To explain the Duckworth/Lewis Method, it is first necessary to explain why we need it. The method is a way of recalculating one-day cricket scores using statistical tables.

A game of cricket is traditionally played over three, four or five days and features two innings for both sides. A game of one-day cricket, or limited-overs cricket, is played on one day, and has a pre-set number of overs to be faced by each side, unless they are bowled out. The number of overs is normally 50, but some tournaments feature 40 or 45 - basically any multiple of five can be used, although fifty is most common. Now, the problem one-day games run into is the fact that cricket games feature breaks for rain. In longer games, this doesn't matter a great deal, but in one-day games, it can lead to many games being unfinished unless there is some provision for innings to be shortened.

Obviously, if the team batting second end up facing fewer overs than the team batting first due to adverse weather conditions, then some provision has to be made for an adjustment of the run target in such cases. The most used system in the past was adjusting according to Average Run Rate - merely decide the winner according to which team got the most runs per over. Now, this was better than the farcical 'Most Productive Overs' system used in some tournaments during the 1990s. The MPO system worked by setting the team batting second a target of the runs scored by the team batting first in their x most productive overs, where x is the number of overs faced by the team batting second. The problem with the MPO system was that it heavily favoured the team batting first, as demonstrated during the 1992 World Cup. The problem with shedding the least productive overs from a target is that the first few least productive may well be maiden overs¹, so that a target of 249 from 50 overs may be revised to, say, 249 from 47 overs, if three overs were lost, and the first innings contained at least three maidens. The team batting second is thus having its bowling efforts nullified to a degree.

So the Most Productive Overs system wasn't working, and Average Run rate failed to take into account the number of wickets taken. So there was still not a particularly fair method of adjusting scores. Which is where Duckworth and Lewis come in.

Duckworth and Lewis

Frank Duckworth and Tony Lewis are a couple of Cambridge University statisticians who, being quite partial to cricket, decided to develop a truly fair system of score-adjustment for these rain-affected games. One which would take into account overs, runs and wickets. Their method has become the recognised system for this sort of thing in all cricketing nations. The rule was first introduced in 1997, and by 1999 it was used in the cricket world cup hosted in England. There are yearly revisions of the statistics used, and the table provided below is an extract from the 2002 version.

The Duckworth/Lewis Method

The Duckworth/Lewis method uses wickets lost and overs left to decide what proportion of a team's 'resources' remain. At the beginning of a match, a team has 100% of its resources - 10 wickets standing, 50 overs remaining. However, in the event of a rain delay, one or both teams will end up with less resources left.

These resources are calculated by a complex mathematical formula, with 100% resources being 50 overs and 10 wickets remaining. The table below gives examples of resources left in different overs/wickets scenarios for a 50 over match. A complete Duckworth/Lewis table would include every number of overs between 1 and 50, and every number of wickets between 1 and 10.

Now, both sides start a game with 100% of their resources intact (all the overs, all the wickets). If their innings is shortened, they lose resources - for example, if they reach 40 overs (10 remaining) with seven wickets lost, they have 17.9% of their resources remaining.

Both teams' targets are recalculated dependent on the resources they have, and some examples of the resources are demonstrated in the table. When there is an interruption, the resources come into play.

The table demonstrated at the bottom is an abridged version of the full D/L table, and resources are calculated from reading across from overs remaining to wickets remaining and calculating starting resources and then subtracting any resources lost due to weather to calculate the resources available to the team. The two teams' resources are then compared and a scaling up or down of the score of the team batting first is made to decide what the team batting second must achieve from their resources to be considered to have done as well as the team batting first with theirs.

It is easier to demonstrate this with examples than to describe, so there are some hypothetical examples below, in which Team 1 refers to the team batting first, and Team 2 refers to the team batting second.

Scenario 1 - A premature ending to Team 2's innings

• For the sake of this example, Team 1 scored 200 runs from their 50 overs, and then Team 2 reaches 146 for the loss of two wickets from their first 40 overs before rain stops play.

• Team 1 - uninterrupted, 100% resources used.

• Team 2 - lost 10 overs, 2 wickets down, lost 32.5% therefore used 67.5%.

• Team 2's target is revised down to 69.2/100 of the original target (due to reduction in resources). The revised target is thus 135. As Team 2 has passed that target, they have won. Any score down to 136 would have been sufficient for victory, 135 would have been declared a tied game, and lower than 138 would have resulted in a defeat.

Scenario 2 - Interruption to Team 2's innings

• For this example, imagine that due to bad weather the match has been reduced to 40 overs before its commencement. 40 overs, no wickets is 90.3% of resources, rather than the normal 100%. Team 1 get through their 40 overs, scoring 223. However, during Team 2's innings, there is rain after thirty overs, by which point they have scored 147 runs and lost five wickets. They lose five overs due to rain, and face the final five overs.

• So, Team 1 got to use 89.3% of their resources. Team 2, by the thirty over mark, have ten overs left and five wickets down, hence they have 27.5% of their 89.3% remaining, and so have used 62.8%. However, the last five overs, with five wickets standing, only account for 17.8%, so they only get to use 80.6 %. To recalculate the target, the target will be 224 x (80.6/90.3). The target is therefore revised to 199.94, which rounds to 200 to win, 199 to tie, so they are left needing 53 runs from the last five overs for victory.

Scenario 3 - Interruption to team 1's innings

• Team 1 have scored 180 from 30 overs, losing five wickets when extended rain means they don't face any more overs, and Team 2 also face 30 overs. Now Team 1 started with 100% resources, but when the rain came, they still had 40% of them remaining (20 overs, five wickets), so used 60% of their resources to get their 180 runs.

• Team 2 starts the innings with 30 overs, no wickets lost, which gives them 77.1% resources. Their target is thus increased by a ratio of 77.1/60 to 231.3, or 232 to win, 231 to tie.

So, what those scenarios hopefully demonstrate is the use of the Duckworth/Lewis, or D/L, method in practice. The fact that the system can be adapted to account for either mid-innings or innings-ending delays to either innings of the game is the key. Now used in one-day cricket around the world, and confusing fans and players alike the world over, it is how rain-delayed games are recalculated.

An extract from the 2003 Duckworth/Lewis tables