The Duckworth Lewis Method - worked examples

Example 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 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.

Note : The above result is quite fair as Team 2 were clearly in a strong position when play was stopped and would very likely have gone on to win the match if it hadn't rained. Most other methods of target revision in use would, unfairly, make Team 1 the winners. The average run rate method gives 201 to win, the ICC (1995) method gives 227 and the parabola method gives 226. [Setting the target by the method of Discounted Total Runs - the Australian rain-rule - requires knowledge of the runs made by Team 1 from their most productive overs but the target would almost certainly be no lower than that required under average run rate and would probably be much higher so that Team 2 would very probably lose by this method as well.]

Example 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 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.

Example 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.

Note: All other target resetting methods currently in use make no allowance for this interruption. They set the target of 191 simply because both teams are to receive the same number of overs. This is clearly an injustice to Team 1 who were pacing their innings to last 50 overs when it was curtailed, whereas Team 2 knew in advance of the reduction of their innings to 40 overs and have been handed an unfair advantage. Duckworth/Lewis neutralises this by setting Team 2 a higher target than the number of runs Team 1 actually scored.