Duckworth-Lewis method

In the sport of cricket, the 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 devised by two English statisticians, Frank Duckworth and Tony Lewis.

Example

A simple example of the D/L method being applied was the first One Day International (ODI) between India and Pakistan in their 2006 ODI series. India batted first, and were all out in the 49th over for 328. Pakistan, batting second, were 7 wickets down for 311 when bad light stopped play after the 47th over.

In this example, Pakistan's target had the match continued 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 favored 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)" [ [http://aus.cricinfo.com/db/ARCHIVE/2005-06/IND_IN_PAK/SCORECARDS/IND_PAK_ODI1_06FEB2006.html Scorecard] for the rain-affected 1st ODI between India and Pakistan on 6 February 2006, from Cricinfo.] .

Theory

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 [Data Analysis Australia's [http://www.daa.com.au/analytical-ideas/cricket/ detailed mathematical analysis] of the Duckworth-Lewis Method daa.com.au.] .

Using a published table which gives the percentage of these combined resources remaining for any number of overs (or, more accurately, balls) left and wickets lost, the target score can be adjusted up or down to reflect the loss of resources to one or both teams when a match is shortened one or more times. This percentage is then used to calculate a target (sometimes called a 'par score') that is usually a fractional number of runs. If the second team passes the target then the second team is taken to have won the match; if the match ends when the second team has exactly met (but not passed) the target (rounded down to the next integer) then the match is taken to be a tie.

Application

The D/L method is relatively simple to apply, but requires a published reference table and some simple mathematical calculation (or use of a computer). As with most non-trivial statistical derivations, however, the D/L method can produce results that are somewhat counterintuitive, and the announcement of the derived target score can provoke a good deal of second-guessing and discussion amongst the crowd at the cricket ground. This can also be seen as one of the method's successes, adding interest to a "slow" rain-affected day of play.

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.

History and Creation

The D/L method was created by two English statisticians, Frank Duckworth and Tony Lewis, originating from an undergraduate final-year project at the University of the West of EnglandFact|date=April 2008. It 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, [ [http://uk.cricinfo.com/db/ARCHIVE/1996-97/ENG_IN_ZIM/ENG_ZIM_ODI2_01JAN1997.html Scorecard] of the 2nd ODI between England and Zimbabwe, 1 January 1997, from Cricinfo.] 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.

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. [ [http://content-uk.cricinfo.com/wc2007/content/story/280142.html "22 off one ball - A farcical rain rule leaves everyone bewildered"] , from Cricinfo.] The D/L method removes - or at least normalises - 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. [ [http://news.bbc.co.uk/sport1/hi/cricket/tms/6502207.stm "Stump the Bearded Wonder"] , Bill Frindall explains how D/L would apply to 1992 WC semi-final]

Updates

The published table that underpins the D/L method is regularly updated, most recently in 2004, as it became clear that one-day matches were achieving significantly higher scores than in previous decades, affecting the historical relationship between resources and runs.

At the same time as this update, the D/L method was also split into a Professional Edition and a Standard Edition. [ [http://www.cricinfo.com/link_to_database/ABOUT_CRICKET/RAIN_RULES/DL_FAQ.html Rain affected rules] from Cricinfo.] The main difference is that while the Standard Edition preserves the use of a single table and simple calculation – suitable for use in any one-day cricket match at any level – the Professional Edition uses substantially more sophisticated statistical modeling, and requires the use of a computer. The Professional Edition has been in use in all international one-day cricket matches since early 2004.

Criticism

The D/L method has been criticised 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). [Bhogle, Srinivas, [http://www.rediff.com/wc2003/2003/mar/06bhogle.htm The Duckworth/Lewis Factor] , rediff.com.]

Another criticism is that the D/L method does not account for changes in the number of overs during which field restrictions are in place. [Booth, Shane, quoted in [http://www.hinduonnet.com/fline/fl1924/stories/20021206004410400.htm For a Fair Formula] , Hindu Online.]

More common informal criticism from cricket fans and journalists of the D/L method is that it is overly complex and can be misunderstood. [Varma, Amit, [http://content-aus.cricinfo.com/ci/content/story/141952.html Simple and subjective? Or complex and objective?] , Cricinfo]

References

Further reading

*Duckworth, FC & Lewis, AJ "Your Comprehensive Guide to The Duckworth Lewis Method for Resetting Targets in One-day Cricket", Acumen Books, 2004. ISBN 0-9548718-0-4
*Duckworth, F "A Role for Statistics in International Cricket" "Teaching Statistics", (June 2001) Volume 23, No. 2 pp 38-44
*Duckworth, FC & Lewis, AJ "A fair method of resetting the target in interrupted one-day cricket matches" "Journal of the Operational Research Society", (Mar 1998) Volume 49, No. 3 pp 220-227

External links

* [http://icc-cricket.yahoo.com/about-icc/d-l-faqs.html ICC's D/L method FAQ]
* [http://www.cricinfo.com/link_to_database/ABOUT_CRICKET/RAIN_RULES/DL_FAQ.html Cricinfo's D/L method FAQ]
* [http://www.duckworth-lewis.com/Calculator/tabid/72/Default.aspx Duckworth-Lewis.com D/L method online calculator]
* [http://in.yimg.com/icccricket/pdfs/d-l_table.pdf ICC's D/L method (standard edition) table of resource percentages]
* [http://www.cricinfo.com/link_to_database/ABOUT_CRICKET/RAIN_RULES/DUCKWORTH_LEWIS_2001.html Cricinfo's explanation of the D/L method]
* [http://in.yimg.com/icccricket/pdfs/d-l_method.pdf ICC's explanation of the D/L method]
* [http://news.bbc.co.uk/sport1/hi/cricket/rules_and_equipment/4184006.stm BBC Sport's explanation of the D/L method]