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O.R. Inside One-day Cricket

When a limited overs cricket match is interrupted by rain or bad light, there may be insufficient time for both teams to complete their full allocation of overs. It is, therefore, necessary to calculate a fair target for the team batting second taking into account the number of overs that they will face.

Until 1997 there was a hotchpotch of various methods in use, none of which gained universal approval and most methods were satisfactory in only a limited set of circumstances. For example, it was common simply to divide the number of runs scored by the team batting first by the number of overs they had completed and then multiplying this 'run rate' by the new reduced number of overs available to the team batting second. Clearly, this took no account of the finer points of the limited overs game - for example, the fact that the 'run rate' varies considerably throughout the duration of an innings because, say, teams with six wickets still standing with ten overs to bat will take risks to score quick runs. Some simplistic target setting led to several infamous disasters where the required demand on the team batting second was very obviously unfair.

The cricketing world, from the international level through domestic to many lower levels, uses the Duckworth/Lewis method of resetting the target in interrupted one-day cricket matches. Starting with the match between Zimbabwe and England on New Year's Day 1997, the Duckworth/Lewis method has gradually been introduced into the game as the method's flexibility, reliability and relative simplicity have become accepted so that it has been adopted as the International standard 'rain-rule'.

Although in application it requires nothing more than a single page table of percentages and a pocket calculator, there is much O.R. inside the Duckworth/Lewis method. The derivation of that table of percentages has used mathematical models of the relationship between average runs scored and overs left and also, as a major innovation, the relationship to the number of wickets that have been lost when a stoppage occurs. Actual match data were used to calibrate the model so that in use the D/L method, as it has come to be called, is generally perceived by players as by far the fairest method devised for target resetting.

Thanks to O.R., what was a major problem in one-day cricket since the limited overs game's inception in the 1960s has now been solved.

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