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Home » Duckworth-Lewis Method » world cup 2007
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Duckworth-Lewis Method for curtailed matches

Introduction

There are many factors that affect a cricket match. So there are certain methods that help in determining the final result of the match. Many a times a cricket match has to be stopped because of the bad weather which is always unpredictable.

So it becomes necessary that there should be some determining factor, which will help in making the final decision of the match. Technically speaking it is a way to calculate the target score to decide the winning team in an interrupted one-day cricket match. Duckworth Lewis Method for curtailed matches has been accepted worldwide.

Two great statisticians named Frank C. Duckworth and Anthony J. Lewis (nickname Tony) devised the Duckworth Lewis Method for curtailed matches. This method was made to overcome the shortcomings of the method in use of that time – namely the average scoring rate and/or the best-scoring overs method, which was used in the 1992 Cricket World Cup when South Africa requiring 22 runs from 13 balls and the inclement weather reduced the target to 22 runs from one ball.

The Method

The Duckworth Lewis Method for curtailed matches is based on “resources”. It is considered that every team has two “resources” and based on that the calculation is made. The two resources are the number of overs the team has to receive and the number of wickets the team has in hand. Keeping these two resources in mind and by applying this method a team’s ability to score runs could be calculated and thus the target score could be set. If the other team crosses this score then it will win otherwise it will lose.

One needs to know the resources available to the team at the time of suspension of the match and at its resumption, to calculate the revised target of the curtailed match.

When the side batting second, have less run scoring resources at their disposal than the side which batted first, than their target is adjusted downwards using the ratio of the resources available to the two sides.

But when the side batting first has its innings interrupted, then the side batting second have more resources at their disposal; and now it is necessary to adjust the target upwards.

In this case the adjustment is based on the runs that would be expected to be scored on average from the extra resources at their disposal. The number of these extra runs required is calculated by applying the excess resource percentage to the average total score in a 50-over innings, the value of 235 runs is used at present.

When the revised target has been calculated and the match has been played out to its completion, the result is described;
if the 2nd team reach the target score – they win by the number of wickets remaining to be out;
and if they do not reach the target – then they lose by the runs needed to achieve a tie.
One run short of the revised target results in a tie.

The figures given in the table are percentages of the resources available for a complete 50-over innings.
Table of resource percentages remaining


Example 1. In an ODI, Team 1 having scored 200 runs for the loss of 6 wickets in 40 overs, from an expected 50 overs ODI; when rain caused Team 1's innings to be terminated and Team 2's innings being restricted to 40 overs. What is the target for Team 2?

Team 1 had 4 wickets remaining and had 10 overs to play, when the rain interrupted the match.
This premature termination of their innings has deprived them of 22.8% of the resources, had the game been played to the full 50 overs.
Having started with 100% they have used 100 - 22.8 = 77.2% of their resources.

Team 2 will also play for 40 overs. With 40 overs remaining and 10 wickets remaining; from the table - the resource percentage available to them is 89.3%.

Thus, Team 2 have 89.3 – 77.2 = 12.1% greater resource than Team 1.

So they are set a target, which is 12.1% of 235 runs more, or 28.435 more runs than what Team 1 had scored.
Using the sum 200 + 28.44 = 228.44; which on rounding down gives 228 to tie and Team 2's target is 229 runs in 40 overs.

Note: This is on the reasoning that Team 1 was playing their innings to last the full 50 overs when it was interrupted, whereas Team 2 now knows in advance that the match is reduced to 40 overs and have been handed an undue advantage. D/L Method negates this by setting Team 2 a higher target than the number of runs Team 1 actually scored.

Example 2. In a 50 over ODI match, Team 1 reaches 80/2 after 20 overs and then the game is suspended. It is decided that 10 overs of each team should be lost for the match.
Team 1 resumes and manages to reach a total of 180 in its resumed innings of 40 overs.

Number of overs per innings at the start of match, = 50
Resource percentage available to Team 1 at start of innings = 100%
Resource percentage remaining at suspension (30 overs remaining, 8 wkts remaining) = 67.3%
Resource percentage remaining at resumption (20 overs remaining, 8 wkts remaining) = 52.4%
Resource percentage lost due to suspension = 67.3 – 52.4 = 14.9%
Resource percentage available to Team 1, is    100 – 14.9   = 85.1%

Number of overs available to Team 2 at the start of its innings = 40
Resource percentage available (40 overs remaining, 10 wkts remaining), = 89.3%

Thus Team 2 has more resources available to them than Team 1 had,
so its target should be increased.

Team 1 score = 180
Team 2’s revised target is = 180 + 235 x (89.3 – 85.1)/100
Team 2 ‘s target              = 180 + 9.87 = 190 (rounded up).
If Team 2 scores 189 runs, then the match is a tie.

Example 3. In an ODI match, Team 1 has scored 260 from 50 overs in an uninterrupted innings.
Team 2 has faced 15 overs and has scored 80/1.
Then the play is suspended and 10 overs are lost.

What is Team 2’s target?
Number of overs at start of match, = 50.
Team 1’s innings was uninterrupted, so resource percentage available = 100%

Resource percentage available to Team 2 at start of its innings = 100%
Resource percentage remaining at suspension (35 overs left, 9 wkts left) = 78.5%
Resource percentage remaining at resumption (25 overs left, 9 wkts left) = 63.9%
Resource percentage lost due to suspension   = 78.5 – 63.9 = 14.6%
Resource percentage available to Team 2,     = 100 – 14.6   = 85.4%

Thus Team 2’s revised target is = 260 x 85.4/100
                                = 222.04 = 223 (rounded up).

If Team 2 scores 222 runs, then the match is a tie.
Thus Team 2 needs a further 143 runs from 25 overs to win the match.

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