Cricket’s Duckworth-Lewis formula
The Duckworth-Lewis Formula (DLF) is the latest of several methods used by the ICC to determine the results of limited-overs matches that are truncated by weather or other factors. The DLF has been in use for a considerably long period, because it has proved to be more acceptable than the methods used earlier.
The essential principle underlying the DL formula is that a team in a limited-overs match has two resources it uses up in chasing down a target or setting. These two resources are the wickets (10 at the start of the innings) and the overs remaining for it to bat. How much it can make in the remaining part of any innings depends on how many overs are left and how many wickets are in hand.
This fits in well with cricketing common sense. For instance if a team has to chase 250 to win off 50 overs in an ODI situation and has been 100 for no loss after 22 overs, it’s run rate at that stage would be less than the required rate, but few cricket viewers would bet against its winning. On the other hand, if it was 100 for six after 15 overs, it would be well ahead of the asking rate, but a few would back it to go on to win.
But merely enunciating the principle does not help us get to precise numbers that can decide who the winner should be in truncated matches. That’s where mathematicians like Duckworth and Lewis enter the picture. They analysed data from thousands of limited overs matches to derive a mathematical relationship between the overs and wickets left and the number of runs that were likely to be scored in the remaining part of the innings, had circumstances not intervened to prevent the completion of the innings.
Two IPL Twenty20 matches so far had been decided by relying on the Duckworth-Lewis Formula.
It is this mathematical relationship that gave us on Saturday that Mohali’s 94/3 after 8 overs meant victory for Yuvraj’s men over the Delhi Daredevils, who had scored 118/4 in 11 overs. Though Delhi had scored only 118, Mohali was set 123 to win of 11 overs, the same number as Delhi had batted. That’s because DL Formula adjusts for the fact that while Mohali knew before their innings began that they would have to bat only 11 overs, Delhi had batted a little more than 8 overs under the impression that they would actually get 20 overs to bat. Thus if Mohali had been asked to make 119 to win off 11 overs, they would have been given an undue advantage since they could squander wickets more easily in the chase for a higher run rate.
Jayawardene’s six off the last ball of the match was also the winning stroke. Had that ball been a dot ball, it would have been a tie between the two teams as 89 was the par score Mohali had to achieve to tie the match with seven wickets in hand at that stage. Had a wicket fallen off the last ball, Mohali would have lost, even if it had been 90/4 through a run-out.
Similarly, in the Chennai-Kolkata match, the fact that the Super Kings were 55/0 after 8 overs chasing 150 to win off 20 gave them a three-run victory under the DL Formula. But things would have been very different if Dinda had not spilled the skier from Parthiv Patel just two balls before the weather forced a close. The par score of 52 after 8 overs was provided because Chennai had not lost any wickets. Had they lost one, 55 would have been too little.
As these two examples show, it is not just the number of runs scored by the team chasing that matters in deciding the winner under the DL Formula, but also how many wickets have been lost. That leaves teams chasing in uncertain weather with a bit of a dilemma. Not knowing quite when the match will end, they have to keep up with the par score after each over while being careful not to lose wickets in the attempt to do so.