Better than Duckworth-Lewis

From Ram Srinivasan, United States of America
With cricket being played throughout the calendar year, weather interruptions are inevitable. In addition, matches are routinely disrupted because of crowd trouble. Since its introduction in 1997, the Duckworth-Lewis (DL) method has been successfully used in more than 200 one-day matches to deal with interruptions. The DL method has almost always set targets that align with our intuition and qualitative understanding of the game and this has been its greatest strength.

In an accompanying technical paper, published in the Journal of the Operations Research Society, Dr. Duckworth and Dr. Lewis provide an excellent mathematical development of their rain rule. They identify two resources that a batting team has at its disposal - (1) number of overs available, and (2) wickets in hand to play out these overs. At the heart of the method is a function that determines the number of runs that a batting team will score in a given number of overs given the number of wickets at its disposal. They determine the form of the function using data from completed matches. Once the form of the function is decided, using it to adjust targets is standard and different rain rules primarily differ in the form of the function.

Let us ponder for a moment. Are we really doing the best by simply noting down the number of wickets and overs left in quantifying the batting team's resources? We haven't really accounted for the quality of the wickets and the quality of the bowlers who are going to bowl the overs. Less runs are likely to be scored when great bowlers like Shane Warne and Glen McGrath bowl the overs than when good bowlers like Ian Blackwell and Liam Plunkett bowl them. In a similar vein, more runs are likely to be scored when we have a Ricky Ponting and Matt Hayden at the crease.

Thus, a sure way of improving the D/L method is to incorporate the current form of the batsmen and bowlers into determining the number of runs that will be scored. While the above argument seems reasonable, we seem to have walked into the realm of subjectivity and personal tastes. How do we determine whether Sachin Tendulkar is better than Owais Shah, and if that is the case, how many more runs is he likely to score? Thankfully, there is already a system in place to compare player and quantify their current form.

The official LG ICC player rankings use a sophisticated algorithm to capture the current form of players by assigning bowling and batting points between 0 and 1000. The points reflect not just the number of runs scored and wickets taken but also the circumstances, manner and the team against which they were secured. Sophisticated heuristics can now be developed to integrate the rating system with the DL method to determine the exact manner in which the bowling points and batting points are to be incorporated into the DL method.

For example, the actual number of overs and wickets available may be scaled depending on the scores of the batsmen and the bowler bowling the overs. The effective resources can then be used in the DL method. From an implementation perspective, the entire procedure can be worked out through software, thereby minimizing human intervention and any consequent errors. The only infrastructure that is required is a computer that can connect through the internet to the LGG ICC database to download the latest player points.