BBC SPORT | Cricket | Laws & Equipment | Rain-affected targets Laws & Equipment The Duckworth-Lewis method is used to help decide rain-interrupted one-day cricket matches. It is named after Frank Duckworth and Tony Lewis who devised the mathematical formula. It means a result can always be reached in a reduced overs match. WHEN IS IT USED? Teams start a match with the same resources - the number of overs they receive and number of wickets in hand. If a match is shortened once it is started, so the resources are reduced. For example, if the team which bats first had their innings interrupted, team two would often be set a larger run target to compensate. But should the team second at the stumps be interrupted, their run target would often be reduced. Duckworth and Lewis came up with the equation which determines how much a run target should be altered. HOW DOES IT WORK? For example: a team have lost five wickets after receiving 25 of their 50 overs when rain stops play. At this point, using the table produced by the Duckworth-Lewis method, the team's remaining resources are valued at 42.2%.

If 15 overs are then lost because of the weather, the innings will be completed after only 10 more overs. The D/L method says that, with 10 overs left and five wickets lost, the team has 26.1% of their resources left. To compensate for the lost overs, we must calculate the resource % lost. This works out to 42.2 - 26.1 = 16.1. If the team had been chasing a total of 250 runs, their new target is calculated in the following way. Resources available at the start = 100% Resources lost = 16.1 Resources available after rain interruption = 83.9% Then reduce team one's score in the following way. Multiply team one's runs scored by the recalculated resources divided by the resources available at the start. That is: 250 x 83.9/100 = 209.75. The target is then rounded to the nearest whole number, so the team batting second would be set a target of 210 to win. Simple! The Duckworth-Lewis method - explained!

| Sport | The Guardian The Duckworth-Lewis method - explained! Tuesday 4 March 2003 08.10 EST First published on Tuesday 4 March 2003 08.10 EST Share on Messenger Close The Duckworth-Lewis method. If every South African and New Zealander didn't know what it was before yesterday, they do now. Last night, host nation South Africa crashed out of the World Cup in excruciating circumstances after the Duckworth-Lewis method decreed that they had drawn their rain-affected match with Sri Lanka. That meant New Zealand qualified for the Super Sixes in their place. Had South Africa scored just one more run before the umpires took the players off, they would have gone through instead. So who or what are Duckworth-Lewis and is there any method in this madness? The D/L method, as it is known to its friends, is the brainchild of two British stattos and is the prevailing system used to adjust victory targets in one day internationals in the event of a rain delay. Stay with us. Frank Duckworth is a consultant statistician and editor of the Royal Statistical Society's monthly news magazine, RSS NEWS.

Tony Lewis is a lecturer in mathematical subjects in the Faculty of Computer Studies and Mathematics at the University of the West of England, Bristol and chairman of the Western Branch of the Operational Research Society. And through a combination of far too much time on their hands and painstaking analysis of lots of rain-affected matches, these chaps have come up with the now widely accepted method. Mathmos have long tried to work out a statistical program which fairly calculates revised targets in the event of rain, but this one has far fewer anomalies than its predecessors. When rain interrupts play, this statistically based program is designed to leave the balance of the match unaltered. The 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 still 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. "Where other, failed methods crucially overlooked the importance of wickets lost at the point of delay, the D/L method incorporates this factor into its involved tapestry of calculation," says Channel 4 cricket's jargon buster and analyst Simon Hughes.

"It is much easier to chase 100 runs with ten wickets left than with one wicket left, but the D/L method is the first of its kind to recognise this." The adjustments that the D/L method makes try to ensure that after a rain break, the status quo of the match is roughly retained so that no one team gains an unfair advantage. If the chasing side is ahead when rain arrives, then they are awarded the match if no further play is permitted. This has given rise to a whole new mentality for teams batting second. If a side is set 300 for victory - a tall order in any conditions - and rain is forecast, it is conceivable that they will go on the attack from the outset to try to stay 'in front' of the opposition. The necessary calculations can apparently be easily performed using nothing more than a single table of numbers and a pocket calculator. Fortunately for umpires who struggle just counting to six, a purpose-built computer program is available to undertake the calculations accurately and quickly in match situations. cricket - How is the Duckworth-Lewis Method applied? - Sports Stack Exchange How is the Duckworth-Lewis Method applied?

up vote 9 down vote favorite I have seen lots of matches in which the D/L method was used to decide victory, but I never found out how it actually works. I know there are two keys in this method: overs and wickets in hand. Can anyone please explain it? And why does it not apply in test matches? 2 I don't think anyone (even Duckwork and Lewis) knows it to the core. The most confusing thing about Cricket – Krishnabhadra Aug 9 '13 at 11:36 3 Plenty of people who've taken the time to read the details understand it. If you read the original paper by Duckwork and Lewis jstor.org/stable/3010471?origin=JSTOR-pdf you'll see they understand it pretty well. Please don't project your willful ignorance onto everyone else. – Bogdanovist Aug 10 '13 at 8:53 Duckworth-Lewis method FAQ Despite much confusion amongst the media, the players, and the public, the actual principle is relatively simple.

When an interruption causes one team to have less resources available than the other team, the target is proportionally adjusted in the ratio of the resources available to each team. For instance, if an interruption reduces the resources of the side batting second (Team 2) by 50% in comparison to Team 1's resources, the target would be reduced by 50%. As you correctly mentioned, resources are composed of both wickets and overs. The D/L method does not add or subtract wickets or overs; it simply calculates what the target should be, given those resources. While the principle is simple, it raises plenty of questions for discussion. I would strongly recommend reading the FAQ linked above, as they clarify many common queries. Test Matches do not use the Duckworth-Lewis method because the number of overs per innings is not defined in a Test Match. Furthermore, a draw is a perfectly acceptable result in a Test Match. up vote -1 down vote If any interruption occurs by rain or audience duckworth luis method is applied to the team that takes batting in second innings of that match.It works on reducing overs limit.

For example if team A makes170 runs for two wicketsafter 33.2 overs and match gets disturbed by rain,then the number of overs will be reduced to42 overs from 50.Number of overs to reduce depends on resources available i,e overs and wickets.probability works here asuming tht if team A plays 50 overs it might have done 296 runs in 42 0vers where the match overs limit was made.soteam B has to do297 runs in 42 overs to win the match .

If team B can't win, it is not completely due to duckworth law as before beginning of 2nd innings itself a sheet will be given to captain stating at what runs will win the match if match stops at what over The Duckworth Lewis Method: 'Cricket forces you to sit on your arse, which is healthy' | Music | The Guardian The Observer The Duckworth Lewis Method: 'Cricket forces you to sit on your arse, which is healthy' Neil Hannon and Thomas Walsh explain why their new album coincides with the Ashes – and why they approve of streaking The Duckworth Lewis Method's Neil Hannon, left, and Thomas Walsh at Lord's: 'Nude hurdling of the stumps is an art.' Photograph: Sarah Lee for the Guardian Saturday 22 June 2013 19.05 EDT First published on Saturday 22 June 2013 19.05 EDT Share on Messenger Close Scour the official calendar of world cricket and you'll surely notice something missing.

Yes, the forthcoming jaunts of the Test-playing nations around the grounds of the world are listed, enabling you to discover whether or not a given city has a Walkabout pub in which to witness an Australian player lamping an English player . But nowhere does the future tours programme make reference to what has become the unofficial opening of an Ashes summer: the release of an album from the Duckworth Lewis Method . Neil Hannon of the Divine Comedy and Thomas Walsh of Pugwash raised the curtain on England's defeat of Australia in 2009 with their first album of cricket-themed, ELO-adoring whimsy. And now the Australians have returned, so have they, with Sticky Wickets, another album of cricket-themed, ELO-adoring whimsy, this time emblazoned with a cover photo of Michael Angelow, the merchant seaman who sprinted naked on to the pitch in the Lord's Test of 1975 to hurdle the stumps , mid-match. Though we are at the site of Angelow's infamy, neither Hannon nor Walsh will be repeating his feat: it is extraordinarily chilly at Lord's as Yorkshire pile on the runs against Middlesex.

Hannon's pith helmet looks less necessary than his white cricket jumper, and both he and Walsh sip hot coffee rather than cold beer. But the home of cricket is the place where the pair have come to unveil their manifesto for cricket and music to a watching world. A watching world of me, a steward and a man with a Tupperware container of ham sandwiches. Clause one: don't believe people who say cricket and rock'n'roll don't mix "It's actually the most rock'n'roll of sports, bizarrely," Hannon says. "Witness the amount of famous rock'n'roll stars who love cricket." Walsh proceeds to list the cricket-loving supergroup a promoter could assemble – Mick Jagger, Eric Clapton, Jeff Lynne, the late George Harrison, if he could play from beyond the grave. Lily Allen, too, "for a bit of female vocals". "That chap from Razorlight," adds Hannon. "The list is endless." What makes cricket so rock'n'roll, Walsh insists, is its duration. "Five days of going out to see a sports game – that's rock'n'roll." He pauses to applaud the century partnership between Yorkshire's Adil Rashid and Andrew Gale.

" These big rock'n'rollers haven't got a second of spare time, but they dedicate five days of it for Tests." "That's right," nods Hannon. "Proportionately, it's bigger than football." Walsh's early cricketing hero, Bob Willis, took the combination of rock'n'roll and greensward to its natural conclusion, adding Dylan as a middle name by deed poll. Though when one hears him speak as a commentator on Sky Sports, it's hard not to wonder if there is anyone less Dylanesque and mercurial in the world. "When he starts talking he reminds me of a Dalek after a stroke," Walsh agrees, sunnily. Hannon giggles, then sighs. "Oh God, don't put that in. If we ever meet him …" "But he does sound like that!" Walsh protests. "I'm just being honest. I love him. But he does sound like that." Duckworth Lewis Method - Barretstown 2010 Performance on MUZU.TV . Clause two: beautiful language must be part of both sport and music "The language of cricket is part of the reason we are writing about it," Hannon says.

They cite the broadcasters whose idiosyncratic approach has inspired them – David "Bumble" Lloyd, for example, who coined the nickname "Boom Boom" for the big-hitting Pakistan batsman Shahid Afridi and thereby inspired the song Boom Boom Afridi. "I love my British psychedelia," Walsh says. "Cricket and its terms lend themselves to that kind of Lewis Carroll, I Am the Walrus period of music – that kind of 19th-century prose that was around in the 1960s." "I don't want to talk about other sports," Hannon concludes. "But the language of tiddlywinks is beautiful." Clause three: streaking – and all the things of which pundits say "No one likes to see that" – should be encouraged. "Everybody likes to see that," Hannon observes, correctly. "What is the sense in showing a slow motion of a bad injury, or spitting on the pitch, but not someone running across in the nip?" Walsh wonders. "I'd definitely be in favour of streaking, but only the attractive ones." "Mr Angelow's pose was too good to ignore," Hannon says of the album cover. "And it's totally rock'n'roll.

The nude hurdle of the stumps is an art. It's very difficult. I know if I attempted it, I'd just crash through them." Clause four: cricket should be employed to teach patience to the young "That's it!" exclaims Hannon, explaining that the very joy of the sport – of anything good, really – is that it lasts long enough to offer complete immersion. "Surely," he says, "if you like sport, the longer it goes on for, the better. What I find in this modern-paced life in which we live, I find it very hard to sit on my arse and do nothing. It's very hard not to pick up the phone and start doing stuff with it. Concentration spans are definitely diminishing. Nobody can sit on the bus and just stare into space any more.

Cricket actually forces you to sit on your arse, which is healthy." Clause five: no pop music should be played during any sporting event (with one exception) A blight on football and cricket in recent years has been the inappropriate anthem – the music played over the PA when a goal is scored, or blared out to a few hundred people at Tring when an unknown No 8 comes out to bat in a dead one-day match. The Duckworth Lewis Method do not approve. "It cheapens the game, no matter how good the music might be. What's the music supposed to be for?" Hannon asks. To make younger people feel cricket must be a go-ahead kind of a sport, to play a few bars of Crazy in Love, perhaps? "And they put some half-naked dancers out there in the freezing cold," Walsh says, shuddering at the thought, before coming to another conclusion. "But hopefully, our tracks will be played over every Tannoy of every game when a player is walking out." In England? "All over the world," Hannon insists. And then the lunch bell sounds. The players of Yorkshire and Middlesex troop off to the pavilion and Walsh and Hannon rise.

There are top-level meetings with the nabobs of English cricket to attend. There is an Ashes campaign to plan. There is, almost certainly, a buffet lunch somewhere. It's the cricket season, after all. Sticky Wickets is released on 1 July on Divine Comedy Records Wolfram Demonstrations Project SNAPSHOTS DETAILS Cricket is a sport that, more than most, needs dry weather, yet it was invented in a rainy country and is played in several others. Moreover, unlike, say, baseball, it is a time-limited game, meaning that losing time to rain can affect a match profoundly. In the oldest form of the sport, this is a problem that takes care of itself, since a rain-interrupted match can simply end with neither team winning. But in the newer (only half a century old!) format of limited overs cricket, that cannot happen, and the need therefore arises of settling rain-affected matches in a way that is fair to both teams, even if the burden of disruption has been uneven. Until quite recently, this was generally done pretty crudely. But starting in the late 1990s, various more-sophisticated algorithms have been proposed.

The one that is used almost universally is the Duckworth–Lewis method, which is based on the idea of resources. In limited overs cricket, each team bats just once. A team's turn at batting (its innings) is over either when it has faced a certain preset number of balls (a bit like pitches in baseball) or when ten of its batsmen are out. The team therefore has two kinds of resources that it can convert into scoring: the number of balls yet to face and the number of batsmen in reserve. The Duckworth–Lewis method involves placing a numerical value on all possible combinations of these resources. By convention, balls are divided into sets of six, called overs. The number of batsmen out so far, out of ten, is called the number of wickets fallen. The Duckworth–Lewis method uses a table to assign a numerical value based on the number of overs (and parts of an over) yet to face and the number of wickets fallen. If the match is uninterrupted by rain, things are straightforward: whichever team scores more runs wins. This is what usually happens. But if rain interrupts either of the innings (or both), the method is invoked.

A calculation is made of the resources at the time of suspension and at the time of resumption (the number of wickets fallen does not change, but the number of overs will be reduced according to the time lost). The difference, the resources lost, is subtracted from the resources at the start of the innings to yield the resources available to the team. There are two such "resources available" figures, one for each team, conventionally expressed as percentages: and runs. If (as usually happens) , then Team 2’s target, , is given by is the floor function (or greatest integer function). If , a different formula is used, namely . (In the Demonstration code, I have added 1.001 instead of 1 inside Floor to correct for problems arising from rounding error.) In this Demonstration, a fairly sparse Duckworth–Lewis table is used, and Interpolation fills in the gaps. Each resource percentage depends on two arguments: overs and wickets. A separate interpolation is carried out for each value of wickets: each should ideally be monotonic in overs, and interpolation orders have been chosen empirically to make this as close to true as possible in all cases.

You can interactively set both teams’ scores (given in runs and wickets fallen), as well as allowing either team's innings, or both, to be interrupted: after a certain number of overs, for a certain number of overs, and with a certain number of wickets having fallen at the time of interruption. You can see a simulated cricket scoreboard (Snapshot 1), or view a graphical illustration of how either team's resource figures are arrived at (Snapshot 2); you can also see the calculation of Team 2's scoring target based on these resource figures (Snapshot 3). All four of these displays—the scoreboard, the two resource diagrams, and the calculation—change interactively when you use the controls. Disclaimer: this demonstration is for illustrative purposes only; it uses values associated with international matches, and should not be used for settling amateur cricket matches. It is an implementation of the public-domain Standard Edition of the Duckworth–Lewis method, rather than the proprietary Professional Edition; targets given may therefore differ slightly from the official values. Reference [1] Wikipedia. "Duckworth-Lewis method." (Nov 5, 2015) in.yimg.com/icccricket/pdfs/d-l_method.pdf .

PERMANENT CITATION Duckworth Lewis Calculator | DL Calculator for Cricket Android In the sport of cricket, the Duckworth Lewis calculator is a mathematical way to calculate the match results and points of Team A and Team B in a one - day or Twenty20 cricket match, when the match has been interrupted by weather or other such natural circumstances. The below DL calculator for cricket helps you to identify which team is the winner based on the inputs such as Team A scores, Team B Scores, runs and wickets during an interrupted match. DL Calculator for Cricket What is the Duckworth-Lewis method and how exactly does it work? - Quora What is the Duckworth-Lewis method and how exactly does it work? How do I calculate runs required from a given scenario? Update Cancel Question merged You were redirected because this question was merged with Cricket (sport): How does the Duckworth Lewis (d/l) method work? Answer Wiki The Duckworth Lewis method is a set of formulas and tables adopted by the International Cricket Council (ICC) in 1999 to address the problem of cricket matches shortened by rain, poor light and floodlight failures or other unforeseen events.

40 Answers Written Feb 26, 2015 The Duckworth-Lewis method is based on the concept of batting resources, and calculates targets by taking into account the remaining resources after an interruption. The method was first proposed in the paper 'A Fair Method for Resetting the Target in Interrupted One-Day Cricket Matches' by FC Duckworth and AJ Lewis, in the Journal of the Operational Research Society in 1998. While formulating the method, Duckworth and Lewis (hereafter DL), took into account certain stipulations that their new method must adhere to. It must be almost equally fair to both sides, furnish realistic targets that are independent of the first team's scoring pattern (as it is in normal games), and it should be easy to apply and comprehend. The method begins by recognizing that the side batting has with it two resources that can be quantified at any point in the innings: the overs remaining, and the wickets in hand. The ability of team to score is directly dependent on these two resources. At the point of interruption, the aim of the method is to basically reset the target score based on the change in these resources for the chasing team.

For this, DL quantify the relationship between the runs that can be scored with the set of available resources. They begin with the expression for the runs that can be made in [math]u[/math] overs: [math]Z(u) = Z_{0}[1 - exp(-bu)][/math] Here, [math]Z_{0}[/math] are the hypothetical average runs a team can score given infinite overs. This factor is calculated using average ODI scoring rates. The factor [math]b[/math] is the exponential decay factor that decays the runs scored, scaling it down based on the number of overs available. So, you can see, in infinite overs a team would score [math]Z_{0}[/math] runs, but this is reduced by a difference of [math]Z_{0}exp(-bu)[/math] in the case of [math]u[/math] overs remaining. This expression is now to be modified to include the effect of having lost some number of wickets. For this, DL simply modify the factors [math]Z_{0}[/math] and [math]b[/math] to include the effect of wickets.

We now have [math]Z_{0}(w)[/math], the runs scored in infinite overs if you have [math]w[/math] wickets down. Similarly, we have [math]b(w)[/math], the decay factor in the case of having [math]10-w[/math] wickets left. This makes sense: the number of runs you can score get affected by the wickets left. The logical assumption here is that more the number of wickets you have left, the more resources you can make, and thus, greater the runs you can make from that point on. Bear in mind, that the two essential functions here, [math]Z_{0}(w)[/math] and [math]b(w)[/math], are empirically calculated after computing scores at different points of hundreds of ODI matches. They are then fit into analytical forms that give sensible values and smooth derivatives for all values of [math]w[/math]. The full form of both these functions is not made public, and they keep getting updated.

Here is a graph of the runs scored as a function of the two parameters from the DL paper: The current tables and graphs might be different, as this is from a 1998 paper. You can clearly see the graphs mimicking expected behaviour. The less the wickets lost, the more the runs you are expected to score for the same number of overs remaining. With this done, we can calculate the proportion of runs remaining to be scored when a certain number of overs remain and a certain number of wickets are down. The expected score at the start of an innings is (N overs and 0 wickets down): [math]Z(N,0)[/math] After facing [math]u[/math] overs and with [math]w[/math] wickets down, this comes down to: [math]Z(u,w)[/math] The proportion of runs to be scored is: [math]P(u,w) = \frac{Z(u,w)}{Z(N,0)}[/math] This is the central number in setting revised scores, as we shall see. Now, let us begin with the case where there is an interruption in the innings of the chasing side.

They have [math]u_{1}[/math] overs remaining and are [math]w[/math] wickets down when play is stopped. When they return, they now only have [math]u_{2}[/math] overs left. As a result of this, they have lost [math]u_{1} - u_{2}[/math] overs. The run-scoring resources they have lost as a result are: [math]P(u_{1},w) - P(u_{2},w)[/math]. So now, the resources they have left are: [math]R = 1 - (P(u_{1},w) - P(u_{2},w)) [/math] If they were chasing [math]T[/math] runs, their revised target is simply:[math]RT[/math] runs. This makes sense, because we multiply the target by the proportion of resources lost due to the interruption. Similarly, we can also compute the par score at every point in the innings. In case the innings stops at that point, the par score monitors the target of the chasing team.

If [math]n[/math] overs have been bowled, and the team chasing is [math]w[/math] wickets down, they have used a proportion [math]R_{u} = 1 - P(N-x,w)[/math] of their resources. Since they have used this much, the score they should have made by this point is simply their target scaled by the resources used: [math]R_{u}T[/math]. In a different set of cases, sometimes overs are lost in the innings of the team batting first, and then the chasing team is given the same number of overs as the setting team. In this instance, the DL method recognizes that overs lost at different points in the innings have different impacts on the scoring ability of Team 1. They factor this in, and provide a method to set revised scores for Team 2. The method recognizes that Team 1 loses coring opportunities through unplanned interruptions, and thus it is only fair to scale the target for Team 2 to take this into account. Suppose Team 1 stops with [math]u_{1}[/math] overs left and comes back to bat with [math]u_{2}[/math] overs left.

They now have: [math]R_{1} = 1 - (P(u_{1},w) - P(u_{2},w))[/math] as the proportion of resources remaining. At the beginning of their innings, with some reduced number of overs, let us say Team 2 has [math]R_{2}[/math] resources remaining. The revised target is now set by comparing the two teams' resources available. If the two are equal, then the target for Team 2 is simply the same as Team 1's final score. If the resources available to Team 2 are less than [math]R_{1}[/math], then a simple scaling is done by multiplying Team 1's final score with the ratio of the resources. DL find in their paper that if the resources for Team 2 are greater than those of Team 1, the scaling method often leads to unrealistic targets. However, they agree that the target should be greater than Team 1's final score.

To resolve this with an easy-to-use method, DL multiply the difference of resources [math]R_{2} - R_{1}[/math] by the average score of all innings of [math]N[/math] overs, where [math]N[/math] is the complete number of overs of the uninterrupted match. They then add this value to the final score of Team 1. [math] T_{Team2} = S_{Team1} + Avg(N)[R_{2} - R_{1}][/math] Phew! The following is an excerpt from a document by the Northwich Cricket Club, as a summarized guide for applying the DL method: The procedure for setting a revised target, which is the same for any number of stoppages at any stage of the match, is as follows. For each team's innings (a) from the table note the resource percentage the team had available at the start of their innings; (b) using the table, calculate the resource percentage lost by each interruption; (c) hence calculate the resource percentage available. If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams.

Team 2's revised target is obtained by scaling down Team 1's score by this ratio. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of the average 50 over score and this gives the extra runs to add on to Team 1's score to give Team 2's target. They also have worked examples for multiple cases. For applying this method, you can find multiple online calculators, and even an Android App. Updated May 8, 2015 Contrary to popular belief, Duckworth-Lewis is actually very easy to understand. It's also a highly efficient means of predicting a total after rain interruptions. The following score-card is why Duckworth Lewis Method Exists. Previous methods would sometimes give erratic results, disastrous for teams (like South Africa in this case ). Note: People often sight this image as an example of D/L Method's inaccuracies but it isn't, the method used in the match in question was not D/L but an older rule called the "Highest Scoring Overs Method" (1).

I'll be using notes on pen and paper to explain the rules, as I found that easier and faster to use mathematical notations (Please excuse my slightly sloppy handwriting). -- The D/L method works using the notion that teams have two resources to make runs - these are: the number of overs left 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. 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. If stoppages cause the team batting second (Team 2) to have less resources available, then their target will be revised downwards. If, on the other hand, when Team 1's (Batting first) innings has been interrupted, the stoppages result in Team 2 having more resources available, then their target is revised upwards to compensate for the extra resources they have at their disposal. Calculating Resources. Each cell of this table represents Resources ‘left’ with team on that situation.

For example: Resources left after 42 overs and with 4 wickets remaining = 19.9% (R(8,6)) How to calculate the revised targets after 'n' rain interruptions: If Team 2 : have less resources available than Team 1, then, calculate the ratio of the resources available to the two teams. (R2/R1) Team 2's revised target is obtained by scaling down Team 1's score by this ratio. (As shown in the above image) However, If Team 2: have more resources available than Team 1, then, calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of 225 and this gives the extra runs to add on to Team 1's score to give Team 2's target. 225 is the par score for a 50 overs match. -- 1. Here's how the Highest Scoring Overs Method Worked: Compare the maximum runs scored by team1 in any set of overs (not necessarily consecutive) equal to the number of completed overs received by team2 against the team2 in those completed overs.

So if team2 received 36.3 overs their score after 36 overs is compared to the highest scoring 36 overs of team1's innings (so could be any 36 of the 50 overs). Just goes to show how much better the D/L method is. 2. The table mentioned is for the Standard Edition (Used until 2004), For international matches a Professional Edition is used. The Professional Edition uses a computer program instead of a manual calculation. The table for that is slightly different, but isn't available for the public. However, the difference in the scores isn't very big. The Table hasn't been updated since 2002, however, Duckworth did suggest a change back in 2009, to account for newer formats. -- Updated Sep 19, 2013 The Duckworth–Lewis method (often written as D/L method) is a mathematical formulation designed to calculate the target score for the team batting second in a limited overs match interrupted by weather or other circumstances. It is generally accepted to be the most accurate method of setting a target score. The D/L method was devised by two English statisticians, Frank Duckworth and Tony Lewis .

The basic principle is that each team in a limited-overs match has two resources available with which to score runs: wickets remaining, and overs to play. Where overs are lost, setting an adjusted target is not as simple as to reduce the batting team's run target proportionally, because a team batting second with ten wickets in hand and 25 overs to play can be expected to play more aggressively than one with ten wickets and a full 50 overs, and can consequently achieve a higher run rate. The Duckworth–Lewis method is an attempt to set a statistically fair target for the second team's innings, based on the score achieved by the first team, taking their wickets lost and overs played into account. 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 still 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 single table gives the percentage of these combined resources that remain for any number of overs left and wickets lost.

An extract of the over-by-over table is given in Table 1. (A ball-by-ball version of the table has also been produced to enable scorers to deal with instances when play is interrupted 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 run-scoring 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 result in Team 2 having more resources available, then their target is revised upwards to compensate for the extra resources they have at their disposal.

Table 1: Extract from the table of resource percentages remaining Wickets lost Overs left 0 2 5 7 9 60 107.1 87.9 50.0 26.5 7.6 50 100.0 83.8 49.5 26.5 7.6 40 90.3 77.6 48.3 26.4 7.6 30 77.1 68.2 45.7 26.2 7.6 25 68.7 61.8 43.4 25.9 7.6 20 58.9 54.0 40.0 25.2 7.6 10 34.1 32.5 27.5 20.6 7.5 5 18.4 17.9 16.4 14.0 7.0 Reading the table The single table applies to all lengths of one

-day matches from 60 overs-per-side downwards.

[In 1997 there was a separate table for all lengths of matches from 60 to 10 overs per side.] Because 50 overs-per-side matches are by far the most common, the resources listed in the table are expressed as percentages of those available at the start of a 50 over innings. Thus when there are 50 overs still to be received and no wickets have been lost, the resource percentage available is 100%. 60 over innings start with a resource percentage of 107.1% compared to a 50 over innings and 40 over innings start with a resource percentage of 90.3% compared to a 50 over innings. In order to determine the correct resource percentage the batting side has remaining at any stage of an innings, the number of overs left must be identified. This number of overs left, in conjunction with the number of wickets lost, is then used to read the resource percentage remaining from the table. For example, suppose that after 20 out of 50 overs a team have lost 2 wickets. They have 30 overs left.

From the table you will see that the resource percentage remaining is 68.2%. Suppose now that there is an interruption in play and 10 overs are lost from the innings of the batting side. When play can resume there are only 20 overs left but there are still, of course, 2 wickets down, and the table now tells us that the resource percentage remaining is 54.0%. Thus the shortening of the innings has caused the team to lose a resource percentage of 68.2 - 54.0 = 14.2%. Having started with a resource percentage of 100% and lost 14.2%, then if they complete their innings with no further loss of overs, they will have had a resource percentage available for their innings of 100 - 14.2 = 85.8%. Applying the D/L method The procedure for setting a revised target, which is the same for any number of stoppages at any stage of the match, is as follows.

For each team's innings (a) from the table note the resource percentage the team had available at the start of their innings; (b) using the table, calculate the resource percentage lost by each interruption; (c) hence calculate the resource percentage available. If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams. Team 2's revised target is obtained by scaling down Team 1's score by this ratio. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of 225 [the average 50 over score in ECB matches and one-day internationals (ODIs)] and this gives the extra runs to add on to Team 1's score to give Team 2's target. Worked examples Example 1: Premature curtailment of Team 2's innings Team 1 have scored 250 runs from their 50 available overs and Team 2 lose 5 wickets in scoring 199 runs in 40 overs.

Play is then stopped by the weather, the rain refuses to relent and the match is abandoned. A decision on the winner is required. Team 1's innings: this was uninterrupted, so the resource percentage available is100%. Team 2's innings: resource % available at start of innings = 100% After 40 overs Team 2 have 10 overs left and have lost 5 wickets. From table, resource % left at suspension of play = 27.5% As play is abandoned all this remaining resource is lost. Hence resource % available for Team 2's innings = 100 - 27.5 = 72.5% Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 72.5/100 Team 1 scored 250, so Team 2's 'target' is 250 x 72.5/100 = 181.25 As there is to be no further play, the winner is decided according to whether or not this target has been exceeded.

With 199 runs on the board, they have exceeded their required target by 17.75 and so are declared the winners by 18 runs. Note : The above result is quite fair as Team 2 were clearly in a strong position when play was stopped and would very likely have gone on to win the match if it hadn't rained. Most other methods of target revision in use would, unfairly, make Team 1 the winners. The average run rate method gives 201 to win, the Current ICC method gives 227 and the parabola method gives 226.

[Setting the target by the method of Discounted Total Runs - the Australian rain-rule - requires knowledge of the runs made by Team 1 from their most productive overs but the target would almost certainly be no lower than that required under average run rate and would probably be much higher so that Team 2 would very probably lose by this method as well.] Example 2: Interruption to Team 2's innings In an ECB Axa Life (Sunday) League match Team 1 have scored 200 runs from their 40 available overs and Team 2 lose 5 wickets in scoring 140 runs in 30 overs. Play is then suspended and 5 overs are lost. What is Team 2's revised target? Team 1's innings: At the start of 40 over innings resource percentage available =90.3% Team 2's innings: resource % available at start of 40 over innings = 90.3% After 30 overs Team 2 have 10 overs left and have lost 5 wickets.

From table, resource % left at start of suspension = 27.5% 5 overs are lost, so when play is resumed 5 overs are left. From table, resource % left at resumption of play = 16.4% Hence resource % lost = 27.5 - 16.4 = 11.1% so resource % available for Team 2's innings = 90.3 - 11.1 = 79.2% Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 79.2/90.3 Team 1 scored 200, so Team 2's target is 200 x 79.2/90.3 =175.42, or 176 to win, and they require a further 36 runs from 5 overs with 5 wickets in hand.

Example 3: Interruption to Team 1's innings In an ODI, Team 1 have lost 2 wickets in scoring 100 runs in 25 overs from an expected 50 when extended rain leads to Team 1's innings being terminated and Team 2's innings is also restricted to 25 overs. What is the target score for Team 2? Because of the different stages of the teams' innings that their 25 overs are lost, they represent different losses of resource. Team 1 have lost 2 wickets and had 25 overs left when the rain arrived and so from the table you will see that the premature termination of their innings has deprived them of the 61.8% resource percentage they had remaining. Having started with 100% they have used 100 - 61.8 = 38.2%; in other words they have had only 38.2% resources available for their innings. Team 2 will also receive 25 overs.

With 25 overs left and no wicket lost you will see from the table that the resource percentage which they have available (compared to a full 50 over innings) is 68.7%. Team 2 thus have 68.7 - 38.2 = 30.5% greater resource than had Team 1 and so they are set a target which is 30.5% of 225, or 68.63, more runs than Team 1 scored. [225 is the average in 50 overs for ODIs] Team 2's revised target is therefore set at 168.63, or 169 to win in 25 overs, and the advantage to Team 2 from knowing in advance of the reduction in their overs is neutralised. Note: Most of the other target resetting methods in use make no allowance for this interruption. They set the target of 101 to win simply because both teams are to receive the same number of overs.

This is clearly an injustice to Team 1 who were pacing their innings to last 50 overs when it was curtailed, whereas Team 2 knew in advance of the reduction of their innings to 25 overs and have been handed an unfair advantage. D/L allows for this by setting Team 2 a higher target than the number of runs Team 1 actually scored, as described above. Credits: Cricinfo - Duckworth-Lewis "The Duckworth-Lewis Method An introduction to the D/L (Duckworth/Lewis) method of resetting targets in interrupted one-day cricket matches by Frank Duckworth & Tony Lewis The D/L method of resetting targets in rain-affected one-day cricket matches was trialled successfully during 1997 by the International Cricket Council(ICC), the ECB (England & Wales Cricket Board) and the Zimbabwe Cricket Union (ZCU). It has already been chosen for use in 1998 by the ECB, the ZCU and New Zealand. 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 mathematical subjects in the Faculty of Computer Studies and Mathematics at the University of the West of England, Bristol and chairman of the Western Branch of the Operational Research Society Following the experience of the method's application in 1997 they have introduced a few modifications designed to make the method's use even simpler. This article provides a summary of the way the method works. Contrary to the belief in some quarters, it does not require a degree in mathematics either to understand it or to use it! Although a purpose-written computer program is available to countries adopting the system to enable calculations to be performed speedily and accurately, this is not necessary. All calculations can easily be performed using nothing more than a single table of numbers and a pocket calculator. With a little practice there is no reason why anyone should not be able to calculate the revised targets more-or-less instantly. The authors firmly believe that the method is simple enough that it could be adopted for use at all levels of limited overs cricket 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 still 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 single table gives the percentage of these combined resources that remain for any number of overs left and wickets lost. An extract of the over-by-over table is given in Table 1. (A ball-by-ball version of the table has also been produced to enable scorers to deal with instances when play is interrupted 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 run-scoring 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 result in Team 2 having more resources available, then their target is revised upwards to compensate for the extra resources they have at their disposal.

Table 1: Extract from the table of resource percentages remaining Wickets lostOvers left0257960107.187.950.026.57.650100.083.849.526.57.64090.377.648.326.47.63077.168.245.726.27.62568.761.843.425.97.62058.954.040.025.27.61034.132.527.520.67.5518.417.916.414.07.0 Reading the table The single table applies to all lengths of one-day matches from 60 overs-per-side downwards.

[In 1997 there was a separate table for all lengths of matches from 60 to 10 overs per side.] Because 50 overs-per-side matches are by far the most common, the resources listed in the table are expressed as percentages of those available at the start of a 50 over innings. Thus when there are 50 overs still to be received and no wickets have been lost, the resource percentage available is 100%. 60 over innings start with a resource percentage of 107.1% compared to a 50 over innings and 40 over innings start with a resource percentage of 90.3% compared to a 50 over innings. In order to determine the correct resource percentage the batting side has remaining at any stage of an innings, the number of overs left must be identified. This number of overs left, in conjunction with the number of wickets lost, is then used to read the resource percentage remaining from the table. For example, suppose that after 20 out of 50 overs a team have lost 2 wickets. They have 30 overs left.

From the table you will see that the resource percentage remaining is 68.2%. Suppose now that there is an interruption in play and 10 overs are lost from the innings of the batting side. When play can resume there are only 20 overs left but there are still, of course, 2 wickets down, and the table now tells us that the resource percentage remaining is 54.0%. Thus the shortening of the innings has caused the team to lose a resource percentage of 68.2 - 54.0 = 14.2%. Having started with a resource percentage of 100% and lost 14.2%, then if they complete their innings with no further loss of overs, they will have had a resource percentage available for their innings of 100 - 14.2 = 85.8%. Applying the D/L method The procedure for setting a revised target, which is the same for any number of stoppages at any stage of the match, is as follows.

For each team's innings (a) from the table note the resource percentage the team had available at the start of their innings; (b) using the table, calculate the resource percentage lost by each interruption; (c) hence calculate the resource percentage available. If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams. Team 2's revised target is obtained by scaling down Team 1's score by this ratio. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of 225 [the average 50 over score in ECB matches and one-day internationals (ODIs)] and this gives the extra runs to add on to Team 1's score to give Team 2's target. Worked examples Example 1: Premature curtailment of Team 2's innings Team 1 have scored 250 runs from their 50 available overs and Team 2 lose 5 wickets in scoring 199 runs in 40 overs.

Play is then stopped by the weather, the rain refuses to relent and the match is abandoned. A decision on the winner is required. Team 1's innings: this was uninterrupted, so the resource percentage available is100%.Team 2's innings: resource % available at start of innings =100%After 40 overs Team 2 have 10 overs left and have lost 5 wickets. From table, resource % left at suspension of play =27.5%As play is abandoned all this remaining resource is lost. Hence resource % available for Team 2's innings = 100 - 27.5 =72.5% Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 72.5/100 Team 1 scored 250, so Team 2's 'target' is 250 x 72.5/100 = 181.25 As there is to be no further play, the winner is decided according to whether or not this target has been exceeded.

With 199 runs on the board, they have exceeded their required target by 17.75 and so are declared the winners by 18 runs. Note : The above result is quite fair as Team 2 were clearly in a strong position when play was stopped and would very likely have gone on to win the match if it hadn't rained. Most other methods of target revision in use would, unfairly, make Team 1 the winners. The average run rate method gives 201 to win, the Current ICC method gives 227 and the parabola method gives 226.

[Setting the target by the method of Discounted Total Runs - the Australian rain-rule - requires knowledge of the runs made by Team 1 from their most productive overs but the target would almost certainly be no lower than that required under average run rate and would probably be much higher so that Team 2 would very probably lose by this method as well.] Example 2: Interruption to Team 2's innings In an ECB Axa Life (Sunday) League match Team 1 have scored 200 runs from their 40 available overs and Team 2 lose 5 wickets in scoring 140 runs in 30 overs. Play is then suspended and 5 overs are lost. What is Team 2's revised target? Team 1's innings: At the start of 40 over innings resource percentage available =90.3%Team 2's innings: resource % available at start of 40 over innings =90.3%After 30 overs Team 2 have 10 overs left and have lost 5 wickets. From table, resource % left at start of suspension =27.5%5 overs are lost, so when play is resumed 5 overs are left.

From table, resource % left at resumption of play =16.4%Hence resource % lost = 27.5 - 16.4 =11.1%so resource % available for Team 2's innings = 90.3 - 11.1 =79.2% Team 2 had less resource available than Team 1 so their target must be scaled down by the ratio of resources, 79.2/90.3 Team 1 scored 200, so Team 2's target is 200 x 79.2/90.3 =175.42, or 176 to win, and they require a further 36 runs from 5 overs with 5 wickets in hand. Example 3: Interruption to Team 1's innings In an ODI, Team 1 have lost 2 wickets in scoring 100 runs in 25 overs from an expected 50 when extended rain leads to Team 1's innings being terminated and Team 2's innings is also restricted to 25 overs. What is the target score for Team 2?

Because of the different stages of the teams' innings that their 25 overs are lost, they represent different losses of resource. Team 1 have lost 2 wickets and had 25 overs left when the rain arrived and so from the table you will see that the premature termination of their innings has deprived them of the 61.8% resource percentage they had remaining. Having started with 100% they have used 100 - 61.8 = 38.2%; in other words they have had only 38.2%resources available for their innings. Team 2 will also receive 25 overs. With 25 overs left and no wicket lost you will see from the table that the resource percentage which they have available (compared to a full 50 over innings) is 68.7%. Team 2 thus have 68.7 - 38.2 = 30.5% greater resource than had Team 1 and so they are set a target which is 30.5% of 225, or 68.63, more runs than Team 1 scored.

[225 is the average in 50 overs for ODIs] Team 2's revised target is therefore set at 168.63, or 169 to win in 25 overs, and the advantage to Team 2 from knowing in advance of the reduction in their overs is neutralised. Note: Most of the other target resetting methods in use make no allowance for this interruption. They set the target of 101 to win simply because both teams are to receive the same number of overs. This is clearly an injustice to Team 1 who were pacing their innings to last 50 overs when it was curtailed, whereas Team 2 knew in advance of the reduction of their innings to 25 overs and have been handed an unfair advantage. D/L allows for this by setting Team 2 a higher target than the number of runs Team 1 actually scored, as described above." The D/L method is used for resetting targets of one-day cricket matches affected by rain. It was developed by Frank Duckworth & Tony Lewis, hence the name D/L method.

Basis of the method The D/L method works using the notion that teams have two resources with which they can make runs and these are - The number of overs remaining with them The number of wickets they have in hand From any point in their innings, their further run-scoring capability depends on both these two resources in combination. The single table gives the percentage of these combined resources that remain for any number of overs left and wickets lost. An extract of the over-by-over table is given in Table 1. (A ball-by-ball version of the table has also been produced to enable scorers to deal with instances when play is interrupted mid-over.) Table 1: Extract from the table of resource percentages remaining When the match is shortened due to rain, the resources of one or both teams are depleted and both teams usually have diff. amount of resource for their innings. The D/L method does this in accordance with the relative run-scoring 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 result in Team 2 having more resources available, then their target is revised upwards to compensate for the extra resources they have at their disposal. Reading the table Since 50 overs are most common, the resources listed in the table are expressed as percentages of those available at the start of a 50 over innings. Thus when there are 50 overs still to be received and no wickets have been lost, the resource percentage available is 100%. 60 over innings start with a resource percentage of 107.1% compared to a 50 over innings and 40 over innings start with a resource percentage of 90.3% compared to a 50 over innings. The no. of overs left along with no. of wickets lost is used to determine the correct resource percentage the batting side has. Example For example, suppose that after 20 out of 50 overs a team have lost 2 wickets. They have 30 overs left. From the table you will see that the resource percentage remaining is 68.2%.

Suppose now that there is an interruption in play and 10 overs are lost from the innings of the batting side. When play can resume there are only 20 overs left but there are still, of course, 2 wickets down, and the table now tells us that the resource percentage remaining is 54.0%. Thus the shortening of the innings has caused the team to lose a resource percentage of 68.2 - 54.0 = 14.2%. Having started with a resource percentage of 100% and lost 14.2%, then if they complete their innings with no further loss of overs, they will have had a resource percentage available for their innings of 100 - 14.2 = 85.8%. Applying the D/L method The procedure is the same for any number of stoppages at any stage of the match, is as follows: For each team's innings (a) from the table note the resource percentage the team had available at the start of their innings; (b) using the table, calculate the resource percentage lost by each interruption; (c) hence calculate the resource percentage available.

If Team 2 have less resources available than Team 1, then calculate the ratio of the resources available to the two teams. Team 2's revised target is obtained by scaling down Team 1's score by this ratio. If Team 2 have more resources available than Team 1, then calculate the amount by which Team 2's resource percentage exceeds Team 1's. Work out this excess as a percentage of 225 [the average 50 over score in ECB matches and one-day internationals (ODIs)] and this gives the extra runs to add on to Team 1's score to give Team 2's target. BBC SPORT | Cricket | A decade of Duckworth-Lewis A decade of Duckworth-Lewis Duckworth (left) and Lewis devised the cricket method Any cricket fan will be familiar with the names Duckworth and Lewis. Frank Duckworth and Tony Lewis to give them their full names were the two statisticians who devised a fair method to decide rain-interrupted one-day cricket matches. And now they are celebrating 10 years since the first ICC-sanctioned match to implement the Duckworth-Lewis method was held.

It was on 1 January 1997 when Zimbabwe beat England by six wickets after the target had been revised following a rain break. You do not have to be a rocket scientist (but it certainly helps) to understand the intricacies of the calculations but by and large the world of cricket has embraced the method. It was after the fiasco of the 1992 World Cup semi-final it was decided something needed to be done. I soon realised that it was a mathematical problem that required a mathematical solution Frank Duckworth After a short rain delay at Sydney Cricket Ground, South Africa went from needing 22 to beat England off 13 balls to needing the same runs but from just one ball according to the system in place at the time.

Consultant statistician 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." Lewis added: "It is very satisfying when watching matches that players generally accept revised targets now as fair, in contrast with the previous systems, and that we have made a significant contribution to the history and development of the game." The Duckworth-Lewis method was first used in the ICC Trophy in Malaysia in 1997 and in 1998 was applied in New Zealand, South Africa, Pakistan, India and West Indies. The International Cricket Council adopted the method for the 1999 World Cup in England but miraculously was not needed at all because the weather stayed fine. It was formally adopted by the ICC in 2001 and was used on a trial basis in all levels of cricket for three years before becoming a permanent method in 2004.

Pollock was South Africa captain when they miscalculated in the 2003 World Cup Duckworth-Lewis is reviewed every three years and in 2004 the Professional Edition was introduced in matches where computers are used. Lower level matches still use the Standard Edition, which is a published list of tables. ICC general manager David Richardson said the method was a success as there had never been much controversy. In the 2003 World Cup, South Africa failed to progress to the second round of the tournament on home soil after they miscalculated the score they needed to secure their passage but this was because of their own failings rather than D-L being wrong. He said: "The D-L method has been adjusted and amended over time taking account of the changing scoring trends in ODI cricket. The lack of a serious controversy surrounding the result of a rain-curtailed match is indicative of the method's proficiency. "No one likes it when the result of a game has to be settled by the mathematicians. Cricket, by its nature, is unpredictable and fortunes can fluctuate extravagantly during the course of a match.

"However, if one is forced to find an answer to the question 'who is winning' at a particular time during a match, the D-L method gives you as fair a method of doing so as you are likely to get." SEE ALSO

Question: The ‘Duckworth-Lewis method’ is used in which sport?
Answer: Cricket