Duckworth Lewis Stern method 2

Duckworth Lewis Stern method

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The Duckworth–Lewis–Stern method (DLS) is designed to calculate the target score for the team batting second in a limited overs cricket match interrupted by weather or other circumstances. This method was devised by two English statisticians, Frank Duckworth and Tony Lewis and was formerly known as the Duckworth–Lewis method (D/L).

Duckworth Lewis Stern method 3

It was introduced in 1997, and adopted officially by the ICC in 1999. After the retirements of Duckworth and Lewis, Professor Steven Stern became the custodian of the method and it was renamed to its current title in November 2014.

History and creation:

Before D/L method initial solution had been to award victory to the side that had scored the highest average number of runs in the overs played which did not took no account of wickets lost. Rain stopped play for 12 minutes with South Africa needing 22 runs from 13 balls. The revised target left South Africa needing 21 runs from one ball, a reduction of only one run compared to a reduction of two overs, and a virtually impossible target given that the maximum score from one ball is generally six runs

After that, an appeal went out to cricket-loving stattos worldwide, initially via Christopher Martin-Jenkins on Test Match Special – can anyone, anywhere, devise a better solution?

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.The D/L method avoids this flaw: in this match, the revised D/L target would have left South Africa four to tie or five to win from the final ball

In 2014, the name of Steven Stern, an Australian professor, was added to what is now known as the “DLS” method, after he took over the day-to-day running of the formula, and made his own adjustments to reflect modern scoring rates.

The D/L method was first used in international cricket on 1 January 1997 in the second match of the Zimbabwe versus England ODI series, which Zimbabwe won by seven runs.The D/L method was formally adopted by the ICC in 1999 as the standard method of calculating target scores in rain-shortened one-day matches.

Calculation Theory

DLS theory calculation is based on 2 resources:

1. Number of overs chasing team have to play
2. Number of wickets chasing team have in hand

These two resources are used at every point of time in the match.On the basis of these two resources, Frank Duckworth and Tony Lewis prepared a chart which suggests that how many resources are left with the batting side in different situations.

On seeing this chart, it is clearly visible  that when a team has entire 50 overs and 10 wickets before the starting of the game; it can be said that the team possesses 100 percent resources.After this, as soon as the team uses its overs and the wickets it means the resources of the team decrease as the game progresses.

If a team has played 20 overs and lost 2 wickets in the match it means the team is left with just 30 overs and 8 wickets in hands. In the language of the Duckworh-Lewis the team is left with just 67.3 percent resources.

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Now suppose the rains comes at this point and match-time of 10 overs washed out it means the batting side is left with only 20 overs and it already has lost two wickets; so as per the Duckworth-Lewis method the batting team  owns just 52.4% resources in hands.

See in the Table below;

duckworth-lewis-method-2

So the rain has washed out  67.3 – 52.4 = 14.9 resources of the batting side.

As we have mentioned earlier that the  team (batting first) had  used its 100 %  resources but the resources available to the team (batting second) are just 100 – 14.9 = 85.10 resources. 

In other words, it can be said that 14.9% resources of the second team have washed out in the rain.

 But till now this explanation seems biased because first team has used 100% while the second team or batting second team has just 85.10 resources.  So  to ensure a fair play, both the team should have equal resources.  In this condition the Duckworth Lewis method will reduce the target set by the batting first team.

The Duckworth Lewis method says that if the rain affects the inning of second team then the target should be modified. Hence the target set  by the first team will be reduced.

And if the rain affects the team batting first, then its target will be increased, which means this team will have to chase more runs.

Let see all this through an Example:

Example 1:

If the rain affects the team which bats later or plays second inning then: –

Suppose the first team scored 300 runs in 50 overs and the second team has scored 250/4 in 40 overs. After this, match could not be played then the Duckworth Lewis method will be applied to find the winner of such match.

The first team played its entire 50 overs that means team used its 100 percent resources. The second team also had 100 percent resources in the beginning of the inning but it could not use them due to rain.  After 40 overs the second team has 10 overs and 6 wickets in hands.

According to the Duckworth Lewis chart, in this situation second batting team is left with 26.1 percent resources. Now suppose from this moment onwards the match is abandoned.

Now there is difference in the resources available to the both team. As we know first team has used its 100% resources while the second team has used just 100-26.1= 73.9%.

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Now the winner of the match will be decided on the basis of equal distribution of resources to both team.

Since the second team got the lesser resources as compared to first team so the target for the second team must be reduced.

Since the first team scored 300 runs so the target for the second team will be 300 x 73.9 / 100 = 221.7

So as per the rules the second team needs to score 222 runs to win the match but is has already scored 250 runs.

Hence the second team will be declared winner by 250 – 222= 28 runs.

 

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