Optimising Batting Partnership Strategy in the First Innings of a Limited Overs Cricket Match
Authors:   , Brown Patrick 
Published: November 2021

<p>In cricket, the better an individual batsman or batting partnership performs, the more likely the team is to win. Quantifying batting performance is therefore fundamental to help with in-game decisions, to optimise team performance and maximise chances of winning. Several within-game metrics exist to summarise individual batting performances in cricket. However, these metrics summarise individual performance and do not account for partnership performance. An expectation of how likely a batting partnership is to survive each ball within an innings can enable more effective partnership strategies to optimise a team’s final total.  The primary objective of this research was to optimise batting partnership strategy by formulating several predictive models to calculate the probability of a batting partnership being dismissed in the first innings of a limited overs cricket match. The narrowed focus also reduced confounding factors, such as match state. More importantly, the results are of practical significance and provide new insight into how an innings evolves.  The model structures were expected to reveal strategies for optimally setting a total score for the opposition to chase. In the first innings of a limited overs cricket match, there is little information available at the commencement and during the innings to guide the team in accumulating a winning total score.  The secondary objective of this research was to validate the final models to ensure they were appropriately estimating the ball-by-ball survival probabilities of each batsman, in order to determine the most effective partnership combinations. The research hypothesised that the more effective a batting partnership is at occupying the crease, the more runs they will score at an appropriate rate and the more likely the team is to win the match, by setting a defendable total.  Data were split into subsets based on the batting position or wicket. Cox proportional hazard models and ridge regression techniques were implemented to consider the potential effect of eight batting partnership performance predictor variables on the ball-by-ball probability of a batting partnership facing the next ball without being dismissed. The Area Under the Curve (AUC) was implemented as a performance measure used to rank the batting partnerships.  Based on One-Day International (ODI) games played between 26th December 2013 and 14th February 2016, the model for opening batting partnerships ranked Pakistani’s A Ali and S Aslam as the optimal opening batting partnership. This method of calculating batting partnership rankings is also positively correlated with typical measures of success: average runs scored, proportion of team runs scored and winning. These findings support the research hypothesis. South African’s, HM Amla and AB de Villiers are ranked as the optimal partnership at wicket two. As at 28th February 2016, these batsmen were rated 6th equal and 2nd in the world respectively. More importantly, these results show that this pair enable South Africa to maximise South Africa’s chances of winning, by setting a total in an optimal manner.  New Zealand captain, Kane Williamson, is suggested as the optimal batsman to bat in position three regardless of which opener is dismissed. Reviewing New Zealand’s loss against Australia on 4th December 2016, indicates a suboptimal order was used with JDS Neesham and BJ Watling batting at four and five respectively. Given the circumstances, C Munro and C de Grandhomme were quantified as a more optimal order.  The results indicate that for opening batsmen, better team results are obtained when consecutive dot balls are minimised. For top order and middle order batsmen, this criteria is relaxed with the emphasis on their contribution to the team. Additionally, for middle order batsmen, minimising the occasions where 2 runs or less are scored within 4 deliveries is important.  In order to validate the final models, each one was applied to the corresponding Indian Premier League (IPL) 2016 data. These models were used to generate survival probabilities for IPL batting partnerships. The probabilities were then plotted against survival probabilities for ODI batting partnerships at the same wicket. The AUC was calculated as a metric to determine which models generated survival probabilities characterising the largest difference between IPL partnerships and ODI partnerships. All models were validated by successfully demonstrating the ability of these models to distinguish between higher survival probabilities for ODI partnerships compared with IPL partnerships at the same wicket.  This research has successfully determined ball-by-ball survival probabilities for individual batsmen and batting partnerships in limited overs cricket games. Additionally, the work has provided a rigorous quantitative framework for optimising team performance.</p>