Thoughts on Duckworth-Lewis, and some interesting papers
I was reading the original 1998 paper of Duckworth and Lewis last week. They came up with a brilliant concept, and avoided so many of the pitfalls that plagued earlier systems. It’s somewhat unfair to consider it merely as a system to reset the target in case of rain. It’s really a better way of thinking about the whole game of limited-overs cricket, using the notion of resources. Indeed, the concepts can be applied to arguably better measures of player performance, as Lewis did here and here.
That said, if there’s a chink in its armor, I think its the fact that (under the original model) the team batting second is expected to consume resources in the same manner that the team batting first did. And the pattern of resource consumption is determined by data from thousands of first innings. I think I can sum up my thoughts in the following two sentences.
- The first team’s optimal strategy will be one that maximizes the expected value of their score.
- The second team’s optimal strategy while batting will instead be one that maximizes the probability their score exceeds that of the first team.
And can lead to fairly different strategies. This difference is because the margin of victory or defeat is (usually) irrelevant. Only the actual outcome matters. In particular, if a team is chasing a very high target, their best approach may be to hit out from the beginning and hope to get lucky, because trying to maximize their expected total will probably lead to a losing score. At least by hitting out, they give themselves a small chance at victory, even though they could face a huge defeat if the strategy backfires. If you read their 2004 paper, Duckworth and Lewis did indeed address the fact that the resource consumption pattern should be different if the team batting second is chasing a high target, and came up with an even better model to account for this scenario. I believe those revisions created the model that is used today – is that correct? I’m still working my way through that paper. Once I finish that paper, I’ll see how it addresses my concerns.
