for cricket match outcome prediction, team structure analysis and player recommendation system using the statistics of the players extracted from a particular tournament. We have devised a method to find the player ranking system using players statistics in terms of tournament statistics. These ranking of players are used to model the SVM for match outcome prediction and team structure analysis. SVM model is trained using linear, poly and RBF and during the testing phase, it was shown that the accuracy, precision and recall rate for SVM with RBF had outperformed from other two methods. The results indicate that our data set is not linearly separable. So we intend to use the SVM with RBF method for match outcome prediction. In our player recommendation system, we have used player performance measures to cluster all the players using k-means clustering and similar players are found using k-nearest neighbor classifier.