Duckworth-Lewis-Stern Method

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Rain interrupts a test at The Oval in London

The Duckworth-Lewis-Stern Method (DLS-Method), originally the Duckworth-Lewis-Method (D / S-Method), is used in the sport of cricket , in One Day Internationals and Twenty20 matches, in the event of interruptions leading to victory to calculate the number of points required by the team batting second, the so-called target .

Problem

In cricket it happens quite often that the game has to be interrupted due to rain or poor visibility, less often for other reasons. The extent to which this reduces the playing time and / or the number of overs in the game or in the innings is not determined by the Laws of Cricket , but depends on the respective special game or league regulations.

In limited on time games, so especially in first-class cricket , suffers none of the two teams by a fundamental drawback, it only increases the probability of a draw ( draw ), there stands for both teams less time available to the victory condition to meet. See result (cricket) .

In one-day cricket, however, with a limited number of overs per innings, an overreduction automatically reduces the chances of scoring runs (points), and in general to a different extent for both teams. This can only be compensated by adjusting the target if a team is not to suffer a disadvantage through no fault of their own.

Example: In a 50-over match, Team A scores 210 runs in their innings. Team B first needs 211 runs to win, this is the target. During their innings, however, there is a one-hour hiatus, after which the innings must be reduced to 36 overs. How high is the target now?

history

The D / L method was developed by the two statisticians Frank Duckworth and Tony Lewis in 1998 and adopted by the International Cricket Council (ICC) as the standard method for calculating the target in one-day matches. After Duckworth and Lewis retired, Steven Stern was entrusted with the continuation of the method and in November 2014 it was renamed to its current name (Duckworth-Lewis-Stern Method).

Until then, various calculation methods had been used. For example, the average run rate method, which used the average number of runs achieved per over to determine the winner. This type of calculation seems to be imposing at first glance, but it is very unfair, as explained below. Another method compared the runs scored by the batting team in the second inning in their available n over with the runs scored by the first batting team in their most successful n over. The latter method was used, for example, during the Cricket World Cup in Australia in 1992 , when the now notorious case occurred that in the semi-final game England - South Africa, after a brief rain break shortly before the end of the game, South Africa was deducted two overs, but only by the target one was reduced. In addition to these, there were also other calculation methods, but they were less common.

All of these older methods suffer from the fact that they take into account the reduced over number of innings, but ignore the fact (or at least try to compensate for it by making less than plausible adjustments) that the criterion for the conclusion of an inning that applies to all forms of play, namely the loss of all 10 wickets , is of course not touched when the number of overs is reduced. Therefore, the batting team can play much more offensively in such a shortened innings without great risk and thus score points faster (per over), as they automatically have fewer overs in which they can lose all their batsmen.

Theory and application

Available resources as a function of the remaining over

The DLS method is based on the theory of impact resources . , As has been indicated above, the respective batting side always two resources from which they want to achieve as many points as possible thereafter: the number of available Over in their innings and ten wickets , so to speak, their ten "Batsmanleben". At any given point in the innings, the ability to score additional points depends on the remaining over and wickets. A statistical study of many games showed that there is a correlation between these two sizes and the proportion of runs in an innings that can be used to assess the team's “score”.

A table was created from this, the so-called DLS table, from which the remaining share of resources can be read off for each combination of remaining over and balls on the one hand and wickets already lost (i.e. batsmen eliminated) on the other. This table is standardized to 50 over, i.e. H. 50 over equals 100% resources.

From this, in turn, the corresponding loss of resources can be determined for any interruption. From the ratio of the resources of both teams, as soon as the first innings has been completed and its total is known, the runs of the second batting team corresponding to this number of points, which is referred to as the par score . One more run is the target.

In the less frequent cases in which team B has more resources available than team A, the ratio of resources is not simply used, but the total of team A is increased by the runs corresponding to the resource difference. As a base value, the so-called G50 number is used, which corresponds to the average runs achieved in a first 50 over innings.

In order to enable the method to be applied fairly, a specified minimum number of overs must have been completed by both teams as batting teams. In One-Day Internationals this is at least 10 overs and in the shorter Twenty20 format at least 5 overs. A game that does not reach this number of overs is counted as a no result .

In 2004, a DLS table with updated resource values ​​was published and a Professional Edition was issued, which dispenses with the case distinction described above, but no longer manages with one table, but instead uses a computer program to create a table based on the total of the first inning with which you can calculate the resource failures as usual (as mentioned without the G50 variant ). The old version was named Standard Edition , the Professional Edition is used almost exclusively in professional cricket.

Examples

Interruption in the 2nd innings

In the first one-day international between India and Pakistan during their 2006 series, India played the first innings and was all out after 49.4 over 328 . Pakistan's target was initially 329 runs. After 47 overs in Pakistan's innings, the game had to be abandoned due to poor visibility when the score was 311 for 7 .

Since there were still 3 overs or 18 balls to play and Pakistan needed exactly 18 runs to win, Pakistan should have had a slight advantage, especially considering the high scores of both teams. In fact, D / L had a par score of 304 runs at this "point in time" (3 overs to play and 7 wickets lost), so Pakistan won with 7 runs (D / L method) .

Interruption in the 1st innings

In the fourth game between India and England of the 2008 series, the first innings of the game (India's innings) was interrupted twice by rain. The game had to be reduced from the original 50 overs per innings (and thus per team) to 22 overs per innings. India scored 166 for 4 , so 166 points.

The D / L method resulted in a target of 198 runs from their 22 overs for England . This is an example of the second batting team having to score significantly more runs than the first team if interruptions occur during the first innings of the game. The D / L method automatically takes into account the fact that England, unlike India, even before the start of their innings knew that they only have 22 Over available and therefore, from the first ball at a higher tempo already beat could. In fact, England only got 178-8 and India won with 19 runs (D / L method).

Special events

Two international games have shown that serious and embarrassing mistakes can occur when using the DLS method.

During the 2003 World Cup in South Africa, the hosts needed a win in the decisive preliminary round match against Sri Lanka in order to advance to the second round. Sri Lanka had scored 268 runs in the first innings. With five overs to go, the game was on a knife edge. Since it was foreseeable that the game was about to be abandoned due to rain, their captain Shaun Pollock sent the message to the batsmen that 229 would be the target at the end of the running overs. In reality, however, the D / L lists made available to the teams list the par scores , i.e. the runs required for a draw and not the respective targets. The South African batsman Mark Boucher, who had just hit a 6 and thus brought South Africa to exactly 229, then blocked the last ball of the overs in order to avoid being eliminated in any case (because this would have raised the target further). The referees actually stopped the game immediately afterwards, and this misunderstanding (or misunderstanding of the D / L table) had given South Africa the victory.

Another "wrong reading" of the D / L table occurred in the West Indies' first one-day game against England in Guyana in 2009 , again shortly before the end of a close game. Due to the now poor visibility, the referees offered the two batsmen from West Indies to abandon the game. Her coach John Dyson gave the batsmen the signal to accept this offer and leave the place. But he had not taken into account that with the last ball immediately before another batsman of his team had been eliminated and therefore the numbers in the next column could be read. The amused English team could hardly believe their luck and won the game with 1 run (D / L method) .

literature

  • Duckworth, FC & Lewis, AJ Duckworth Lewis The method and the men behind it , Sportsbooks, 2011. ISBN 978-1907524004
  • Duckworth, FC & Lewis, AJ Your Comprehensive Guide to The Duckworth Lewis Method for Resetting Targets in One-day Cricket , Acumen Books, 2004. ISBN 0-9548718-0-4
  • Duckworth, F A Role for Statistics in International Cricket Teaching Statistics , (June 2001) Volume 23, No. 2 pp 38-44
  • Duckworth, FC & Lewis, AJ A fair method for resetting the target in interrupted one-day cricket matches Journal of the Operational Research Society , (Mar 1998) Volume 49, No. 3 pp 220–227 3010471 ( JSTOR )
  • Duckworth, FC & Lewis, AJ A successful operational research intervention in one-day cricket Journal of the Operational Research Society , (2004) 55, pp 749-759

Web links

Notes and sources

  1. ↑ In order to be able to evaluate a one-day game and not have to state it as a no result , the game regulations almost always require that the second batting team has the opportunity to complete a certain minimum number of points. Today (2009) 20 overs in a 50-over innings are common internationally.
  2. ↑ Introducing Duckworth – Lewis – Stern method . Cricbuzz. February 12, 2015. Accessed March 30, 2015.
  3. ^ S Rajesh: How the Duckworth – Lewis – Stern method works . In: Cricinfo . ESPN. June 8, 2017. Retrieved April 13, 2018.
  4. ↑ World Cup semi-finals '92, England - South Africa
  5. ↑ The result of the calculation is always rounded down to the next whole number.
  6. ↑ FAQ on the D / L method
  7. ^ Scorecard of the 1st ODI between India and Pakistan, February 6, 2006
  8. ↑ This case of an aborted game is the only one in which the second batting team can win with runs contrary to the usual results .
  9. ^ Scorecard of the 4th ODI between India and England, November 23, 2008 .
  10. ^ Scorecard of the World Cup match between South Africa and Sri Lanka, March 3, 2003
  11. ^ Scorecard of the 1st ODI between West Indies and England, March 20, 2009
  12. ↑ This process, which is called in English to offer the light , was common in cricket until the end of 2010 and was defined by the rules. Only the batsmen, not the field team, could accept the referee's “offer”.