Elsevier

Applied Soft Computing

Volume 13, Issue 1, January 2013, Pages 402-414
Applied Soft Computing

Multi-objective optimization and decision making approaches to cricket team selection

https://doi.org/10.1016/j.asoc.2012.07.031Get rights and content

Abstract

Selection of players for a sports team within a finite budget is a complex task which can be viewed as a constrained multi-objective optimization and a multiple criteria decision making problem. The task is specially challenging for the game of cricket where a team requires players who are efficient in multiple roles. In the formation of a good and successful cricket team, batting strength and bowling strength of a team are major factors affecting its performance and an optimum trade-off needs to be reached. We propose a novel gene representation scheme and a multi-objective approach using the NSGA-II algorithm to optimize the overall batting and bowling strength of a team with 11 players as variables. Fielding performance and a number of other cricketing criteria are also used in the optimization and decision-making process. Using the information from the trade-off front obtained, a multi-criteria decision making approach is then proposed for the final selection of team. Case studies using a set of players auctioned in Indian Premier League (IPL) 4th edition are illustrated and players’ current statistical data is used to define performance indicators. The proposed computational techniques are ready to be extended according to individualistic preferences of different franchises and league managers in order to form a preferred team within the budget constraints. It is also shown how such an analysis can help in dynamic auction environments, like selecting a team under player-by-player auction. The methodology is generic and can be easily extended to other sports like American football, baseball and other league games.

Highlights

► Based on statistics of performance of players in different aspects of the game of cricket, a bi-objective optimization problem is formulated. ► An evolutionary multi-objective optimization (EMO) method (NSGA-II) is employed to find multiple trade-off teams of 11 players. ► An analysis of trade-off teams has identified 29 key players from a set of 129 players considered in the study. ► A number of obtained trade-off teams have better scores than the winning Indian Premier League (IPL) team of 2011, thereby indicating the potential importance of this study. ► Finally, an auction-based bi-objective optimization method is suggested to form a competitive team following the IPL rules. ► Methods of this study can be extended to other games to construct a winning team and also to identify key players to choose in an auction-oriented team selection process.

Introduction

Formation of a good team for any sport is vital to its eventual success. Team selection in most sports is a subjective issue involving commonly accepted notions to form a good team. Application of objective methods for team selection is a relatively new phenomenon and the effect seems more pronounced after the involvement of various competitive leagues involving large budgets to buy players. In this study, we have chosen the game of cricket for which different performance measures for choosing players have been suggested [10], [3], [13], [14]. Cricket is a bat-and-ball game played between two teams of 11 players where one team bats, trying to score as many runs as possible, while the other team bowls and fields, trying to dismiss the batsmen one at a time and thus limiting the runs scored by the batting team [1]. Batting and bowling performance of a team are the major criteria affecting its success along with many other objective and subjective factors like fielding performance, captaincy (the ability of a captain to choose the right bowler and field placement according to the situation), home advantage etc. [11], [12]. Optimization studies have been done in many sports in the past [18], [9] and also has been done in various issues in the game of cricket [17]. Just as in most league competitions, a pool of players is available along with their performance statistics. Each player is paid a certain amount of money by the team owners for playing for their team, which we refer to as player's cost. League organizers impose an upper limit on budget for each franchise/club to avoid giving undue advantage to rich franchises. Player cost is either fixed by organizers, decided through auction or determined by some contract.

Twenty20 (T20) is the latest innovation in the game and is even shorter version than One Day International cricket. The total duration of the T20 game is about 3 h, and each team gets to play a maximum of 20 overs. We have considered Twenty20 cricket game and the Indian Premier League (IPL) as a test case for our analysis. IPL is a professional league for Twenty20 cricket competition in India and is gaining a lot of popularity [23], [16]. As of now, only a few recent studies have explored team formation in this format since the concept of IPL and other such competitions are relatively new. Lemmer [13] analyzes the performance of players for the first T20 World cup series. Lourens [14] identifies three main categories of the game (batting, bowling, and fielding) and devises a number of performance criteria for evaluating players for each category of the game. Thereafter, a linear programming model is constructed and solved to build a team of 15 players (11 plus four reserve players) for the South African domestic Pro20 cricket team by maximizing a single objective calculated by adding the performance value of each player in the team. Another study [24] uses more sophisticated statistical performance measures and also employs a single-objective linear programming approach to construct a fantasy league team. These are nice studies in which some earlier efforts were also discussed and compared. However, one aspect clearly mentioned by these authors is that all three categories of the game involve multiple performance measures and often they are in conflict to each other. For example, a batsman may have an excellent record in terms of ‘batting average’ (average runs scored by the player in past games), but may have a poor ‘strike rate’ (rate at which the player scores runs), trading-off the performance of the player in the batting category of the game. They are in conflict, since a slow but steady player will have a better batting average, but a poor strike rate. Ideally, the game requires a batsman with both qualities, but an important question then remains: ‘What performance criterion should one use to select a batsman in the team?’ Such questions become even difficult to answer in choosing a batsman over a bowler or a batsman over a fielder. Although these past studies either choose one criterion for each category or use a priori preference of one criterion over other, the studies make one aspect amply clear: a decision-making task in choosing players is truly multi-objective in nature and a priori consideration of performance measures may result in a team that may not be agreeable to all. In [20], 35 all-rounders (who can bat, bowl and field well) are classified based on ‘strike rate’ (a batting aspect) and ‘economy rate’ (a bowling aspect) into four non-overlapping classes – performer, batting all-rounder, bowling all-rounder, and under-performer. Although no optimization study is performed, a Bayesian approach is used for the classification purpose. The key aspect of this study is the use of two conflicting criteria for classifying all-rounder players and the use of recent statistical techniques in ranking players. Above-mentioned studies make one aspect clear: players can be evaluated from their past performance data using well-established statistical and machine learning procedures for them to be included in a future team and multiple criteria must be considered to analyze the data for the purpose of constructing a team for optimal performance.

Interestingly, such a data-mining procedure can be generically applicable to different games for which players’ past performance data is available. For example, in the soccer league matches, players can be chosen for their positions as goal-keeper, fullbacks, midfielders, and forwards depending on their past recorded performances in different positions. A team can be constructed from such information for two conflicting team performances – goals scored versus goals conceded.

In Indian Premier League (IPL) of Twenty20 cricket, the franchise have the task of building a winning team within the budget cap, restricted by the IPL board. Individual players are bought by the franchises during a public auction of the players. Since the total number of players in the market pool is large, the challenge of finding a high-performing team becomes an increasingly complicated procedure. Data used for this work (downloaded from the public domain sources) has a pool of 129 players from IPL 4th edition and is tabulated elsewhere [2]. The player costs are the IPL 4th edition auction prices for respective players. We have used other performance statistics of each player from the public domain sources on the International Twenty20 version of the game.

With so many players available for choosing a team, the need for an effective optimization technique can be justified by making a rough calculation of the apparent size of the decision space. From the given data of only 129 players from IPL 4th edition auction, containing 10 captains and 15 wicket-keepers, the total number of possible teams under the constraints of at least one wicket-keeper and one captain are included in each team can be calculated as follows:total number of teams=1011511279.Considering the large number of different possible team combinations (to the order of 1015), finding optimal teams under the added constraint of budget is not a trivial task. Currently most of the team selections are done using different heuristics, past experiences, or at most using some crude methodologies. For example, one strategy is to choose two or three high performance batsmen or bowlers and the remaining team slots are filled according to budget constraints. But, this approach may not always give an optimal or a near-optimal solution, since matches are won by a team effort and not by having one or two star players in the team. Hence, our aim in this paper is to investigate the formation of an overall team that is optimal or near-optimal from the point of multiple criteria. Since batting and bowling performances of a team are generally considered to be conflicting to each other, we use these two criteria in our optimization study, while all other objective and subjective criteria, such as fielding performance, captaincy, wicket-keeper's performance, brand value of a team and others, are used during the subsequent decision making phase. It is difficult to argue whether a batting-dominant team is better or a bowling-dominant team is better. This is an unavoidable dilemma that the team selectors face while forming a team. Due to our consideration of both bowling and batting performances in forming a team, we attempt to find a number of high-performing teams having a good trade-off between these two main objectives. Thereafter, we argue and demonstrate that a consideration of a number of other criteria applied on the obtained high-performing teams makes it convenient for the team managers to identify a preferred team of their choice.

In this paper, we have explored the problem of building a high-performing team out of a set of players given their past performance statistics and suggested, for the first time, a computational and decision-making methodology from the perspective of a multi-objective consideration. A novel representation scheme of a team of 11 players is suggested to handle different constraints associated with the team selection problem. The elitist evolutionary multi-objective optimization algorithm (NSGA-II [6]) is extended to find multiple high-performing teams. A number of realistic decision-making considerations are then used to pick a suitable team.

In the remainder of this paper, we describe the optimization problem corresponding to the cricket team selection problem in Section 2. A novel scheme to represent a 11-player team that automatically satisfies a number of constraints is described next. The computing procedures of different objective functions are then discussed. Section 3 presents the results obtained through our multi-objective optimization study. Our obtained high-performing teams are compared against the IPL 4th edition winning team. The (theoretical) superiority of our teams is clear from the figure. The obtained solutions are analyzed for their sensitivity to the overall allowable budget and interesting conclusions are made. Section 4 then suggests a number of decision making techniques to choose a single preferred team from the set of trade-off teams. This includes the standard knee-point approach, a dynamic approach simulating the real auction procedure, and a couple of other interesting criteria. A multi-objective optimization study to find a set of teams providing a trade-off between batting and bowling performances and then a multi-criterion decision making analysis procedure to finally pick a preferred team remain as a hallmark feature of this study. The procedure is ready to be applied in practice with a minimal fine-tuning needed to suit various other rules of the IPL team selection process. Conclusions of this study are made in Section 5.

Section snippets

Proposed methodology

In the game of cricket, player statistics have multiple parameters, like number of matches played, total runs made, batting strike rate, number of wickets taken by a bowler, number of overs bowled, etc. Importantly and interestingly, the values of these parameters for most active players are available. However, it is important to first identify the statistical parameters that reliably indicate a player's performance. The overall aim of a franchise is to build a team of 11 players with optimum

Multi-objective optimization results

Here we present the simulation results of the above-mentioned algorithm applied to the player database. The budget constraint is considered to have TotalBudget=6 million dollars. At least one wicket-keeper, one captain, and a maximum of four foreign players must be included in a team, as mentioned before. We use the following standard parameter settings in all our simulations: population size = 400, maximum generations = 400, crossover probability = 0.9, mutation probability = 0.05, SBX distribution

Team selection as a decision making process

The objective of the entire process is to obtain a high-performing single team of 11 players, rather than just finding and suggesting a number of trade-off teams. Having identified a set of high-performing trade-off teams with different bowling, batting and fielding performance values, we shall now discuss a few pragmatic methodologies in choosing a particular team. Toward this goal, we use certain multi-criteria decision making (MCDM) methods [15] combined with certain subjective

Conclusions

We have proposed and used for the first time emergent computing methodologies for an objective evaluation of cricket team selection using a multi-objective genetic algorithm and multiple criteria decision making aids. Such problems usually must consider a number of objective and subjective criteria that all must be paid attention to. In this paper, we have suggested choosing a couple of main functional criteria – batting and bowling performances – during the initial multi-objective optimization

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