Player Performance Predictive Analysis in Cricket Using Machine Learning

Two teams of eleven players each compete in a game of cricket, with each team getting to bat and bowl against the other based on the outcome of a necessary act called a toss, which involves flipping a coin and asking for the face of the coin to land on the ground. If the call is accurate, the side selects whether to bat first or ball first. The teams are selected based on performance parameters like consistency, Form, venue, opposition, and weather. The role of a batsman is to score the maximum runs, while the role of the bowlers of the same team is to defend the total runs scored by the batter of their team. The performance parameter includes four basic parameters: the performance of a player throughout their career, the performance of a player in the last certain months, called Form, the performance of the player against the opponent, and the performance of the player at the particular venue [1]. Other parameters include weather, pitch, toss, type of match, etc. The role of a captain and team management is to pick a set of players that can perform better in both innings, i.e., batting and bowling. Generally, a team consists of four types of players: batters, wicketkeepers, all-rounders, and bowlers. Batters are the players that bat mostly; they start the game and go down to five wickets. The wicketkeeper is the player who bats and does wicketkeeping only; they do not do bowling. Bowlers are the players who are good at bowling and do not have much of a batting record. All-rounders are the players who bat and bowl in the match and have a considerable record in both [2].

The following research aims to analyze the performance parameters of each player, including consistency, Form, performance against opposition, and performance at a venue in a One Day International (ODI) match based on supervised machine learning algorithms by segmenting the problem into a set of two problems: batsman performance prediction and bowler performance prediction.

The data was classified into different class labels depending on a certain range and then calculated as the performance parameter. The labeled class is given a weighted average according to its impact on performance. The resultant parameter reflects a certain class label for the runs a batsman will score or the wickets a bowler will take in a match.

The primary objective of this research was to enhance predictive analysis within the context of cricket matches. To further develop and extend this study, an initial approach involves conducting similar research across various cricket matches. This expansion is deemed essential for a comprehensive predictive analysis application, considering the substantial impact of match characteristics on outcomes.

Future work in this research could incorporate additional diverse inputs, such as the player’s role on the field (e.g., Opening Batsman, All-rounder, Captain, WK), the specific tournament in which the match is played (categorized into Two Team Tournament, Three-Four Team Tournament, and Five Team Tournament), and factors influencing performance, including the psychological aspect denoted by the Toss and Pressure attributes.

The Toss attribute acknowledges the psychological advantage associated with winning the coin toss. At the same time, pressure quantifies the mental stress a player faces, ranging from 1 to 5 and varying based on the match type, such as normal matches, quarterfinals, semifinals, and finals. These additional dimensions aim to enrich the predictive capabilities of the analysis, providing a more nuanced understanding of cricket match dynamics.

In Table 5, data for the consistency parameter functions as a metric to evaluate a bowler’s overall performance throughout innings. It classifies each bowler based on the total number of innings bowled, overs delivered, and the occurrences of five or four-wicket hauls concerning their overall innings. This classification provides insights into a bowler’s effectiveness and consistency in achieving significant milestones during their bowling spells. The other parameter form concentrates on a narrower set of innings to systematically assess and categorize a bowler’s performance. Specifically, it scrutinizes the bowler’s recent achievements and current Form based on the most recent 15 innings. This approach offers valuable insights into the bowler’s present effectiveness and highlights their recent accomplishments on the field.

In assessing a bowler’s performance against various oppositions, key parameters such as the number of innings bowled, occurrences of five-wicket and four-wicket hauls, total overs bowled, and total innings come into play for classifying performance. By scaling these values, a comprehensive analysis can be conducted to determine the comfort level of a bowler against different opponents. This approach allows us to identify the oppositions where a bowler excels and those where they find it more challenging, contributing to a nuanced understanding of their effectiveness. Further, in evaluating a bowler’s performance across various venues, the classification considers key parameters such as the number of innings bowled, occurrences of five-wicket and four-wicket hauls, total overs bowled, and total innings bowled. By scaling these values, a detailed analysis can be conducted to ascertain the comfort level of a bowler at different venues. This approach allows for identifying venues where a bowler performs exceptionally well and encounters greater challenges, contributing to a nuanced understanding of their overall effectiveness across different playing environments. The common rating for bowling performance is shown in Table 6.

Table 6. Common ratings of a bowling performance

Utilizing common ratings bucketing is a valuable approach for scaling multiple common ratings in bowling, such as bowling average and bowling strike rate, especially given the prevalence of decimal values. This method categorizes these numerical ratings into specific buckets or ranges, allowing for a more straightforward and insightful analysis. By grouping the data this way, trends and patterns can be more easily identified, facilitating a comprehensive examination of the bowling performance metrics.

3.3 Weighing attributes

Different attributes reflect different characteristics of a player’s career, but every attribute has a unique impact, and no two attributes can have the same impact and priority. For example, the strike rate doesn’t play an important role as the average. Hence, the average weight must be more than the strike rates. To do that, weights were determined using a technique known as the Analytic Hierarchy Process (AHP) [20]. This technique gave each attribute a certain weighted value according to their priorities and impact. Every aspect of decision-making, both subjective and objective, is covered by the Analytic Hierarchy Process (AHP). By having the decision maker compare each assessment criterion pairwise, AHP generates weights for each criterion [21]. The higher the weight, the greater the importance assigned to the corresponding criterion. Subsequently, AHP assigns scores to each option for a fixed criterion based on the decision maker’s pairwise comparisons of the options within that criterion. A greater score denotes an improved choice performance concerning the criterion under consideration. Ultimately, AHP combines the criteria weights and the alternatives’ scores to produce a global score for every option and a corresponding ranking. A particular option’s global score is the weighted total of the ratings it received for each criterion. The four performance parameters to be calculated are:

1. Consistency of Batting Performance=0.4262*average+0.2566*no. of innings+0.1510*SR+0.0787*Centuries+0.0556*Fifties–0.0328*Zeros
2. Consistency of Batting Performance=0.4174*no. of overs+0.2634*no. of innings+0.1602*SR+0.0975*average+0.0615*FF
3. Form of Batting Performance=0.4262*average+0.2566*no. of innings+0.1510*SR+0.0787*Centuries+0.0556*Fifties–0.0328*Zeros
4. Form of Bowling Performance=0.3269*no. of overs+0.2846*no. of innings+0.1877*SR+0.1210*average+0.0798*FF
5. Player Batting performance in opposition=0.4262*average+0.2566*no. of innings+0.1510*SR+0.0787*Centuries+0.0556*Fifties–0.0328*Zeros
6. Player Bowling performance in opposition=0.3177*no. of overs+0.3177*no. of innings+0.1933*SR+0.1465*average+0.0943*FF
7. Player Batting performance in particular venue=0.4262*average+0.2566*no. of innings+0.1510*SR+0.0787*Centuries+0.0556*Fifties+0.0328*HS
8. Player Bowling performance in particular venue=0.3018*no. of overs+0.2783*no. of innings+0.1836*SR+0.1391*average+0.0972*FF

The predicted classification output in the ratings is shown in Table 7 below:

Table 7. Predicted class labels

Table 7 signifies the class labels the model predicts upon mapping the output labels. Based on the inputs, it can be estimated how much or in which range the batter will score runs or take wickets. For four estimation purposes, the four supervised algorithms, i.e., Naïve Bayes’, Decision Tree, Random Forest, and SVM, are used to train the model and fit the data.

(a). Naïve Bayes’: Bayesian classifiers are statistical tools used for predicting the probability that a given tuple belongs to a specific class [22]. The Naïve Bayes classifier, a Bayesian classifier, operates under the assumption that each attribute independently affects the class label, regardless of the values of other attributes. This assumption is known as class-conditional independence. Bayesian classifiers rely on Bayes’ theorem for their foundation.

Bayes’ Theorem: Let X be a data tuple and C a class label. Let X belongs to class C, then (Eq. (1)):

$\frac{P(C \mid X)=(P(X \mid C) * P(C))}{P(X)}$            (1)

where,

• $P(C \mid X)$ is the posterior probability of the $C$ given predictor $X$.
• $\quad P(C)$ is the prior probability of class.
• $\quad P(X \mid C)$ is the posterior probability of $X$ given the class $C$.
• $\quad P(X)$ is the prior probability of predictor.

The classifier computes $P(C \mid X)$ for each class $C_i$ with respect to a given tuple $X$. Subsequently, it predicts that $X$ belongs to the class with the highest posterior probability conditioned on $X$. That is $X$ belongs to class $C_i$ (Eq. (2)):

$P\left(C_i \mid X\right)>P\left(C_j \mid X\right)$ for $1 \leq j \leq m, j \neq i$             (2)

(b). Decision Tree: Creating decision trees for class-labeled training tuples is the method referred to as decision tree induction. A decision tree is a flowchart in a tree structure [23]. Every internal node in it represents a test for a certain characteristic, and every branch depicts the test’s result. A class label is known as a leaf node. The root node is the initial node at the tree’s top. Starting from the root node all the way downwards to the leaf node, where the class prediction of the tuple is stored, the attributes of the tuple are evaluated beside the decision tree to classify the tuple. In his publication, Ross Quinlan described the ID3 decision tree algorithm [24]. Later, in the study [25], Lou et al. unveiled ID3’s substitute, C4.5, to address a few drawbacks, such as over-fitting. C4.5 is competent enough to handle training data with missing values, characteristics with diverse prices, and both continuous and discrete characteristics, unlike ID3. Each training pair is placed at the root node at the start of a simple decision tree induction process. Next, the tuples are partitioned recursively according to predetermined attributes. An attribute selection approach that outlines a heuristic method for figuring out the splitting criteria is used to choose attributes. If all of the training tuples are used, all of the training tuples belong to the identical class, or there are no more attributes for partitioning, the algorithm stops. ID3 employs an attribute choice metric known as information gain, the difference between the information essential for tuple classification and the information essential after a split. These two may be articulated in the following way: Anticipated data required for categorizing a pair in a training set D (Eq. (3)):

Information Gain

$(D, A)=\operatorname{entropy}(D)-\sum\left(\frac{\left|D_i\right|}{|D|}\right) * \operatorname{entropy}\left(D_i\right)$                  (3)

where, pi represents the non-zero probability that a tuple in D belongs to class $C_i$.

Information needed after the split (Eq. (4)):

Information Needed

$(D, A)=\sum\left(\frac{\left|D_i\right|}{|D|}\right) * \operatorname{entropy}\left(D_i\right)$             (4)

where, A is the attribute on which the tuples are to be divided.

Then, information gain (Eq. (5)):

$\operatorname{gain}(A)=\inf (D)-i n f_A(D)$                   (5)

The attribute with the maximum information gain is elected as the splitting attribute.

(c). Random Forest: Random Forests, an ensemble approach applicable to classification and regression, consists of decision trees where each relies on an independently sampled vector, maintaining the same distribution across the entire forest [26]. The algorithm recurrently generates decision trees, creating a forest. Random attributes are selected at each node to assess the split [27]. Ho [28] presented the first random forest technique, which emphasized the idea of a random subspace. Later, Breiman [29] improved the method and called it Random Forests. A dataset D of d tuples is the first step in the random forests decision tree construction process. To construct k decision trees, a training set Di of d tuples is selected with replacement from D for each iteration, k. A subset of attributes is randomly chosen at each node for potential splits, aiding in constructing a decision tree classifier. Trees are developed using the CART methods and left unpruned after reaching full growth. CART, a non-parametric decision tree induction method, recursively selects rules based on variable values to identify the best split. The splitting process stops when further gain is unattainable or specific predetermined criteria are met [30].

(d). SVM, or support vector machine: In their work [31], introduced the idea of a support vector machine. SVMs have a lower propensity for overfitting and are quite accurate. SVMs are useful for both classification and numerical prediction. Using a nonlinear mapping, SVM raises the original data into a higher dimension [32]. Next, this new dimension looks for a linear optimum hyperplane that divides the tuples of one class from another. Tuples from two classes may always be separated by a hyperplane given a suitable mapping to a high enough dimension. The method locates this hyperplane using support vectors and margins that are determined by the support vectors. The algorithm’s support vector discoveries provide a compact explanation of the learned prediction model. One way to express a separating hyperplane is (Eq. (6)):

$W \cdot X+b=0$               (6)

where, W denotes a weight vector, n represents the quantity of attributes, denoted by a, and b as a scalar commonly referred to as a bias. If two attributes, A1 and A2, are provided as inputs, training tuples become 2-D.