The Duckworth-Lewis method (henceforth referred to as the D/L method) is a well-known method used for resetting targets, or deciding the outcome of rain-affected limited over Cricket games. Ever since the method was officially adopted by the International Cricket Council in 2001, the method has been dissected, analyzed and criticized by players, commentators, reporters and fans alike.
Briefly speaking, in the D/L method, both the balls remaining in the inning and the wickets in hand are viewed as “resources”. A table lists the resources percentages remaining for a given number of balls left and the wickets in hand. Using this percentage, the target is accordingly reset if the number of overs in the games is to be reduced, or the outcome of the game decided if the game ends because of the rain interuption.
As the title of the article suggests, we focus exclusively on those matches where the game ends early because of rain. At present, the D/L method is used to decide the outcome of the game only if both the teams have played at least 20 overs in a 50-over game (5 overs in a Twenty-20 game). If the score of the team batting second is greater than the par score, the team batting second wins, and if the score is below the par score then that team loses. The game is called a tie if the two scores are equal.
My main argument against the use of this method is that it uses an absolute, fixed par score to decide the outcome of the game. However, the D/L method is a statistical model, and like any other statistical model, it has a margin of error. If the game has not been played to completion, how can we be absolutely sure about the eventual outcome of the game based on a single score given by the D/L method?
Consider for example, the one day game between Pakistan and West Indies played on May 2, 2011 at Barbados. Pakistan batted first and scored 248 runs in 50 overs. Because of rain after the first innings, the target for West Indies was reset to 223 runs in 39 overs. However, the game was interrupted again near the end of the 30th over, at which point West Indies had scored 154 runs and still had 6 wickets in hand. The game ended right there, and West Indies was declared the winner, winning the game by 1(!) run.
This is indeed a very close victory margin for a game, whose result was decided by the D/L method. One can argue that the game was evenly poised at this stage, and so the most fair outcome of the game was a tie. However, because the ICC believes that the D/L method is a gold standard (it is clearly far from being one), therefore the right outcome of the match was West Indies as the winner. There is a good chance that 1 run is within the error margin of the D/L model, and so the game should have been ruled a tie. Consider this: if this was a league match of the World Cup, then West Indies would have been awarded 2 valuable points and Pakistan 0 – which could eventually decide which team reaches the knock-out stage. That a statistical model like D/L should lead to a quantum difference of 1 point awarded to the teams, is grossly unfair.
A better way of deciding the outcome of the rain-terminated matches would be to declare the match a tie if the difference between the second inning score and the D/L par score is not significant. A good margin for the 50 over game will be, say 10 runs. If the difference is more than 10 runs, then there is a good chance that the team ahead at this stage of the game would have eventually won the game. Otherwise the game is too close to call in favor of one team over the other.
Yet another bold proposal that I put forward for deciding the outcome of games in such situations is to use the win probability. If the win probability of the batting team when the game ended is, say, between 0.25 and 0.75, then the game is a tie. If it is less than 0.25, then the batting team loses, and if it is more than 0.75, the batting team wins. In the above example, the win probability of West Indies at the time the match was called off was 0.68, therefore according to our method the outcome will be a tie. In fact, one can extrapolate the method for awarding points in rain-terminated matches in the league stage of a tournament. If this was, for example, a league match in the world cup, then West Indies would be awarded 1.36 points (twice the win probability), whereas Pakistan would be awarded 0.64 points, instead of splitting the points 1-1 to the two teams. In the end, this may not make a difference in which team eventually gets to the knock-out stage. However, it will be a more fair way of deciding the outcome of rain-terminated limited over games.
Very good idea, Shashi. If the margin (m) is less than some pre-determined number-of-runs (s), then the match could be called a tie. However, consider a case where s=10, and it was found that the chasing team was 9 runs behind the par score (m=9). In this case, I am not sure whether it will be right to declare the match as a tie. Because of the same argument .. there might be some “error” in the calculation. Well, I agree that a team loses maximum one point (assuming a 2-1-0 point system) because of the “error”, as opposed to two points in the existing system. Determining the value of “s” will be a tough challenge, though.
It makes complete sense, now that i think about it, it is actually quite silly to use D/L method down to one run go no go threshold.
Agree with maunendra too about the potential difficulty in finding a good ‘s’. Also, just to be evil (:D), would s be different at different points of game suspension? a wider window of chance in the beginning and a narrower window at the end
Maunendra and Sandeep, both of you make very good points. The cutoff margin for the uncertainty interval itself might look quite arbitrary – but the point is that this will be less so than deciding the outcome based on a single D/L score. And as Sandeep suggested, this margin can be different at different stages of the second inning. Even now, the D/L method is not employed to decide the outcome unless 20 overs have been played in the second innings – which means that there is a greater uncertainty margin in the D/L model in the first 20 overs of the second innings.
If we want to do away with any absolute scores/margins totally, then we can simply employ the idea of using the win probability, as suggested above. This will be especially useful in awarding points in the league matches of a tournament (such as the IPL or the World Cup, for example).
Dude, I totally agree with you on D/L method is an unfair way of deciding par score at any moment of the game. I totally agree with you on splitting the points as you did. I think that is a masterstroke. But I don’t totally agree with win probability being a good method of predicting games. You know that it failed once in a extreme scenario. Also, what if the match is at earlier stages of 2nd innings when batting team is getting in tempo and out of probability range. e.g. Pakistan’s inning in first 15 overs of India-Pak ’96 QF. Pakistan would be way ahead of winning the match at that moment. And it is not one off case, there are many instances from the past where a team fielding second have pulled off a match after say 15-20 overs. So, I don’t see even your method of predicting results as too good a method. But it certainly looks more good to a layman. It makes more sense than D/L.
Tanmay, I agree with your concerns regarding the use of win probability for deciding the outcome of rain terminated games. The win probability we have right now for the one-day games has a bigger error margin than what we would like to have (it is much better for the 20 over format). But that was also the reason which made me skeptical about the D/L method, as it is also a statistical model that uses past data to decide the outcome of games.
The D/L method is not applied to decide the outcome unless 20 overs have been played, and any other statistical model will probably have the same restriction as well. I think after 20 overs, the predictions become more accurate. Even the India-Pakistan match you talk about, the game had swung in India’s favor by the 20 over mark, and was probably evenly balanced at that stage. I do believe that using win probability is a better idea. The challenge is to come up with the right win probability numbers (and we continue to work on that!)
Nice analysis Shashi. Both of your suggestions; having some margin in D/L score and using win probability to declare the outcome, will definitely improve the current method. Though I think extrapolating the win probability in awarding points will not be useful in most of the cases. For e.g in a world cup, there is very less probability of D/L affected matches. A team having 1.36 points will be equivalent to having 2 points and similarly a team having 0.64 points will be equivalent to having 0.
I guess in 90’s, both teams had to play atleast 25 overs to apply the D/L method and later they changed the limit to 20 overs.
“For e.g in a world cup, there is very less probability of D/L affected matches. A team having 1.36 points will be equivalent to having 2 points and similarly a team having 0.64 points will be equivalent to having 0.”
I disagree with your premise. If you check out the 1992 World Cup matches, then there were 7 of them where the targets had to be revised because of rain, including the farcical semi-final match between South Africa and England (at that time a different rule was used for revising targets). And the league stage of this world cup was fairly close, Pakistan edged out Australia by just 1 point. There were two such matches where one of these two teams were involved, and a couple more which had the teams eventually reaching the semi-final stage.
And to think that the next World Cup is again in Australia ….
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