The Duckworth Lewis Method-Part 2

Case 1: Premature curtailment of Team 2’s innings


Team 1 have scored 250 runs from their 50 available overs and Team 2 lose 5 wickets in scoring 199 runs in 40 overs. Play is then stopped by the weather, the rain refuses to relent and the match is abandoned. A decision on the winner is required.

Team 1’s innings: this was uninterrupted, so the resource percentage available is

100%.

Team 2’s innings: resource % available at start of innings =

100%

After 40 overs Team 2 have 10 overs left and have lost 5 wickets.

From table, resource % left at suspension of play =

27.5%

As play is abandoned all this remaining resource is lost.

Hence resource % available for Team 2’s innings = 100 – 27.5 =

72.5%

Team 2 had less resource available than Team 1 and so to give the target Team 1’s score must be scaled down by the ratio of resources, 72.5/100

Team 1 scored 250, so Team 2’s ‘target’ is 250 x 72.5/100 = 181.25

For competitions commencing April 1999, the next lower whole number, 181, is the score to tie, or the ‘par score’ for the match situation at the stoppage.

As there is to be no further play, the winner is decided according to whether or not the par score has been exceeded. With 199 runs on the board, they have exceeded this by 18 and so are declared the winners by 18 runs.

Case 2: Interruption to Team 2’s innings

A one-day match has been shortened to 40 overs per side before it commenced. Team 1 have scored 200 runs from their 40 available overs and Team 2 lose 5 wickets in scoring 140 runs in 30 overs. Play is then suspended and 5 overs are lost. What is Team 2’s revised target?

Team 1’s innings: At the start of 40 over innings resource percentage available =

90.3%

Team 2’s innings: resource % available at start of 40 over innings =

90.3%

After 30 overs Team 2 have 10 overs left and have lost 5 wickets.

From table, resource % left at start of suspension =

27.5%

5 overs are lost, so when play is resumed 5 overs are left.

From table, resource % left at resumption of play =

16.4%

Hence resource % lost = 27.5 – 16.4 =

11.1%

so resource % available for Team 2’s innings = 90.3 – 11.1 =

79.2%

Team 2 had less resource available than Team 1 and so to give the target Team 1’s score must be scaled down by the ratio of resources, 79.2/90.3

Team 1 scored 200, so Team 2’s ‘target’ is 200 x 79.2/90.3 =175.42 which rounds down to 175 to tie with a revised target of 176. They then require a further 36 runs to win from 5 overs with 5 wickets in hand.

Case 3: Interruption to Team 1’s innings

In an ODI, Team 1 have lost 7 wickets in scoring 190 runs in 40 overs from an expected 50 when extended rain leads to Team 1’s innings being terminated and Team 2’s innings is also restricted to 40 overs. What is the target for Team 2?

Because of the different stages of the teams’ innings that their 10 overs are lost, they represent different losses of resource. Team 1 have lost 7 wickets and had 10 overs left when the rain arrived and so from the table you will see that the premature termination of their innings has deprived them of the 20.6% resource percentage they had remaining. Having started with 100% they have used 100 – 20.6 = 79.4%; in other words they have had 79.4% resources available for their innings.

Team 2 will also receive 40 overs. With 40 overs left and no wicket lost you will see from the table that the resource percentage which they have available (relative to a full 50 over innings) is 90.3%. Team 2 thus have 90.3 – 79.4 = 10.9% greater resource than had Team 1 and so they are set a target which is 10.9% of 225, or 24.53, more runs than Team 1 scored. [225 is the average in 50 overs for ODIs]

Using the sum 190 + 24.53 = 214.53 rounding down gives 214 to tie and Team 2’s target is 215 in 40 overs.

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