51-623: [REDACTED] Look up Duckworth in Wiktionary, the free dictionary. Duckworth may refer to: Duckworth (surname) , people with the surname Duckworth Duckworth ( DuckTales ) , fictional butler from the television series DuckTales Duckworth Books , a British publishing house HMS Duckworth (K351) , a frigate Duckworth, West Virginia , an unincorporated community, United States an earlier name of Bluff, Queensland , Australia "Duckworth" (song) (stylized DUCKWORTH. ),
102-453: A 2017 song by Kendrick Lamar (named after his surname) Duckwrth , a stage name of Jared Lee Duckworth , a 2011 Adult Swim pilot See also [ edit ] Duckworth-Lewis method , a statistical method for match calculations in cricket The Duckworth Lewis Method , an Irish pop group named after the cricketing term Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
153-453: A 2017 song by Kendrick Lamar (named after his surname) Duckwrth , a stage name of Jared Lee Duckworth , a 2011 Adult Swim pilot See also [ edit ] Duckworth-Lewis method , a statistical method for match calculations in cricket The Duckworth Lewis Method , an Irish pop group named after the cricketing term Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with
204-427: A combined resources remaining percentage figure (with 50 overs and 10 wickets = 100%), and these are all stored in a published table or computer. The target score for the team batting second ('Team 2') can be adjusted up or down from the total the team batting first ('Team 1') achieved using these resource percentages, to reflect the loss of resources to one or both teams when a match is shortened one or more times. In
255-548: A flaw in how it handled very high first innings scores (350+) became apparent 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 that would give a noticeable advantage to the side chasing a total in excess of 350. A correction was built into the formula and the software, but was not fully adopted until 2004. One-day matches were achieving significantly higher scores than in previous decades, affecting
306-427: A full 50 overs, for example, and can consequently achieve a higher run rate . The DLS method is an attempt to set a statistically fair target for the second team's innings, which is the same difficulty as the original target. The basic principle is that each team in a limited-overs match has two resources available with which to score runs (overs to play and wickets remaining), and the target is adjusted proportionally to
357-522: A further reduction to 44, or a par score of 43, and hence Sri Lanka won the match by 14 runs. The DLS method was also used after the rain disruption in the 2023 Indian Premier League final , when Chennai Super Kings had scored 4/0 (0.3 overs) and the Gujarat Titans just scored 214/4 (20 overs). The target was reduced at 171 runs from 15 overs from earlier target of 215 runs from 20 overs for Chennai Super Kings. Chennai Super Kings won by 5 wickets by
408-424: A given number of overs remaining (called u {\displaystyle u} ) and wickets lost (called w {\displaystyle w} ), takes the following exponential decay relationship: where the constant Z 0 {\displaystyle Z_{0}} is the asymptotic average total score in unlimited overs (under one-day rules), and b {\displaystyle b}
459-433: A particular combination of u {\displaystyle u} and w {\displaystyle w} (by putting in u {\displaystyle u} and the values of these constants for the particular w {\displaystyle w} ), and dividing this by the score achievable at the start of the innings, i.e. finding gives the proportion of the combined run scoring resources of
510-590: A reference table for the Standard Edition, or from a computer for the Professional Edition) can be entered into the formula, with the rest left blank. Note that a delay at the start of an innings counts as the 1st interruption. Standard Edition G50 G50 is the average score expected from the team batting first in an uninterrupted 50 overs-per-innings match. This will vary with the level of competition and over time. The annual ICC Playing Handbook gives
561-498: A result of the outcome of the semi-final in the 1992 World Cup between England and South Africa , where the Most Productive Overs method was used. When rain stopped play for 12 minutes, South Africa needed 22 runs from 13 balls, but when play resumed, the revised target left South Africa needing 21 runs from one ball, a reduction of only one run compared to a reduction of two overs, and a virtually impossible target given that
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#1732851920231612-525: A revised target of 139. Perth won the game by 8 wickets with a boundary off the final ball. The published table that underpins the D/L method is regularly updated, using source data from more recent matches; this is done on 1 July annually. For 50-over matches decided by D/L, each team must face at least 20 overs for the result to be valid, and for Twenty20 games decided by D/L, each side must face at least five overs, unless one or both teams are bowled out and/or
663-499: A second rain interval, England, who had scored some quick runs (knowing they needed to get ahead in D/L terms) would correspondingly have won if play had not resumed. Play was finally called off with just 7 balls of the match remaining and England's score equal to the Duckworth–Lewis 'par' score, therefore resulting in a tie. This example does show how crucial (and difficult) the decisions of the umpires can be, in assessing when rain
714-553: Is 229, and the score to tie is 228. The actual resource values used in the Professional Edition are not publicly available, so a computer which has this software loaded must be used. If it is a 50-over match and Team 1 completed its innings uninterrupted, then they had 100% resource available to them, so the formula simplifies to: The original D/L model started by assuming that the number of runs that can still be scored (called Z {\displaystyle Z} ), for
765-475: Is a mathematical formulation designed to calculate the target score (number of runs needed to win) for the team batting second in a limited overs cricket match interrupted by weather or other circumstances. The method was devised by two English statisticians , Frank Duckworth and Tony Lewis , and was formerly known as the Duckworth–Lewis method ( D/L ). It was introduced in 1997, and adopted officially by
816-399: Is actually the same each time − it's just that different scenarios, with more or less interruptions and restarts, need to use more or less of the same formula. The total resources available to a team are given by: which can alternatively be written as: Each time there's an interruption or a restart after an interruption, the resource remaining percentages at those times (obtained from
867-402: Is heavy enough to justify ceasing play. If the umpires of that match had halted play 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, India could have won the match with a dot ball – indicating how finely-tuned D/L calculations can be in such situations. During the 2012/13 KFC Big Bash League , D/L was used in
918-459: Is the exponential decay constant. Both vary with w {\displaystyle w} (only). The values of these two parameters for each w {\displaystyle w} from 0 to 9 were estimated from scores from 'hundreds of one-day internationals' and 'extensive research and experimentation', though were not disclosed due to 'commercial confidentiality'. Finding the value of Z {\displaystyle Z} for
969-512: Is this number rounded down to the preceding integer. If Team 2 reaches or passes the target score, then they have won the match. If the match ends when Team 2 has exactly met (but not passed) the par score then the match is a tie. If Team 2 fail to reach the par score then they have lost. For example, if a rain delay means that Team 2 only has 90% of resources available, and Team 1 scored 254 with 100% of resources available, then 254 × 90% / 100% = 228.6, so Team 2's target
1020-637: The International Cricket Council (ICC) in 1999. After the retirement of both Duckworth and Lewis, the Australian statistician Steven Stern became the custodian of the method, which was renamed to its current title in November 2014. In 2014, he refined the model to better fit modern scoring trends, especially in T20 cricket, resulting in the updated Duckworth-Lewis-Stern method. This refined method remains
1071-494: The notation of the ICC Playing Handbook, the team that bats first is called Team 1, their final score is called S, the total resources available to Team 1 for their innings is called R1, the team that bats second is called Team 2, and the total resources available to Team 2 for their innings is called R2. After each reduction in overs, the new total batting resources available to the two teams are found, using figures for
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#17328519202311122-513: The 2nd semi-final played between the Melbourne Stars and the Perth Scorchers . After rain delayed the start of the match, it interrupted Melbourne's innings when they had scored 159/1 off 15.2 overs, and both innings were reduced by 2 overs to 18, and Melbourne finished on 183/2. After a further rain delay reduced Perth's innings to 17 overs, Perth returned to the field to face 13 overs, with
1173-557: The DLS method. This was achieved by reaching 171/5 from 15 overs. An example of a D/L tied match was the ODI 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 tactical decisions during those overs. At one point, India were leading under D/L during one rain delay, and would have won if play had not resumed. At
1224-406: The Professional Edition are not publicly available, so a computer must be used which has the software loaded. [REDACTED] [REDACTED] [REDACTED] These are just the different ways of having one interruption. With multiple interruptions possible, it may seem like finding the total resource percentage requires a different calculation for each different scenario. However, the formula
1275-553: The Team 1 innings. This became the Professional Edition. In the 4th India–England ODI in the 2008 series , the first innings was interrupted by rain on two occasions, reducing the match to 22 overs each. India (batting first) made 166/4. The D/L method increased England's target to 198 from 22 overs. As England knew they had only 22 overs, the expectation is that they could score more runs from those overs than India had from their (interrupted) innings. England made 178/8 from 22 overs, and so
1326-568: The Team 1 innings." The Professional Edition has been in use in all international one-day cricket matches since early 2004. This edition also removed the use of the G50 constant when dealing with interruptions in the first innings. The decision on which edition should be used is for the cricket authority which runs the particular competition. The ICC Playing Handbook requires the use of the Professional Edition for internationals. This also applies to most countries' national competitions. At lower levels of
1377-625: The Twenty20 game." For the 2015 World Cup , the ICC implemented the Duckworth–Lewis–Stern formula, which included work by the new custodian of the method, Professor Steven Stern , from the Department of Statistics at Queensland University of Technology . These changes recognised that teams need to start out with a higher scoring rate when chasing high targets rather than keep wickets in hand. Using
1428-564: The change in the combination of these two resources. Various different methods had been used previously to resolve rain-affected cricket matches, with the most common being the Average Run Rate method , and later, the Most Productive Overs method . While simple in nature, these methods had intrinsic flaws and were easily exploitable: The D/L method was devised by two British statisticians , Frank Duckworth and Tony Lewis , as
1479-569: The final ball. The D/L method was first used in international cricket on 1 January 1997 in the second match of the Zimbabwe versus England ODI series , which Zimbabwe won by seven runs. The D/L method was formally adopted by the ICC in 1999 as the standard method of calculating target scores in rain-shortened one-day matches. The essence of the D/L method is 'resources'. Each team is taken to have two 'resources' to use to score as many runs as possible:
1530-554: The 💕 [REDACTED] Look up Duckworth in Wiktionary, the free dictionary. Duckworth may refer to: Duckworth (surname) , people with the surname Duckworth Duckworth ( DuckTales ) , fictional butler from the television series DuckTales Duckworth Books , a British publishing house HMS Duckworth (K351) , a frigate Duckworth, West Virginia , an unincorporated community, United States an earlier name of Bluff, Queensland , Australia "Duckworth" (song) (stylized DUCKWORTH. ),
1581-446: The game, where use of a computer cannot always be guaranteed, the Standard Edition is used. 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
Duckworth - Misplaced Pages Continue
1632-454: The historical relationship between resources and runs. The second version uses more sophisticated statistical modelling, but does not use a single table of resource percentages. Instead, the percentages also vary with score, so a computer is required. Therefore, it loses some of the previous advantages of transparency and simplicity. In 2002 the resource percentages were revised, following an extensive analysis of limited overs matches, and there
1683-507: The innings remaining when u {\displaystyle u} overs are left and w {\displaystyle w} wickets are down. These proportions can be plotted in a graph, as shown right, or shown in a single table, as shown below. This became the Standard Edition. When it was introduced, it was necessary that D/L could be implemented with a single table of resource percentages, as it could not be guaranteed that computers would be present. Therefore, this single formula
1734-436: The interruption, so the total resource used by Sri Lanka was still slightly more than England had available, hence the slightly decreased target for England. A simple example of the D/L method being applied was the 1st ODI between India and Pakistan in their 2006 ODI series . India batted first, and were all out for 328. Pakistan, batting second, were 311/7 when bad light stopped play after the 47th over. Pakistan's target, had
1785-436: The match continued, was 18 runs in 18 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 retrospective target score of 305 (or par score of 304) at the end of the 47th over, with the result therefore officially listed as " Pakistan won by 7 runs (D/L Method)". The D/L method
1836-578: The match was listed as "India won by 19 runs (D/L method)". During the 5th ODI between India and South Africa in January 2011 , rain halted play twice during the first innings. The match was reduced to 46 overs each. South Africa scored 250/9. The D/L method increased India's target to 268. As the number of overs was reduced during South Africa's innings, this method takes into account what South Africa were likely to have scored if they had known throughout their innings that it would only be 46 overs long. The match
1887-442: The maximum score from one ball is generally six runs. Duckworth said, "I recall hearing Christopher Martin-Jenkins on radio saying 'surely someone, somewhere could come up with something better' and I soon realised that it was a mathematical problem that required a mathematical solution." The D/L method avoids this flaw: in this match, the revised D/L target of 236 would have left South Africa needing four to tie or five to win from
1938-510: 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 they have left. 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. The D/L method converts all possible combinations of overs (or, more accurately, balls) and wickets left into
1989-461: The second team reaches its target in fewer overs. If the conditions prevent a match from reaching this minimum length, it is declared a no result . Until 2003, a single version of D/L was in use. This used a single published reference table of total resource percentages remaining for all possible combinations of overs and wickets, and some simple mathematical calculations, and was relatively transparent and straightforward to implement. However,
2040-403: The side batting first score at or below the average for top level cricket ..., the results of applying the Professional Edition are generally similar to those from the Standard Edition. For higher scoring matches, the results start to diverge and the difference increases the higher the first innings total. In effect there is now a different table of resource percentages for every total score in
2091-492: The standard for handling rain-affected matches in international cricket today. The target score in cricket matches without interruptions is one more than the number of runs scored by the team that batted first. When overs are lost, setting an adjusted target for the team batting second is not as simple as reducing the run target proportionally to the loss in overs, because a team with ten wickets in hand and 25 overs to bat can play more aggressively than if they had ten wickets and
Duckworth - Misplaced Pages Continue
2142-500: The title Duckworth . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Duckworth&oldid=1257467110 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Duckworth From Misplaced Pages,
2193-539: The title Duckworth . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Duckworth&oldid=1257467110 " Categories : Disambiguation pages Place name disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Duckworth-Lewis method The Duckworth–Lewis–Stern method ( DLS )
2244-399: The total amount of batting resources remaining for any combination of overs and wickets. While the process for converting these resources remaining figures into total resource available figures is the same in the two Editions, this can be done manually in the Standard Edition, as the resource remaining figures are published in a reference table. However, the resource remaining figures used in
2295-475: The values of G50 to be used each year when the D/L Standard Edition is applied: Duckworth and Lewis wrote: We accept that the value of G50, perhaps, should be different for each country, or even for each ground, and there is no reason why any cricket authority may not choose the value it believes to be the most appropriate. In fact it would be possible for the two captains to agree a value of G50 before
2346-407: The version of D/L most commonly in use in international and first-class matches (the 'Professional Edition'), the target for Team 2 is adjusted simply in proportion to the two teams' resources, i.e. If, as usually occurs, this 'par score' is a non- integer number of runs, then Team 2's target to win is this number rounded up to the next integer, and the score to tie (also called the par score),
2397-554: Was a change to the G50 for ODIs. (G50 is the average score expected from the team batting first in an uninterrupted 50 overs-per-innings match.) G50 was changed to 235 for ODIs. These changes came into effect on 1 September 2002. As of 2014, these resource percentages are the ones still in use in the Standard Edition, though G50 has subsequently changed. The tables show how the percentages were in 1999 and 2001, and what they were changed to in 2002. Mostly they were reduced. The original version
2448-537: Was listed as "South Africa won by 33 runs (D/L method)". On 3 December 2014, Sri Lanka played England and batted first, but play was interrupted when Sri Lanka had scored 6/1 from 2 overs. At the restart, both innings were reduced to 35 overs, and Sri Lanka finished on 242/8. D/L reduced England's target to 236 from 35 overs. Although Sri Lanka had less resource remaining after the interruption than England would have for their whole innings (about 7% less), they had used up 8% of their resource (2 overs and 1 wicket) before
2499-445: Was named the Standard Edition, and the new version was named the Professional Edition. Tony Lewis said, "We were then [at the time of the 2003 World Cup Final ] using what is now known as the Standard Edition. ... Australia got 359 and that showed up the flaws and straight away the next edition was introduced which handled high scores much better. The par score for India is likely to be much higher now." Duckworth and Lewis wrote, "When
2550-417: Was used giving average resources. This method relies on the assumption that average performance is proportional to the mean, irrespective of the actual score. This was good enough in 95 per cent of matches, but in the 5 per cent of matches with very high scores, the simple approach started to break down. To overcome the problem, an upgraded formula was proposed with an additional parameter whose value depends on
2601-456: Was used in the group stage match between Sri Lanka and Zimbabwe at the T20 World Cup in 2010 . Sri Lanka scored 173/7 in 20 overs batting first, and in reply Zimbabwe were 4/0 from 1 over when rain interrupted play. At the restart Zimbabwe's target was reduced to 108 from 12 overs, but rain stopped the match when they had scored 29/1 from 5 overs. The retrospective D/L target from 5 overs was
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