Duckworth–Lewis method
The Duckworth - Lewis method (D / L method) is used in the sport of cricket to in the event of interruptions, the time required to victory score of the batting as the second team, the so-called target to calculate in one-day games.
Problem
In cricket, it happens quite often that the game must be rare for other reasons, interrupted due to rain or due to poor visibility. Extent by the playing time and / or the number of the Over in the game or in the innings is reduced, is not covered by the rules of Cricket ( The Laws of Cricket ) fixed, but depends upon the particular specific game or league rules from.
In on time limited games, so especially in first-class cricket, does not suffer from the two teams by a fundamental drawback, it only increased the probability of a draw ( draw), there is less time available for both teams, the victory condition to fulfill. See Result (cricket).
In one-day cricket, however, that with a limited number of overs per innings reduce automatically to achieve through a reduction over the possibilities runs (points), and although generally for both teams to varying degrees. This can only be compensated in that the target is adjusted, should not suffer an undeserved disadvantage a team.
Example: In a 50 -over match will Team A 210 runs in their innings. Team B therefore first needed 211 runs to win, this is the target. During their innings However, there is a one-hour break, and then the innings must be reduced to 36 over. What is the target now?
History
The D / L method was developed by the two statisticians Frank Duckworth and Tony Lewis in 1998 and by the International Cricket Council (ICC ) as a standard method for calculating the targets adopted in One - Day matches.
Until then, different calculation methods in use had been. For example, the average run rate method, which heranzog the number of runs scored per over average to determine the winner. This method of calculation appears to impose at first sight almost, but it is very unfair, as explained below. Another method compared the runs scored by the batting side of the second innings in its available N over with the runs that had achieved the first batting team in their successful N Over. The latter method was used, for example during the Cricket World Cup in 1992 in Australia, as of now entered the infamous case in the semi-final match England - shortly before the end of the game, South Africa, although two over were deducted South Africa, after a brief rain delay, the target but just to one was reduced. Besides these, there were other calculation methods, which were rare, however.
All these older methods suffer from the fact that although they take into account the reduced number of overs of the innings, however, ignore the fact (or at least compensate by little plausible adjustments to try ), that the law applicable to all forms of play criterion for completion of an inning, namely the loss of all 10 wickets, will of course not be touched with a decrease in number over. Therefore, the batting side, in such a truncated, play innings without great risk far more aggressively and thus faster ( per over) score points because they automatically also has fewer Over, where they can lose all their batsmen.
Theory and Application
The D / L method is based on the theory of impact resources. After that has, as indicated above, the respective batting team always has two resources available from which they want to score as many points: The number of available over in their innings and ten wickets, so to speak, their ten " Batsmanleben ". At any given time in the innings, the ability to achieve depends on other points of the then remaining overs, and wickets from. A statistical study of many games showed that between these two variables and the proportion of runs in an innings is a correlation, which can be used to assess the " Score " on the team can.
From this, the so-called D / L table from the wickets lost for each combination of remaining Over and balls on the one hand and already (ie retired batsmen ) a table is created, on the other hand, the remaining amount of resources is read. This chart is normalized to 50 over, that is, Over 50 correspond 100 % resources.
This in turn can then be determined at any interruption of the corresponding loss of resources. From the ratio of the resources of both teams arises when the first innings and finished the total is known, the appropriate score that runs the second batting side, which is called the par score. A run is more then the target.
In less frequent cases where Team B more resources available than Team A, the ratio of the total resources used is not easy, but increased from Team A to the runs corresponding resource difference. The underlying this case the so-called G50 - number is used, which corresponds to the average runs scored in a first 50 -over innings.
In 2004, a D / L table was published with updated resource values and a Professional Edition released, which dispenses with the distinction of cases described above, but no longer uses just one table, but creates a dependent of the total of the first innings table by computer program, with which one can as usual ( as mentioned without the G50 variant) calculate resource failures. The old version was called the Standard Edition, the Professional Edition is also used almost exclusively in professional cricket.
Examples
Break in the second innings
In the first One- Day International between India and Pakistan during their 2006-spec series India played the first innings and was by 49.4 Over 328 all out. Pakistan's target was therefore first 329 runs. After 47 Over in Pakistan's innings, the game had to be stopped for 7 because of poor visibility at the score of 311.
So there still 3 Over or 18 balls were playing and Pakistan also needed just 18 runs for victory, Pakistan may have been a slight advantage, particularly given the high scores of both teams. In fact, D / L resulted in a par score of 304 runs for this " time " (3 over to play and 7 wickets lost ), so Pakistan won by 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 innings ) was interrupted twice by rain. The game had originally Over 50 per innings (and thus per team) will be reduced to 22 per innings over. India reached 166 for 4, ie 166 points.
The D / L method yielded a target of 198 runs from their 22 over for England. This is an example of the impact as the second team must achieve significantly more runs than the first team, if disruption during the first innings of the game occur. The D / L method automatically takes into account the fact that England, unlike India, already knew before the start of their innings, that they will have only 22 available Over and therefore could already hit the first ball at a higher pace. In fact England came but only on 178-8 and India won by 19 runs (D / L method).
Special Events
That it can cause serious and embarrassing mistakes in applying the D / L method, has been shown in two international matches.
During the World Cup in 2003 in South Africa, the hosts needed in the decisive group match against Sri Lanka a victory to move into the second round. Sri Lanka had scored 268 runs in the first innings. Over five before the end of the game was on a knife edge. Since it was clear that the game was about to be canceled due to rain, was their captain Shaun Pollock the batsmen to get the news that 229 was the target at the end of the current overs. In reality, however, are the, the teams made available, D / L lists the par scores, so the needed to draw runs and not the respective targets are listed. 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 to avoid definitely a departure ( because this would have further increased the target ). The referee broke the game actually directly from a wish and South Africa had by this misunderstanding (or the faulty understanding of the D / L table) presented the victory.
At another " Falschablesen " of the D / L table it came in the first one-day match of the West Indies against England in 2009 in Guyana, shortly before the end of a tight game. Due to many poor visibility, the referee offered the two batsmen of West Indies to continue the game. Your coach John Dyson gave the batsmen the character to accept this offer and go from the square. But he had not considered that with the last ball before another batsman of his team was eliminated immediately and therefore the numbers of the next column were read. The amused English team could not believe their luck and won the game with 1 run (D / L method).