Duckworth and Lewis

The Duckworth and Lewis method or the D/L method is a set of formulae and tables created by Frank Duckworth and Tony Lewis. The method was adopted by the International Cricket Council (ICC) in 1999 to address the problem of delayed one-day cricket matches for reasons of rain, poor light and floodlight failures..  Frank is a consultant statistician and editor of the Royal Statistical Society's monthly news magazine, RSS NEWS. Tony is a lecturer in Quantitative Methods in Management in the Business School at Oxford Brookes University. The method was developed in the early part of the 1990s when Tony was working at the University of the West of England, Bristol and when Frank and Tony lived quite close to each other in Gloucestershire. 

The DL method works on the following principles:

• A team's ability to make runs at any given point in a match is depends on the number of overs remaining and the number of wickets in hand..
• When a match is shortened, the resources of one or both teams are affected. The D/L method sets targets based on the relative resources available to the teams.

Simple graphical resource allocator

If the side batting first in a 50-over match makes 250 runs, the target for the side batting second is 250 to tie, 251 to win. Their average run-rate must therefore exceed 5 per over if they are to win in a full 50 overs. But if rain or bad light stops further play after only 20 overs, during which the second side score 101 runs, then comparing average run-rates would make the second side the winner. But if they had lost nine wickets in scoring those 101 runs, then few would give much for their chances in an uninterrupted 50 overs. So the average-run rate system gave an unfair advantage to the side batting second if the number of overs was reduced. They could blaze away without worrying too much about losing wickets. Other variants were tried, such as basing the target on the best overs of the side batting first, but this was unfair to the side batting second.

A detailed Ball by Ball resource table is available for the referees and the teams playing.. A reduced over by over table is also available.. 

Example 1 (Suspension during Team 1’s innings) :Team 1 bats first and Team 2 bats next..

In a 50 over-per-innings match, Team 1 reaches 79/3 after 20 overs and then there is a suspension in play. It is decided that 20 overs of the match should be lost, 10 of these by each team. Team 1 resumes to reach a final total of 180 in its revised allocation of 40 overs.

• Number of overs per innings at the start of match, N = 50
• Resource percentage available to Team 1 at start of innings = 100%
• Resource percentage remaining at suspension (30 overs left, 3 wkts lost = 61.6%
• Resource percentage remaining at resumption (20 overs left, 3 wkts lost) = 49.1%
• Resource percentage lost due to suspension = 61.6 – 49.1 = 12.5%
• Resource percentage available to Team 1, R1 = 100 – 12.5 = 87.5%
• Number of overs available to Team 2 at the start of its innings = 40
• Resource percentage available (40 overs left, 0 wkt lost), R2 = 89.3%
• R2 is greater than R1, i.e. Team 2 has more resource available than had Team 1, so its target should be increased. 
• Team 1 score S = 180
• Team 2’s revised target is
• T = S + G50 x (R2 – R1)/100 + 1 = 180 + 235 x (89.3 – 87.5)/100 + 1 = 185 (rounded down). 

average total score in a 50-over innings, referred to here as G50. For men's 50overcricket it is 235

Example 2 (suspension during Team 2’s innings) 


In an One Day International match (50 overs per innings), Team 1 has scored 250 from its allocation of 50 overs in an uninterrupted innings. Team 2 has received 12 overs and has scored 40/1. Then play is suspended and 10 overs are lost.

• Number of overs at start of match, N = 50.
• Team 1’s innings was uninterrupted, so its resource percentage available, R1 = 100%
• Resource percentage available to Team 2 at start of innings = 100%
• Resource percentage remaining at suspension (38 overs left, 1 wkt lost) = 82.0%
• Resource percentage remaining at resumption (28 overs left, 1 wkt lost) = 68.8%
• Resource percentage lost due to suspension = 82.0 – 68.8 = 13.2%
• Resource percentage available to Team 2, R2 = 100 – 13.2 = 86.8%
• R2 is less than R1; 
• S = 250.
• Team 2’s revised target is
• T = S x R2/R1 + 1 = 250 x 86.8/100 + 1 = 218 , and it needs a further 178 runs from 28 overs.