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On the distribution of runs scored and batting strategy in test cricket
Author(s) -
Scarf Philip,
Shi Xin,
Akhtar Sohail
Publication year - 2011
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/j.1467-985x.2010.00672.x
Subject(s) - outcome (game theory) , statistics , position (finance) , covariate , binomial distribution , cricket , parametric statistics , mathematics , point (geometry) , econometrics , economics , mathematical economics , ecology , geometry , finance , biology
Summary. 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.