Using Conditional Estimates to Simulate In-Play Outcomes in Limited Overs Cricket

This paper uses conditional probability distributions to simulate batsman outcomes—that is, runs and dismissals—while a limited overs cricket match is in play. The research was motivated by the potential to assess, and reassess, the likelihood of a batsman achieving a certain score within a specified interval. These likelihoods were conditional on the batsman type, a linear combination of batsman order, strike rate and contribution to team runs, and the delivery number, both discrete variables. A Visual Basic program, SimScore, was written to simulate batsman scores from the probability distributions pertaining to the match stages of interest. The scores were then adjusted for team strength, innings and venue effects, using multiple regression. The paper demonstrates the benefits of the model by fitting log-normal distributions to simulated innings (n=500) by Australia’s Ricky Ponting in the 2011 cricket World Cup quarter final. The distributions allowed us to approximate how likely he was to achieve a certain score prior to the match and at 10-, 20- and 30-over stages. It is anticipated that real-time information of a batsman's score expectations will add confidence to wagering in individual performance markets—such as “highest individual score”—as well as making possible in-play player rating revisions.