How does the Duckworth-Lewis Method work?

Question

It is a method used for setting targets in cricket.

Answer 1

The D/L method of resetting targets in rain-affected one-day cricket matches has now been in operation for over four years and has been called into use on more than 200 occasions. It has been adopted by the International Cricket Council as the standard 'rain-rule' in the test playing countries and in many associate member countries for a two year period from Sept 1999 following its adoption for the 1999 World Cup competition

The method is the invention of Frank Duckworth and Tony Lewis. Frank is a consultant statistician and editor of the Royal Statistical Society's monthly news magazine, RSS NEWS. Tony is a lecturer in Quantitative Methods in Management in the Business School at Oxford Brookes University. The method was developed in the early part of the 1990s when Tony was working at the University of the West of England, Bristol and when Frank and Tony lived quite close to each other in Gloucestershire.

The method that they have invented is simple to apply provided one is prepared to take a few minutes to understand its logic. The calculations can easily be performed using nothing more than a single table of numbers and a pocket calculator although a purpose built computer program is available to undertake the calculations accurately and quickly in match situations (see further information on this below). With a little practice, however, there is no reason why anyone should not be able to calculate the revised target and in quick time. The authors firmly believe that the method is simple enough for it to be adopted for use at all levels of limited-overs cricket. Already this belief is being realised as the method is in use in several lower levels of competition, including, for example, some local leagues in England and Sydney Grade Cricket in Australia. This article provides a summary of the way the method works.

Basis of the method

The D/L method works using the notion that teams have two resources with which to make as many runs as they can - these are the number of overs they have to receive and the number of wickets they have in hand. From any stage in their innings, their further run-scoring capability depends on both these two resources in combination. The table gives the percentage of these combined resources that remain for any number of overs left and wickets lost. An extract from the table is given in Table 1. Information is provided later on how the full table can be obtained, including the ball-by-ball version which is used when stoppages occur mid-over.

When a match is shortened after it has begun, the resources of one or both teams are depleted and the two teams usually have different amounts of resource for their innings. In this case a revised target must be set. The D/L method does this in accordance with the relative resources available to the two teams. If stoppages cause the team batting second (referred to here as Team 2) to have less resources available, as is more often than not the case, then their target will be revised downwards. If, on the other hand, as often happens when Team 1's innings has been interrupted, the stoppages usually result in Team 2 having more resources available then their target is revised upwards to correct for the extra resources they have at their disposal

Answer 2

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 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. It is not used in first-class cricket or Test matches.

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History
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The D/L method was devised by two English statisticians, Frank Duckworth and Tony Lewis. 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.[1]

In 2001, it was formally adopted by the International Cricket Council as the standard method of calculating target scores in rain shortened one-day matches.

Previous methods used to achieve the same task included the use of run-rate ratios, the use of the score that the first team had achieved at the same point in their innings, and the use of targets derived by totalling the best scoring overs in the initial innings.

All of these older methods have flaws that are easily exploitable. 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. The best-scoring overs method, used in the 1992 Cricket World Cup, left the South African cricket team requiring 21 runs from one ball – where the maximum score from any one ball is generally six runs – where prior to the brief rain interruption, they had a target of 22 from 13 balls, a target that although difficult, was at least attainable, leaving an exciting conclusion to the game in prospect, a finish destroyed when the team was given the same target off 12 fewer balls.[2] These flaws are not present, or at least effectively normalised, by the D/L method.

Answer 3

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 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 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...

Answer 4

The D/L method of resetting targets in rain-affected one-day cricket matches has now been in operation for over four years and has been called into use on more than 200 occasions. It has been adopted by the International Cricket Council as the standard 'rain-rule' in the test playing countries and in many associate member countries for a two year period from Sept 1999 following its adoption for the 1999 World Cup competition

The method is the invention of Frank Duckworth and Tony Lewis. Frank is a consultant statistician and editor of the Royal Statistical Society's monthly news magazine, RSS NEWS. Tony is a lecturer in Quantitative Methods in Management in the Business School at Oxford Brookes University. The method was developed in the early part of the 1990s when Tony was working at the University of the West of England, Bristol and when Frank and Tony lived quite close to each other in Gloucestershire.

The method that they have invented is simple to apply provided one is prepared to take a few minutes to understand its logic. The calculations can easily be performed using nothing more than a single table of numbers and a pocket calculator although a purpose built computer program is available to undertake the calculations accurately and quickly in match situations (see further information on this below). With a little practice, however, there is no reason why anyone should not be able to calculate the revised target and in quick time. The authors firmly believe that the method is simple enough for it to be adopted for use at all levels of limited-overs cricket. Already this belief is being realised as the method is in use in several lower levels of competition, including, for example, some local leagues in England and Sydney Grade Cricket in Australia. This article provides a summary of the way the method works.

Basis of the method

The D/L method works using the notion that teams have two resources with which to make as many runs as they can - these are the number of overs they have to receive and the number of wickets they have in hand. From any stage in their innings, their further run-scoring capability depends on both these two resources in combination. The table gives the percentage of these combined resources that remain for any number of overs left and wickets lost. An extract from the table is given in Table 1. Information is provided later on how the full table can be obtained, including the ball-by-ball version which is used when stoppages occur mid-over.

When a match is shortened after it has begun, the resources of one or both teams are depleted and the two teams usually have different amounts of resource for their innings. In this case a revised target must be set. The D/L method does this in accordance with the relative resources available to the two teams. If stoppages cause the team batting second (referred to here as Team 2) to have less resources available, as is more often than not the case, then their target will be revised downwards. If, on the other hand, as often happens when Team 1's innings has been interrupted, the stoppages usually result in Team 2 having more resources available then their target is revised upwards to correct for the extra resources they have at their disposal .

ITS NOW USED OFFENTLY, THOUGH THE MATCH COULD ALSO BE PLAYED THE NEXT DAY.

Answer 5

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.

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.

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. 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.


Example
A simple example of the D/L method being applied was the first one-day International 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.

This is a relatively uncontroversial example, because with three full overs left to play (18 balls) and three wickets in hand, most cricket fans would agree that Pakistan would be almost certain to close the 17-run gap and take the match. In fact, application of the D/L method showed that at the end of the 47th over, the target was 304, so the result of the match is officially listed as "Pakistan won by 7 runs (D/L Method)".

Criticisms
Some observers believe that the D/L method does not take into account certain noticeable trends in the scoring rates during an innings, such as the sharp rise in difficulty as higher numbers of runs need to be scored per over, or the trend to increased scoring rates towards the end of an innings. However, any such trend that is statistically real over the historical record of one-day matches is automatically taken into account by the fact that the D/L tables use historical match data to determine the relationship between resources and run rates.

More detailed criticism is 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, it is more sensible not to lose wickets and score at just an above average rate (if the asking rate, for example, is 6.1, it's enough to score at 4.75 or 5 an over for the first 20-25 overs).

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

Answer 6

this method works only when 25 overs is completed in an innings of a cricket match. an average is calculated of the overs left and targets are being set by the match refree and other officials by keeping in mind about the overs left in the session. this system is helpful for team which are chasing the target, especially when target is huge.

Answer 7

Ask Sachin, please! He is worth a duck when it comes to the crunch. Be it a match in Karachi, in South Africa, or West Indies, or...He will score, but when it matters most..worth a duck or Duckworth.

By the way it is one of the most stupid systems devised in case a match does not go the full distance, i.e. it is curtailed. It is not worth an elaboration.

Answer 8

this method is a method used if weather or bad light or etc, stop a match. people then determine the run rate of those two teams, and see who wins based on the run rates.

Answer 9

Mysteriously!

Answer 10

The D/L method sets a revised target for the side batting second (Team 2) when overs have been lost by a suspension in play. The revision is not in proportion to the numbers of overs the two sides can receive but is in accordance with the run-scoring resources the two sides have at their disposal. These resources include both overs and wickets in combination.

A single table gives the resources remaining at any stage of an innings for any number of overs left and wickets lost. The resources are expressed in terms of the percentages of the resources of a full 50-over innings.

If either innings is shortened after it has started then the balance of resources of the two sides is upset and a revised target needs to be set in accordance with the resources available to the two sides. To find the resources available for either innings, you use the table to find out the resources lost from that innings and subtract this from the resources with which the innings started. If the innings started with 50 overs to be received, the resources at the start of the innings are 100%. But if the innings is shortened before it starts, or if the match is of less than 50 overs per side, then the resources at the start are less than 100%.

To find the resources lost from an innings due to an interruption:

(i) note the numbers of overs left and wickets lost at the start of the suspension; use the table to find the resources remaining

(ii) note the same at the resumption of play and from the table read off the resources now remaining

(iii) subtract (ii) from (i) to give the resources lost.

To find the resources available subtract the resources lost from the resources that were available when the innings started.

When a revised target has to be set, find the resources available for both sides and calculate the revised target as follows, always rounding down to a whole number.

If the resources available to Team 2 (denote this by R2) are less than those for Team 1 (R1), then the target is revised downwards in proportion to the resources.

Thus Team 2's revised target = Team 1's actual score x R2/R1, plus one run. (One run less than the target gives a tie.)

If the resources available to Team 2 are greater than those for Team 1, then Team 2's target must be revised upwards. The excess runs required are calculated by applying the excess resource to the average 50-over total of 235 (or whatever number is decided upon for the appropriate class of game).

Thus Team 2's revised target = Team 1's actual score + (R2 - R1) x 235/100, plus one run. (One run less than the target gives a tie.)

The Duckworth/Lewis method - General Information
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Background

The Duckworth/Lewis (D/L) method of target resetting in one-day cricket was first used early in 1997 and has since spread to most of the cricketing world. On 1 Sept 2001 the method became the official 'rain-rule' in use in all one-day competitions in ICC full, associate and affiliate member countries and is likely to be used also in domestic competitions in these countries. Its great virtue is that, unlike other methods of correction previously in use, it maintains the balance of the game across a suspension in play. If one team are in the ascendancy when play is halted and the match has to be shortened, they are still in the ascendancy, and by just as much, when play can resume with fewer overs remaining.

Concept of the method

The method is based on the concept that a match starts with both teams possessing the same resources to build their innings. They have a fixed number of overs to receive, usually 50 in international matches, and they have ten wickets to lose.

As the innings progresses these two resources are gradually used up and a single table of figures gives the percentages of the run scoring resources of the innings that remain for all possible combinations of overs left and wickets lost. The table has been constructed from a detailed study of the scorecards from many hundreds of one-day matches, mainly internationals, played over recent years.

If an innings is interrupted and has to be shortened, the table is used to find out what percentage of the resources are lost.

Any shortening of the match after it has started upsets the balance of resources and a revised target is necessary to compensate the team that have suffered the more. This is the case even if the two teams both end up with the same number of overs to receive.

The target adjustment is based on the relative run scoring resources available to the two sides after the resources lost by each team have been taken into account.

The table reflects the fact that the resources lost by a loss of a certain number of overs depend on:-

How many overs remained, and

How many wickets were down at the time.

For instance, a loss of overs near the end of an innings, especially when there are plenty of wickets still in hand, is usually a far greater loss of resource than the same loss of overs at the beginning of an innings.

How it works

Suppose the team batting first (Team 1) have completed their innings and an interruption occurs during the second innings. The team batting second (Team 2) will then have less resources for their innings than Team 1. In this case Team 2 will be set a reduced target based on the smaller amount of resources they had for their innings compared with Team 1.

But if an interruption occurs during Team 1's innings, it often happens that Team 2 end up with more resources for their innings than Team 1 have had and in this case their target is revised upwards to compensate Team 1 for the way they were more disadvantaged by the timing of the stoppage.

This is best understood by considering the case where Team 1's innings is curtailed after 40 of an intended 50 overs and Team 2 have just time to face the same 40 overs. Team 1 had been pacing their innings to last 50 overs and provided they had wickets in hand might have expected to have made 60 or 70 runs from the final 10 overs.

Team 2, on the other hand, knew they had only 40 overs to face from the moment they started their innings and were able to take greater risks to achieve a higher scoring rate right from the start. On average a team only make about 20 - 25 fewer runs from a 40-over innings than they make from a 50-over innings.

Par score

Provided that the minimum number of overs have been faced by each side, if a match has to be terminated before a result has been obtained, this is decided by comparing Team 2's score at the termination with the ‘par score' for their target. The par score is calculated in the same way as a revised target and is the score that Team 2 would have to have exceeded to win if the game were abandoned at that point. Like a revised target it depends on how many overs remain and wickets are lost.

If Team 2's innings has to be abandoned, Team 2 will win if they are ahead of the par score, by the amount that they are ahead. If they are behind par then Team 1 win by the corresponding amount. If they are equal to par, the match is tied.

During the progress of Team 2's innings, and regardless of whether or not rain is threatening, the par score provides a useful guide as to how Team 2 are performing relative to their target. This information is sometimes displayed on scoreboards, usually as the par score for the end of the over in progress.

The revised target

Match regulations dictate that a tied match will always be possible even when a revised target has been set. The revised target is the minimum number of runs that Team 2 require to win the game. The calculated score to beat is rounded down as necessary (i.e. ignore any figures after the decimal point) to give the score needed for a tie. The target is one more run than this.

For more information, please check the following links:

http://www.surreydowns.org/DL-Method.htm

http://en.wikipedia.org/wiki/Duckworth-Lewis_method