Accuracy and fairness of rain rules for interrupted one-day cricket matches

In this paper, we investigate the relative merits of rain rules for one-day cricket matches. We suggest that interrupted one-day matches present a missing data problem: the outcome of the complete match cannot be observed, and instead the outcome of the interrupted match, as determined at least in part by the rain rule in question, is observed. Viewing the outcome of the interrupted match as an imputation of the missing outcome of the complete match, standard characteristics to assess the performance of classification tests can be used to assess the performance of a rain rule. In particular, we consider the overall and conditional accuracy and the predictive value of a rain rule. We propose two requirements for a 'fair' rain rule, and show that a fair rain rule must satisfy an identity involving its conditional accuracies. Estimating the performance characteristics of various rain rules from a sample of complete one-day matches our results suggest that the Duckworth--Lewis method, currently adopted by the International Cricket Council, is essentially as accurate as and somewhat more fair than its best competitors. A rain rule based on the iso-probability principle also performs well but might benefit from re-calibration using a more representative data base.