In the
sportA Sport is all forms of physical activity which, through casual or organised participation, aim to use, maintain or improve physical fitness and provide entertainment to participants. Sport may be competitive, where a winner or winners can be identified by objective means, and may require a degree...
of
cricketCricket is a bat-and-ball game played between two teams of 11 players on an oval-shaped field, at the centre of which is a rectangular 22-yard long pitch. One team bats, trying to score as many runs as possible while the other team bowls and fields, trying to dismiss the batsmen and thus limit the...
, the
Duckworth–Lewis method (
D/L method) is a mathematical formulation designed to calculate the target score for the team batting second in a
one-day cricketLimited overs cricket, also known as one-day cricket and in a slightly different context as List A cricket, is a version of the sport of cricket in which a match is generally completed in one day, whereas Test and first-class matches can take up to five days to complete...
or Twenty20 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
statisticianA statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
s,
Frank DuckworthFrank Carter Duckworth, MBE is a retired English statistician, one of the two statisticians who developed the Duckworth–Lewis method of resetting targets in interrupted one-day cricket matches. He studied physics and earned a PhD in metallurgy at the University of Liverpool...
and
Tony LewisAnthony John Lewis, MBE is a mathematician who, along with Frank Duckworth, developed the Duckworth-Lewis method of resetting targets in interrupted cricket matches....
.
Stoppage in first innings
In the 4th
IndiaThe Indian cricket team is the national cricket team of India. Governed by the Board of Control for Cricket in India , it is a full member of the International Cricket Council with Test and One Day International status....
– 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.
During the fifth ODI between India and South Africa in January 2011, rain halted play twice during the first innings. The match was reduced to 46 overs and South Africa scored 250/9. The D/L method was applied which adjusted the target to 268. As the number of overs was reduced in between South Africa's innings, this method takes into account what South Africa would have scored before the first interruption.
Both examples illustrate how the D/L method is applied. In the case of the first match, as 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)".
Stoppage in second innings
A simple example of the D/L method being applied was the first One Day International (ODI) between
IndiaThe Indian cricket team is the national cricket team of India. Governed by the Board of Control for Cricket in India , it is a full member of the International Cricket Council with Test and One Day International status....
and
PakistanThe Pakistan cricket team is the national cricket team of Pakistan. Pakistan, represented by the Pakistan Cricket Board , is a full member of the International Cricket Council, and thus participates in , and cricket matches....
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 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)".However, this was a controversial result and gave rise to a challenge posted by two Indian Engineers named Sourav Agarwalla and Ananyabrata Chakravorty, who went on to create RAM (Rule for Affected Matches) that has won them several prizes, though they are still looking to be recognised by the ICC.
Examples in T20 matches
During the 2010 ICC World T20, the D/L method was used in the group stage match between Sri Lanka and Zimbabwe. Sri Lanka scored 173/7 in 20 overs batting first and Zimbabwe were 29/1 in 5 overs when rain interrupted play. Sri Lanka won the match by 14 runs according to the D/L method.
On the same day, another group match between England and West Indies was also decided by the D/L method. England scored 191/5 in 20 overs, and rain interrupted play after 2.2 overs of the chase when West Indies had scored 30/0. According to the D/L method, West Indies were set a target of 60 runs in 6 overs, which they achieved with a ball to spare. The then English captain Paul Collingwood heavily criticized the usage and appropriateness of the D/L method in T20 matches.
Theory
The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to make as many
runsIn the sport of cricket, a run is the basic unit of scoring. Runs are scored by a batsman, and the aggregate of the scores of a team's batsmen constitutes the team's score. A batsman scoring 50 or 100 runs , or any higher multiple of 50 runs, is considered a particular achievement...
as possible: the number of
overIn the sport of cricket, an over is a set of six consecutive balls bowled in succession. An over is normally bowled by a single bowler. However, in the event of injury preventing a bowler from completing an over, it is completed by a teammate....
s they have to receive; and the number of
wicketIn the sport of cricket the word wicket has several distinct meanings:-Definitions of wicket:Most of the time, the wicket is one of the two sets of three stumps and two bails at either end of the pitch...
s they have in hand. At any point in any
inningsAn inning, or innings, is a fixed-length segment of a game in any of a variety of sports – most notably cricket and baseball during which one team attempts to score while the other team attempts to prevent the first from scoring. In cricket, the term innings is both singular and plural and is...
, 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.
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
integerThe integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
) then the match is taken to be a tie.
An example of such a tie was found in the one day international between England and India on 11 September 2011. This match was frequently interrupted by rain in the final overs, and a ball-by-ball calculation of the Duckworth-Lewis 'par' score played a key role in the tactical decisions made during those overs. At one point, India were ahead according to this calculation, during one rain delay (and would have won if play was unable to be resumed). At a second rain interval, England, who had scored some quick runs (precisely because they were aware of the need to get ahead in terms of D/L) would correspondingly have won if play hadn't resumed. Play was finally called off with just 7 balls of the match remaining, with England's score exactly at the Duckworth-Lewis 'par' score, resulting in a tied match. This example does show how crucial (and difficult) the decisions of the Umpires can be, in terms of assessing at exactly what point the rain is heavy enough to justify ceasing play. If they had done so one ball earlier, England would have been ahead on D/L, and so would have won the match (equally, if play had stopped one ball later, without England scoring off that ball, India would have won the match - indicating how finely-tuned D/L calculations can be in such situations).
Application
The Duckworth/Lewis method is fairly simple to apply, but requires a published reference table and some simple mathematical calculations. As with most non-trivial statistical derivations, the D/L method can produce results that are somewhat
counterintuitiveThe word "counterintuitive" literally means counter to intuition, and so it essentially means that something does not seem right or correct.A counterintuitive proposition is one that does not seem likely to be true when assessed using intuition or gut feelings...
, 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 must face at least 20 overs before D/L can decide the game. In
Twenty20Twenty20 is a form of cricket, originally introduced in England for professional inter-county competition by the England and Wales Cricket Board , in 2003. A Twenty20 game involves two teams, each has a single innings, batting for a maximum of 20 overs. Twenty20 cricket is also known as T20 cricket...
games, each side must face at least five overs.
History and creation
The D/L method was devised by two British
statisticianA statistician is someone who works with theoretical or applied statistics. The profession exists in both the private and public sectors. The core of that work is to measure, interpret, and describe the world and human activity patterns within it...
s,
Frank DuckworthFrank Carter Duckworth, MBE is a retired English statistician, one of the two statisticians who developed the Duckworth–Lewis method of resetting targets in interrupted one-day cricket matches. He studied physics and earned a PhD in metallurgy at the University of Liverpool...
and
Tony LewisAnthony John Lewis, MBE is a mathematician who, along with Frank Duckworth, developed the Duckworth-Lewis method of resetting targets in interrupted cricket matches....
. 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 seven runs, and was formally adopted by the
International Cricket CouncilThe International Cricket Council is the international governing body of cricket. It was founded as the Imperial Cricket Conference in 1909 by representatives from England, Australia and South Africa, renamed the International Cricket Conference in 1965, and took up its current name in 1989.The...
in 2001 as the standard method of calculating target scores in rain shortened
one-dayLimited overs cricket, also known as one-day cricket and in a slightly different context as List A cricket, is a version of the sport of cricket in which a match is generally completed in one day, whereas Test and first-class matches can take up to five days to complete...
matches.
Various different methods had been used previously, including
run-rateIn cricket, the run rate , or runs per over is the number of runs a batsman scores in an over of 6 balls. It includes all runs, even the so-called extras awarded due to errors by the bowler. Without extras and overthrows, the maximum run rate is 36 – if every ball were struck for six and, as...
ratios, the score that the first team had achieved at the same point in their
inningsAn inning, or innings, is a fixed-length segment of a game in any of a variety of sports – most notably cricket and baseball during which one team attempts to score while the other team attempts to prevent the first from scoring. In cricket, the term innings is both singular and plural and is...
, and targets derived by totaling the best scoring
overIn the sport of cricket, an over is a set of six consecutive balls bowled in succession. An over is normally bowled by a single bowler. However, in the event of injury preventing a bowler from completing an over, it is completed by a teammate....
s in the initial innings. All these methods have flaws that are easily exploitable. For example, run-rate ratios take no account of how many
wicketIn the sport of cricket the word wicket has several distinct meanings:-Definitions of wicket:Most of the time, the wicket is one of the two sets of three stumps and two bails at either end of the pitch...
s the team batting second have lost, but simply reflect how quickly they were scoring when the match was interrupted; so, 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-New Zealand:-Round Robin Stage:Co-hosts New Zealand proved the surprise packet of the tournament, winning their first seven games to finish on top of the table after the round robin. The other hosts, Australia, were one of the pre-tournament favourites but lost their first two matches. They...
, left the
South African cricket teamThe South African national cricket team represent South Africa in international cricket. They are administrated by Cricket South Africa.South Africa is a full member of the International Cricket Council, also known as ICC, with Test and One Day International, or ODI, status...
requiring 21 runs from one ball (when the maximum score from one ball is generally six runs). Before a brief rain interruption, South Africa was chasing a target of 22 runs from 13 balls but, following the stoppage, the team's amended target became 21 (a reduction of only one run) to be scored off just one ball (a reduction of 12 balls). The D/L method avoids 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.
Updates
The published table that underpins the D/L method is regularly updated, using source data from more recent matches. From the 1999 Cricket World Cup match in Bristol between India and Kenya, Tony Lewis noticed that there was an inherent weakness in the formula used at the time that would give a noticeable advantage to the side chasing a total in excess of 350. A correction was very soon built into the formula and the software to correct this, by including a 'match' factor. However, this minor correction was not fully adopted by users until the 2004 update. Updating the source data in its own right would reflect the overall trend 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. 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 modelling, and requires the use of a computer. The Professional Edition has been in use in all international one-day cricket matches since early 2004.
In June 2009, it was reported that the D/L method would be reviewed for the Twenty20 format after its appropriateness was questioned in the quickest version of the game. Lewis was quoted admitting that "Certainly, people have suggested that we need to look very carefully and see whether in fact the numbers in our formula are totally appropriate for the Twenty20 game."
Criticism
The D/L method has been criticized on the grounds that wickets are (necessarily) a much more heavily weighted resource than overs, leading to the suggestion 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 the innings for 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 20 March 2009, the West Indies coach (
John DysonJohn Dyson is a former international cricketer who is now a cricket coach, most recently in charge of the West Indies....
) called his players in for bad light, believing that his team would win by one run under the D/L method, but not realising that the loss of a wicket with the last ball had altered the Duckworth-Lewis score. In fact
Javagal SrinathJavagal Srinath is a former Indian cricketer. He was a frontline fast bowler for the Indian cricket team until his retirement, being the second Indian pace bowler after Kapil Dev to take 200 Test wickets. One ball that he bowled during the 1996 tour of South Africa measured...
, the match referee, confirmed that the West Indies were two runs short of their target, giving the victory to England.
Cultural influence
"The Duckworth Lewis Method" is the name of a band formed by
Neil HannonNeil Hannon is a Northern Irish singer and songwriter, best known as the creator and frontman of the chamber pop group The Divine Comedy. The band's official website even goes so far as to say, "The Divine Comedy is Neil Hannon," and Hannon is quoted in an interview as saying, "The Divine Comedy...
of
The Divine ComedyThe Divine Comedy are a chamber pop band from Ireland, fronted by Neil Hannon. Formed in 1989, Hannon has been the only constant member of the group, playing, in some instances, all of the non-orchestral instrumentation bar drums. To date, ten studio albums have been released under the Divine...
and Thomas Walsh of
PugwashPugwash is an Irish pop band fronted by Drimnagh-born musician Thomas Walsh. Pugwash has released four albums since its debut LP Almond Tea in 1999. The band signed a five-year deal with XTC founding member Andy Partridge's label Ape House in 2009...
, which recorded a self-titled concept album of cricket songs.
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 for 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