Optimal strategies in one-day cricket

Using a dynamic programming formulation, an analysis is presented of both the first and second innings of a one-day cricket match assuming variation in type of ball bowled and subsequent selection of a strategy by the batsman. We assume that the team batting first uses the strategy to maximize the expected score, and the team batting second uses the strategy to maximize the probability of outscoring the first team and thus of maximizing the probability of a win. The dynamic programming formulation allows a calculation, at any stage of the innings, of the optimal scoring strategy depending on the type of ball bowled, along with an estimate of the maximum of the expected number of runs scored in the remainder of the first innings, and the maximum probability of a win in the second innings. Modifications are then introduced to examine the effect of tailender batsmen and a ‘fifth bowler’. Finally a simulation is done to estimate the variance in total score by following the optimal strategy used in the first innings.