GRADUALLY, TRUNCATING CRICKET MATCHES

ANISUDDIN KHAN
(feedback@pgeconomist.com)

May 17 - 23, 2010

Rain, bad light and random riots are unpredictable parts of world's most unpredictable sport-cricket. Without nature's interference the game would not have been complete and earned the most unpredictable tag.

In the era when pitches were not covered overnight dew, occasional showers played major role in making tests an exciting affair in which only the best survived. And when the shorter version of cricket-50 overs a side one day game was introduced to light up the bleak, dull and dreary five day tests and make the sport result oriented, cricket got a new life. Fans across the globe were attracted to the newer shorter version which was quick and ended in a result which was not the case in tests which mostly ended in a dull draws.

Birth of 50 overs a side competition was a result of a freak incident when the organisers of Australia and England Ashes series in Melbourne arranged a one day competition after rain had washed out four days of the test to compensate the fans.

However birth of T20 version the shortest version of the sport was result of a well thought plan to attract dwindling support to the game in England the mother of all modern sports and also the home of cricket. The cricket organisers there faced with low attendance and lower revenues at cricket matches came up with the idea of the shortest version of sports the T20. If tests were five day dull affairs, 50 overs a side internationals were seven hours duration played either totally in day light or in night under floodlights. The T20 international cricket is the quickest and shortest version and each match lasts mere 180 minutes.

Because of its short duration and the amount of excitement it produces and its marketing value T20 has been accepted as the most loved kind of cricket in the world.

The International Cricket Council realizing the importance of the financial and marketing impact of the T20 immediately launched an ICC World T20. The third edition of the competition is currently underway in the West Indies. India won the first edition defeating Pakistan in the final on the last ball in South Africa and Pakistan won the second edition in England defeating Sri Lanka.

When the twelve nation 2010 ICC World T20 began April 30 few would have thought that a rule dictating rain interrupted play known as Duckworth/Lewis formula/rule would draw controversy and become topic of hot discussions. But it happened when England lost its group league match to host West Indies when the target was reset under D/L formula. England skipper was furious when the West Indies were given a target to clinch the match which they did. Paul Collingwood's reaction was fair because after scoring huge 191 for five, the West Indies under the D/L formula was given target of 60 runs to clinch victory in six overs which they achieved with one ball to spare.

However Collingwood's reaction was more due to frustration than facts. He and his team staff knew little that D/L method would be activated when rain interrupted West Indies innings in 2.2 overs with host reaching 30 runs. But in ignorance they were complacent and paid no attention when the West Indies went in for the target.

It is important to know what is the history of D/L formula and why was it approved by the ICC and also to know why an ordinary mathematical formula has attracted calls from across the globe for its removal or revision. There is nothing wrong with the formula it is only the ignorance and complacent attitude of team management that had created the avoidable furor.

The formula 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.

The method that they have invented is simple to apply provided one is prepared to take a few minutes to understand its logic.

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 method is simple enough for it to be adopted for use at all levels of limited-overs cricket.

The D/L method of resetting targets in rain-affected one-day cricket matches has now been in use for well over two years and has been adopted for use in most test playing countries of the world.

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.

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 and then their target is revised upwards to correct for the extra resources they have at their disposal

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 or Twenty20 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.

In the 4th India - England ODI in the 2008 series, the first inning was interrupted by rain on two occasions, resulting in the match being reduced to 22 overs a side. India (batting first) made 166/4.

England's target was therefore set by the D/L method at 198 from 22 overs.

This example illustrates how the D/L method sets a higher target for the team batting second when the delay occurs in the 1st inning.

Because England knew they had only 22 overs the expectation is that they will be able to score more runs from those overs than India had from their (interrupted) innings. England made 178/8 from 22 overs, and so the match was listed as "India won by 19 runs".

A simple example of the D/L method being applied was the first One Day International (ODI) 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.

In this example, Pakistan's target, had the match continued, was 18 runs in as many balls, with three wickets in hand.

Considering the overall scoring rate throughout the match, this is a target most teams would be favored to achieve. And indeed, application of the D/L method resulted in a target score of 304 at the end of the 47th over, with the officially listed result as "Pakistan won by 7 runs".

EXAMPLES IN T20 MATCHES

During the 2010 ICC World T20, the D/L method was used in the group stage match between Sri Lanka and Zimbabwe. Sri Lanka scored 173/7 in 20 overs batting first and Zimbabwe were 29/1 in 5 overs when rain interrupted play. Sri Lanka won the match by 14 runs according to the D/L method.

On the same day, another group match between England and West Indies was also decided by the D/L method. England scored 191/5 in 20 overs, and rain interrupted play after 2.2 overs of the chase when West Indies had scored 30/0. According to the D/L method, West Indies were set a target of 60 runs in 6 overs, which they achieved with a ball to spare.

The English captain Paul Collingwood heavily criticized the usage and appropriateness of the D/L method in T20 matches Theory.

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.

Applied to 50 over matches, each team has to face at least 20 overs before D/L can decide the game. In Twenty20 games, each side has to face at least 5 overs.

The D/L method 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 and was formally adopted by the International Cricket Council in 2001 as the standard method of calculating target scores in rain shortened one-day matches.

Various different methods had been previously used to achieve the same task, including run-rate ratios, the score that the first team had achieved at the same point in their innings, and targets derived by totaling the best scoring overs in the initial innings. All of these methods have flaws that are easily exploitable. For example, 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. Notoriously, the "best-scoring overs" method, used in the 1992 Cricket World Cup, left the South African cricket team requiring 21 runs from one ball (when the maximum score from any one ball is generally six runs). Prior to a brief rain interruption, South Africa was chasing a target of 22 runs from 13 balls - which was difficult but at least attainable - but the possibility of an exciting conclusion to the game was destroyed when the team's target was reduced by only one run, to be scored off 12 fewer balls. The D/L method removes - or at least normalizes - this flaw: in this match, the revised D/L target would have been four runs to tie or five to win from the final ball.

In June 2009, it was reported that the D/L method would be reviewed for the Twenty20 format after its appropriateness was questioned in the quickest version of the game. Lewis was quoted admitting that "certainly, people have suggested that we need to look very carefully and see whether in fact the numbers in our formula are totally appropriate for the Twenty20 game."

The D/L method has been criticized 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, a winning strategy could be to not lose wickets and score at what would seem to be a "losing" rate (e.g. if the asking rate was 6.1, it could be enough to score at 4.75 an over for the first 20-25 overs).

Another criticism is that the D/L method does not account for changes in the proportion of number of overs during which field restrictions are in place compared to a completed match.

More common informal criticism from cricket fans and journalists of the D/L method is that it is overly complex and can be misunderstood.

For example, in a one-day match against England on 20 March 2009, the West Indies coach (John Dyson) called his players in for bad light, believing that his team would win by one run under the D/L method, but not realising that the loss of a wicket with the last ball had altered the Duckworth-Lewis score. In fact Javagal Srinath, the match referee, confirmed that the West Indies were two runs short of their target, giving the victory to England.