Cricket:Duckworth - Lewis Method : an Eluding Mystery

April 25, 2009

In the sport of cricket,   millions of die-hard fans have either rejoiced at their team’s victory or bitterly cursed when their team lost due to the Duckworth-Lewis method.  A term so commonly used , referred and implemented these days.  But how many of us actually know who are these two individuals who gave a different twist to limited over cricket.

It will be interesting to note that both of them who developed the D/L method were British statisticians who never played professional cricket not did they officiate in any international cricket matches.

One of them is Frank Duckworth , consultant statistician, and the editor of the Royal Statistical Society's monthly news magazine  in the UK.  Tony Lewis ( not the cricketer)  is a mathematician and by inference  jointly  developed the Duckworth-Lewis method . It  was developed  from an undergraduate final-year project at the University of the West of England

Frank Duckworth and Tony Lewis are the men behind the method

Duckworth-Lewis method (D/L method) is a mathematical way to calculate the target score for the team batting second in a one-day cricket or Twenty-20 cricket match interrupted by weather or other circumstance. It is generally accepted to be a fair and accurate method of setting a target score, but as it attempts to predict what would have happened had the game come to its natural conclusion, it generates some controversy.

The D/L method was first used in international cricket in the second game of the 1996/7 Zimbabwe versus England One Day International series, which Zimbabwe won by 7 runs, and was formally adopted by the International Cricket Council in 2001 as the standard method of calculating target scores in rain shortened one-day matches.

Earlier to the D/L method, various different methods had been previously used to achieve the same task, including run-rate ratios, the score that the first team had achieved at the same point in their innings, and targets derived by totaling the best scoring overs in the initial innings. All of these methods have flaws that are easily exploitable. For example, run-rate ratios do not account for how many wickets the team batting second have lost, but simply reflect how quickly they were scoring at the point the match was interrupted; thus, if a team felt a rain stoppage was likely, they could attempt to force the scoring rate without regard for the corresponding highly likely loss of wickets, skewing the comparison with the first team. Notoriously, the "best-scoring overs" method, used in the 1992 Cricket World Cup, left the South African cricket team requiring 21 runs from one ball (when the maximum score from any one ball is generally six runs). Prior to a brief rain interruption, South Africa was chasing a target of 22 runs from 13 balls - which was difficult but at least attainable - but the possibility of an exciting conclusion to the game was destroyed when the team's target was reduced by only one run, to be scored off 12 fewer balls The D/L method removes - or at least normalizes - this flaw: in this match, the revised D/L target would have been four runs to tie or five to win from the final ball

The D/L method can be used for interruptions either in the first or second innings.  Let us take an example of a game interruption in the first innings.

It was the 4th India - England ODI in the 2008 series, the first innings was interrupted by rain on two occasions, resulting in the match being reduced to 22 overs a side. India (batting first) made 166/4. England's target was therefore set by the D/L method at 198 from 22 overs. This example illustrates how the D/L method sets a higher target for the team batting second when the delay occurs in the 1st innings. Because England knew they had only 22 overs the expectation is that they will be able to score more runs from those overs than India had from their (interrupted) innings. England made 178/8 from 22 overs, and so the match was listed as "India won by 19 runs (D/L method)".

Another example of an interruption in the second innings was the first One Day International (ODI) between India and Pakistan in their 2006 ODI series. India batted first, and was all out in the 49th over for 328. Pakistan, batting second, was 7 wickets down for 311 when bad light stopped play after the 47th over. In this example, Pakistan's target, had the match continued, and was 18 runs in as many balls, with three wickets in hand. Considering the overall scoring rate throughout the match, this is a target most teams would be favoured to achieve. And indeed, application of the D/L method resulted in a target score of 304 at the end of the 47th over, with the officially listed result as "Pakistan won by 7 runs (D/L Method)" much to the disappointment of the India fans.

The D/L method has a fairly simple theory although many times it becomes difficult for fans and players to understand. The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to make as many runs as possible: the number of overs they have to receive; and the number of wickets they have in hand. At any point in any innings, a team's ability to score more runs depends on the combination of these two resources. Looking at historical scores, there is a very close correspondence between the availability of these resources and a team's final score, a correspondence which D/L exploits. Applied to 50 over matches, each team has to face at least 20 overs before D/L can decide the game. In Twenty20 games, each side has to face at least 5 overs. Applying this method means giving chance to the team chasing second.  This can also be seen as one of the method's successes, adding interest to a "slow" rain-affected day of play.

The D/L method has been criticized based on the fact that wickets are (necessarily) a much more heavily weighted resource than overs, leading to the observation that if teams are chasing big targets, and there is the prospect of rain, a winning strategy could be to not lose wickets and score at what would seem to be a "losing" rate (e.g. if the asking rate was 6.1, it could be enough to score at 4.75 an over for the first 20-25 overs).

Another criticism is that the D/L method does not account for changes in the proportion of number of overs during which field restrictions are in place compared to a completed match. More common informal criticism from cricket fans and journalists of the D/L method is that it is overly complex and can be misunderstood. For example, in a one-day match against England on 20th March 2009, the West Indies coach (John Dyson) called his players in for bad light, believing that his team would win by one run under the D/L method. In fact Javagal Srinath, the match referee, confirmed that the West Indies were two runs short of their target, giving the victory to England.
All said and done, no matter what method the officials use in an interrupted game of cricket, disappointment will be written on the faces of the losing team and their fans.

Naveen Frank - Archives:

Researched by: Naveen Frank Sharjah
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Comment on this article

  • Parvez, mangalore/Dubai

    Mon, Apr 27 2009

    It is not injustice done to any of the teams playing. It would be better for the readers go through the formula calculation(norms table) before suggesting any comments.

  • bilal, Karkala/riyadh

    Mon, Apr 27 2009


  • Rathnakar Sheregar, Byndoor / Dubai

    Sun, Apr 26 2009

    First of all I sincerely thank Mr. Frank for giving us general idea about D/L Method. If you take any method there will be advantages and disadvantages. According to me the D/L method is favouring to batting second in 20/20 and on the other hand it will be more benefited to batting 1st in the one day match interrupted by rain or any other reasons. In 20/20 batting 1st if they score 180 in 20 over then the batting second should score 100 in 10 over. It is quite easy target as D/L method does  not tell about the wickets. The system should tell in 10 over 100 runs with loss of 5 wickets. So batting 2nd will win most of the matches. Similarly in 50 over match batting 1st if they score 280 in 50 overs then batting second should score 281 in 45 over. As we all know that chasing is not easy to achieve 281 in 50 over match. So batting 2nd will loose most of the matches.

  • Vasanth Kumar Kandadka, Sullia/Doha

    Sun, Apr 26 2009

    Many fans feel that D/L method is discriminatory, especially when thier team looses. Every cricket fan should read this article to understand that this is the best among the available methods. Having said that, this method may have to be modified futher to apply reasonably to T20 matches. Thank you Frank for giving cricket fans an insight into D/L. Bye the way does ant body has the formula of D/L?

  • Tom, Mangalore

    Sat, Apr 25 2009

    Nice article, Mr. Frank, Thanks for taking your time to gather the information through various sources and share it with us.

  • Dr.Anand Pereira, Sakleshpur

    Sat, Apr 25 2009

    Thank you Naveen for the well researched article. we do hope that Duckworth & Lewis will release yet another version that will be more appropriate for T-20 MATCHES.

  • Reyan, Kuwait

    Sun, Apr 26 2009

    This article can compete for the "Best article of the Year in Daijiworld"  Good research Frank

  • Kabeer Karnad, Mulki / Dammam

    Sun, Apr 26 2009

    Informative one , thanks.

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