Study and Analysis of Duckworth Lewis Method

Designed for one-day cricket, this paper considers the use of the Duckworth-Lewis method as an approach to resetting targets in interrupted cricket matches. The Duckworth-Lewis table is reviewed and an alternative resource table is presented. A desideratum of a resource table is monotonicity in both the rows and columns corresponding to wickets and overs respectively. Consequently, a Gibbs sampling scheme related to isotonic regression is applied to the observed scoring rates to provide a nonparametric resource table. A discussion is provided concerning the use of the Duckworth-Lewis method applied to International Cricket matches. It is designed so that neither team benefits or suffers from the shortening of the game and so is totally fair to both. It is easy to apply, requiring 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 is 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 reflect the relative run scoring resources available to the two teams, that is overs and wickets in combination.