ICC World Twenty20 2010 May 4, 2010

Duckworth defends rain-rules formula


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."

Andrew Miller is UK editor of Cricinfo

Comments have now been closed for this article

  • Sumedha on May 6, 2010, 6:33 GMT

    In my opinion, the big problem that ICC has done is calling it a game after 5 overs. In 50 over matches, it's 20 overs and its 40% of the full match where as in Twenty20, it's 5 overs and 25% of the full quota. One other thing they need to consider is, team batting second knows the advantage of having fielding restrictions when the game is curtailed. At least, they should stop this rule, when they are making targets using D/L

    There is no doubt ICC needs to revise their strategy for curtailed Twenty20 games. I guess they could start doing this by changing the minimum overs (to call it a game) to at least 10 overs and if there is no result, going for a ball out.

    I guess many won't complain about it.

  • Vee on May 6, 2010, 4:07 GMT

    Did duckworth ever played cricket?? I doubt it... Cricket is played on a cricket ground rather on a paper with mathematical brilliance. The Phase of the game is so swift that the end result can be changed by an individual brilliance in a matter of over. So, where is the place for so-called D/L. I am a big fan of cricket & since the game is already short, it should be decided on the ground by letting each team have a fair share of opportunities. Lets say, they play a one over eliminator, instead of D/L. Any lay-man can understand the game & its very satisfying to all of them. That way, cricket will grow

  • Dummy4 on May 5, 2010, 17:44 GMT

    i agree with collingwood that the duckworth lewis system which works perfectly fine with ODIs appears to suffer from anomalies in T20s...this i think is due to the ridiculous rule of 5 overs constituting a complete game...on a per over basis 60 from 6 overs which is slightly more than the original required rate and the fact that WI had not lost any wickets...it seems low because of the ridiculously low number of overs to bat with all ten wickets in hand ...in my opinion there should be no rain shortened T20 games as the number of overs per side is too less to begin with...the game should be abandoned in case of a long rain delay...an alternative to this is to have the super over

  • Steve on May 5, 2010, 13:41 GMT

    The DL method is not deeply flawed but was designed for ODIs with a minimum of 20 overs to decide a match not a T20 game where less than 20 overs will decide a rain-affected match. If the ICC has made a ridiculous decision to set 5 overs as the minimum number of overs and then use DL as the method for determining the required score then it is they who should be blamed.

    There should be NO rain affected T20 matches as they are too short to start with - play all 20 overs per side or abandon the match as anything less is a waste of time.

  • Nick on May 5, 2010, 11:43 GMT

    Narayanan The D/L system was brought in after the 1992 game with South Africa as the old system was unfair so not a correct comparison I'm afraid.

  • Dummy4 on May 5, 2010, 10:56 GMT

    I totally agree with the England captain. I think the target should be set taking the wickets to consideration. For example Zimbabwe needed 104 off 11 overs against SL but they could have batted aggressively because they had all 10 in hand, and it is unfair. The target has to be set to achieve with the certain amount of wickets, like 5 wickets. The target could have been reasonable in that game had they given 95 in 11 overs before the 6th wicket fell.

  • David on May 5, 2010, 9:48 GMT

    Frank Duckworth's comments come across as smug and self satisfied. It doesn't really matter what Collingwood thinks of the system - would he have commented if England had won? - but from a spectator's perspective the England/Windies match was simply unsatisfactory as a contest. Gayle bowled first because DL favours the team that's chasing, just as Ireland knew their best chance of victory was to bat 2nd in a rain-affected match. So teams are exploiting a flawed system and matches are potentially being decided by the toss of a coin. The Windies DL target was clearly too small in comparison to England's total - in a 36 ball innings the side batting second should have to score well above the other side's run rate - especially if loss of wickets is not taken into account....how Duckworth can defend a farce like Monday night is beyond me! The fact that England werwe 10-1 outsiders after a couple of overs tells you all you need to know about the stiff task they were faced with.

  • Chris on May 5, 2010, 9:29 GMT

    I think the D/L method is valid for deciding games in it's current form. The problem lies in the minimum overs bowled requirement. I would like to hear Mr D's thoughts on whether 5 overs is enough to decide a 20 over game - the D/L method becomes more accurate with more over bowled. Perhaps minimum overs should be 10?

  • Asim on May 5, 2010, 9:16 GMT

    DL is a stupid mathematical theoratical, away from the reality equation. It should be scraped right now for the betterment of cricket.

    Instead, we should have a jury of ex-cricketers, un baised, the day the rain falls, who then sit down, analyze everything, the rain, the runs, the pitch damage, the wickets, type of batsmen to follow etc. and come up with a fair equation every time. The pannel should be 3 to 5 un baised ex professionals.

  • Asim on May 5, 2010, 9:12 GMT

    I think that the D/L rule is very theoratical and far away from the actual realities on the cricket field. I think that it has always come up with unfair figures like in the 1992 world cup and then twice already in this 20 20 world cup. It is a funny system.

    Inthe practical world there are so many things that we need to look at, the number of wickets, the conditions, the type of batsmen (1st five or the tail enders), which DL does not cater for.

    I think this mathematical rule needs to be altered tremendously to cater for many other factors, which I think would not really be possible, as every game is a new game. Every pitch is a new pitch.

    I think we need to scrap DL and instead, make a committee of un-baised ex cricketers, on the day of the match, who sit down during the rain, and analyze the exact factors like runs, wickets, state of the pitch, and set a fair target.

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