A fair method for resetting the target in interrupted one-day cricket matches
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Statistical Consultant, Stinchcombe, Glos. and 2 Univeristy of the West of England, UK
A method is described for setting revised target scores for the team batting second when a limited-overs cricket match has been forcibly shortened after it has commenced. It is designed so that neither team bene®ts or suffers from the shortening of the game and so is totally fair to both. It is easy to apply, requring nothing more than a single table of numbers and a pocket calculator, and is capable of dealing with any number of interruptions at any stage of either or both innings. The method is based on a simple model involving a two-factor relationship giving the number of runs which can be scored on average in the remainder of an innings as a function of the number of overs remaining and the number of wickets fallen. It is shown how the relationship enables the target score in an interrupted match to be recalculated to re¯ect the relative run scoring resources available to the two teams, that is overs and wickets in combination. The method was used in several international and domestic one-day competitions and tournaments in 1997. Keywords: sports; modelling; practice of OR; cricket
Introduction and background The use of mathematical modelling in sport in general and cricket in particular has been growing in recent years. OR techniques have been used in scheduling cricket ®xtures.1±5 In the game of limited overs cricket, Clarke6 and Johnston et al7 have used dynamic programming, the former to assist in determining optimal scoring rate strategies and the latter in assessing comparative player performances particularly between batting and bowling. In his paper Clarke6 suggests that his methodology could be used to assist in setting a fair target in rain interrupted one-day matches but his ideas have not been taken up. It is this problem which is the topic of this paper. In `®rst-class' cricket each side has two innings, each with ten wickets to lose and with no limit on the number of overs that can be bowled. As the time scheduled for the match often expires before the game has ®nished the most common result is a draw. It was as a natural response to this intrinsic weakness of the ®rst-class game that limited overs, or `one-day', cricket evolved in the 1960s. In this game, each side has only one innings with a limited number of overs in which to bat, generally either 40, 50 or 60 according to the rules of the competition. As the game is played out to a ®nish in a single day and often yields exciting ®nishes, it has proved very popular with the spectators and there can be little doubt that it is here to stay. But one-day cricket has a major problem. It is intolerant of interruptions due to the weather. In ®rst class cricket a Correspondence: AJ Lewis, Faculty of Computer Studies and Mathematics, University of the West of England, Bristol, BS16 1QY, UK.
stoppage because of rain or bad light is a natural, though generally unwelcome, part of the game. A one-day match, however, is intended to be ®nished in a single day and the
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