Modeling joint survival probabilities of runs scored and balls faced in limited overs cricket using copulas

Abstract

In limited overs cricket, the goal of a batsman is to score a maximum number of runs within a limited number of balls. Therefore, the number of runs scored and the number of balls faced are the two key statistics used to evaluate the performance of a batsman. In cricket, as the batsmen play as pairs, having longer partnerships is also key to building strong innings. Moreover, having a steady opening partnership is extremely important as a team aims to build such a stronger innings. In this study, we have shown a way to evaluate the performance of opening partnerships in Twenty20 (T20) cricket and the performance of individual batsmen in One Day International Cricket (ODI) by modeling the joint distribution of runs scored and balls faced using copula functions. The joint survival probabilities derived from this approach are then used to evaluate the batting performance of opening partnerships and individual batsmen for different stages of the innings. Results of the study have shown that cricket managers and team officials can use the proposed method in selecting appropriate partnership pairs and individual batsmen in an efficient manner for specific situations in the match.