An introduction to the D/L (Duckworth/Lewis) method of resetting targets in interrupted one-day cricket matches by Frank Duckworth & Tony Lewis

Frank Duckworth and Tony Lewis, inventors of the now well-known system of resetting targets in interrupted matches that bears their names, have announced an update to their tables. This follows an extensive analysis of limited overs cricket matches in recent years that they have undertaken. "The nature of the one-day game is changing," said Duckworth "and our tables need to reflect developments in playing strategies". These changes come into effect for competitions starting on or after 1st September. And they have already been used for the tour match between the 'A' teams of South Africa and Australia on 4th September.

There will be no change to the way that the well-established D/L method works, which is described in published books and summarised on the Cricinfo webpage. Lewis said that the effects of the new tables "will in most cases be to lower slightly the enhanced targets when the first innings is interrupted and to raise slightly the D/L par scores during the early part of the reply".

Duckworth and Lewis felt that it was in the interests of the game that the D/L method should be stable whilst the world got used to it. "The time is now ripe to reflect recent advances in the game" they said.

Here is an extract of the new tables

Wickets lost
Overs left

Effects of the new tables
The examples that Duckworth and Lewis use to explain their method are now reworked using these new tables

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 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 =
As play is abandoned all this remaining resource is lost.
Hence resource % available for Team 2's innings = 100 - 26.1 =

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, 73.9/100.
Team 1 scored 250, so Team 2's 'target' is 250 x 73.9/100 = 184.75. The next lower whole number, 184, 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 15 and so are declared the winners by 15 runs.

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 1's innings: At the start of 40 over innings resource percentage available =   89.3%
Team 2's innings: resource % available at start of 40 over innings =   89.3%
After 30 overs Team 2 have 10 overs left and have lost 5 wickets.
From table, resource % left at start of suspension =
5 overs are lost, so when play is resumed 5 overs are left.
From table, resource % left at resumption of play =
Hence resource % lost = 26.1 - 15.4 =   10.7%
so resource % available for Team 2's innings = 89.3 - 10.7 =   78.6%

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, 78.6/89.3 Team 1 scored 200, so Team 2's 'target' is 200 x 78.6/89.3 =176.04 which rounds down to 176 to tie with a revised target of 177. They then require a further 37 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 17.9% resource percentage they had remaining. Having started with 100% they have used 100 - 17.9 = 82.1%; in other words they have had 82.1% 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 89.3%. Team 2 thus have 89.3 - 82.1 = 7.2% greater resource than had Team 1 and so they are set a target which is enhanced by 7.2% of 235, or 16.92, more runs than Team 1 scored. [235 is the revised average in 50 overs for ODIs in recent years].

Using the sum 190 + 16.92 = 206.92, rounding down gives 206 to tie and Team 2's target is 207 in 40 overs.

Note: Most other target resetting methods previously used would 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. D/L neutralises this by setting Team 2 an enhanced target over the number of runs Team 1 actually scored.

The explanatory booklet Your comprehensive guide to the Duckworth/Lewis method for target resetting in one-day cricket by Frank Duckworth and Tony Lewis is temporarily out of print, pending an update to incorporate the new tables. Recent purchasers of this booklet should see page 61 for information on how to obtain the updated tables.

The computer program CODA, which carries out all calculations of D/L targets and provides many features besides, has also been updated. Arrangements for obtaining this program have now changed. These will be advised on this website in due course. Existing owners of CODA should email Tony Lewis as below requesting information on how to update their copy.

Frequently asked questions
After responding to many enquiries the authors have drawn up a list of frequently asked questions with their responses.

Further questions or comments may be made directly to the authors via email.

Frank Duckworth

Tony Lewis