Optimising cricket team selection for the Indian Premier League

Abstract

The sport of cricket represents a complex bat-and-ball game predominantly played by the Commonwealth nations. Cricket has long since transitioned from an exclusive pastime to a multi-billion-dollar industry. The global recognition of cricket primarily stems from highly competitive Twenty20 (T20) leagues, which require rivalling franchises to execute effective team selection for success. Traditional team selection methods often involve considerable subjectivity due to several internal and external factors. Although ample research has been conducted on utilising different optimisation techniques to improve the objectivity of team selection in T20 leagues, various shortcomings exist. These include limitations in multiple objectives and constraints, squad selection, and the differentiation between auction types. This study addresses these shortcomings by proposing a contemporary goal programming approach for optimising cricket team selection, using the 2022 Indian Premier League (IPL) mega auction as a case study. Applying a modified version of the scientific method as the research methodology, this study presents two solutions, formulated as non-preemptive and preemptive models. These solutions are developed, programmed, and solved using Elytica with the CPLEX optimisation solver. The proposed goal programming approach promotes team selection by balancing the trade-off between various conflicting and incommensurable cricketing abilities. The multifaceted nature of cricket allows players to specialise in unique cricketing abilities, such as bowling, batting, all-rounding, and wicketkeeping. This study extends existing research by presenting two new performance measures for batting and all-rounding. Utilising these statistics in conjunction with existing metrics for bowling and wicketkeeping gave performance scores for the 173 players considered for selection, which are scaled using Gaussian membership functions. The correctness of the formulation and coding for both models is verified by assessing the impact of each constraint on the results. The importance of each cricketing ability and the corresponding number of players required for selection are computed objectively using an I optimal crossed mixture design developed in Design-Expert. The non-preemptive goal programming model is validated by illustrating its effectiveness in selecting a team superior to the winning franchise of the 2022 IPL. The preemptive goal programming model is validated by illustrating its effectiveness in selecting a more specialised team relative to the non-preemptive model. This study contributes by presenting a unique, multipurpose approach to objective cricket team selection.