On the distribution of runs scored and batting strategy in test cricket

Negative binomial distributions are fitted to partnership scores and innings scores in test cricket. For partnership scores, we use a parametric model that allows us to consider run rate as a covariate in the distribution of runs scored and hence to use run rate as a surrogate for batting strategy. Then we describe the implied influence of run rate on match outcome probabilities given the state of the match at some point during the third innings; we refer to such a point in the match as the current position. Match outcome probabilities are calculated by using a model for the outcome given the end of the third-innings position, and a model for transitions from the current position to the end of the third-innings position, with transition probabilities considered as a function of run rate. Although the run rate is not wholly in the control of the batting side, our approach at least allows a captain or team analyst to consider the match outcome probability if the team can bat towards a target at a particular run rate. This will then at least indicate whether an aggressive or defensive batting strategy is desirable.