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A Bayesian Approach to Inferring the Contribution of Unobserved Ground Conditions to Observed Scores in Sports: The Example of Cricket
Mathematics and Computer Sciences Journal (MCSJ), Volume 2, Sep 2017

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This paper is part of a wider research programme using a dynamic-programming approach to modelling the choices about the amount of risk to take by teams and players in International Cricket. An important confounding variable in this analysis is the ground conditions (size and shape of stadium, condition of playing surface and weather conditions) that affect the trade off between risk and return that teams and players face. This variable does not exist in our historical data set and would in any event be very difficult to accurately observe on the day of a match. In this paper, we consider a way of estimating a distribution for the ground conditions using only the information contained in the scores and result of the match. In our approach we use the difference between the cumulative density function of scores and a probit estimate of the probability of each score being a winning score in order to infer the extent to which high scores on average reflect easy conditions rather than good performance. Using a Monte Carlo method we estimate the percentage of the variation in total scores that is due to the variation in conditions and we subsequently use Bayes Law to estimate a distribution of conditions for each match. We develop our method using the example of cricket and we outline some potential applications of the method to other sporting contests.

Author(s): Scott R. Brooker, Seamus Hogan
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