The statistician Frank Duckworth has launched a robust defence of the eponymous formula that he devised, in partnership with Tony Lewis, to recalculate run-chases in rain-affected one-day games, and believes that the current criticism of his calculations stems entirely from Paul Collingwood's frustrations, following England's failure to beat West Indies in their opening contest of the World Twenty20 in Guyana.
The Duckworth-Lewis system was devised in the 1990s and formally adopted by the ICC in 2001, and is widely regarded as the fairest means of resolving rain-shortened contests in 50-over cricket, even if the workings of the formula are a mystery to all but the most mathematically gifted. However, for the second time in consecutive World Twenty20 contests against West Indies, Collingwood was left feeling aggrieved following defeats that he believed might not have occurred had the matches been played out over their full distance.
At The Oval in June 2009, West Indies progressed to the semi-finals by chasing 80 in nine overs after England had posted an imposing 161 for 6, while Monday's discrepancy seemed even more stark - England made 191 for 5, but West Indies were left needing 60 in six overs, thanks to an early onslaught from their captain, Chris Gayle, who admitted he had chosen to bat second in the contest precisely because he anticipated D/L would be a factor.
"There's a major problem with Duckworth-Lewis in this form of the game," Collingwood told reporters after the match. "I've got no problem with it in one-dayers ... but it's certainly got to be revised in this form. Ninety-five percent of the time when you get 191 runs on the board you are going to win the game. Unfortunately Duckworth-Lewis seems to have other ideas and brings the equation completely the other way and makes it very difficult."
However, when asked if he accepted that a recalibration was required to reflect the higher tempo of Twenty20 cricket, Duckworth was emphatic in his rebuttal.
"No I don't, quite frankly," he told Cricinfo's Switch Hit podcast. "Remember that there have been a total of about 70 matches decided by Duckworth-Lewis since Twenty20 was invented in 2002, and there's only been two instances where any dissent has been expressed, and both of those were by Paul Collingwood and the England team, as a result of failing to win against West Indies.
"That revised target of 60 from six overs was set because, before the rain interruption, West Indies had faced 14 balls and scored a massive 30 runs without losing any wickets," Duckworth added. "They were 11 runs ahead of the D/L par, and if the match hadn't been able to restart, and if for the sake of argument you allowed a match to be valid with only 2.2 overs bowled, then West Indies would have won by 11 runs. They were winning easily when the rain came."
"Remember that there have been a total of about 70 matches decided by Duckworth-Lewis since Twenty20 was invented in 2002, and there's only been two instances where any dissent has been expressed, and both of those were by Paul Collingwood and the England team, as a result of failing to win against West Indies"
Nevertheless, that winning position was largely due to the exploits of Gayle, who cracked 15 runs off Ryan Sidebottom's first over of the reply en route to 25 from 12 balls. He was eventually dismissed seven balls after the resumption, at 41 for 1 after 3.3 overs, although by that stage of the recalculated run-chase, West Indies required just 19 more runs to win from 15 balls, whereas in a full 20-over innings, the figure would have been a more daunting 151 from 99.
Duckworth, however, insisted that his maths still added up. "We don't know what would have happened [in a full contest]," he said. "I've seen Gayle score a Twenty20 century in absolutely no time, so you've no idea. His dismissal didn't affect the situation at that stage. If he'd got out before the rain, when there were still ostensibly 20 overs still to face, that would have been important because it would have significantly affected the run-scoring capability.
"Wickets start to diminish in importance the shorter the game," he added. "The fact that the match had been reduced to a further 3.4 overs only meant that his wicket was fairly immaterial. The only thing that was lost was the momentum [that his innings had generated], but there are plenty other good West Indians who could come in and pick up the mantle."
On another day, one of those men might have been Kieron Pollard, but as Duckworth himself conceded, his unusual dismissal - stumped off a leg-side wide for 0 - actually worked in West Indies' favour on this occasion, because they earned a run for the extra, without using up any deliveries. However, he did not accept that such anomalies ought to be factored into future Twenty20 scenarios, with sides permitted to lose only, say, three or four wickets in the case of a six-over chase.
"It would have made no difference," he said. "When the target was revised, the resources [we factored in] were whatever wickets are left and the fewer overs. We only alter the overs. The consideration of losing wickets came in over ten years ago, right at the start, and there are very good reasons why this would be totally impractical."
Duckworth did, however, confirm that small alterations to the formula are made from time to time, as came to light during a CB40 fixture between Leicestershire and Durham on Monday, when it transpired that the scorers at Grace Road had been using the 2009 calculations to set Leicester a chase of 176 in 26 overs, when the 2010 figure ought to have been 181.
"We do recalibrate quite regularly," he said. "We review the data every four years, and last summer as part of a series of regular reviews, we did reanalyse all the data that existed, and this for the first time included an extremely large pot of Twenty20 data.
"We reached two important conclusions. The first was that the scoring patterns in Twenty20 matches fitted in absolutely perfectly with the formula that we'd always used satisfactorily with 50-over games. Secondly, however, there were one or two small changes needed to the numbers going into our formula, so that the tables and the targets would be ever so slightly different. But the changes were very small, and were accepted by the ICC in an independent assessment by their statistical advisors."