Duckworth/Lewis method

Australia eased to their first ever ICC Champions Trophy title in November 2006, beating West Indies by eight wickets in the rain-marred final by the Duckworth/Lewis method.
The Australia-West Indies ODI match was one among several others that have been interrupted by rain and inclement weather, calling for the final result to be declared on the basis of the Duckworth/Lewis method.Australia had beaten Sri Lanka by 48 runs in a semi-final match in the 2003 World Cup.
Though the method has often been criticised due to some blind spots, the fact remains a result can always be reached in a reduced over match by using it.
The Duckworth/Lewis method was invented by two statisticians, Frank Duckworth and Tony Lewis in an attempt to solve the problem of creating a fair target for the teams in a limited-over match shortened by weather.
Basis of the method
The method works on the premise that teams have basically two resources with which they can make as many runs as possible: (1) Number of overs to be faced (2) Number of wickets in hand.
From any stage in the innings, a team's further run-scoring capability depends on both the two resources in combination.
When a match is shortened due to rain after it has begun, the resources of one or both teams are depleted and both have usually different amounts of resources for their innings. This requires a revised target to be set in order to accord a level-playing field to both teams. The D/L method does this in accordance with the relative resources available to the two teams.
A table made by the two statisticians gives the percentage of these combined resources that remain for any number of overs left and wickets lost.
The method has two editions: standard and professional. While the former requires manually using the published table of resource percentages to come up with revised targets, the latter uses a computer programme, which is limited to games basically at the international level.
The usage of the method is best described by the following three examples highlighting three scenarios in a limited-over match:
(1) Premature curtailment of Team 2 innings
(2) Interruption to Team 2 innings
(3) Interruption to Team 1 innings

Scenario 1: Premature curtailment of Team 2 innings
Example: Team 1 has scored 250 runs from 50 overs and Team 2 has lost 5 wickets after having scored 199 runs in 40 overs. Play has been stopped due to bad weather and the abandoned match requires a decision on the winner.
Team 1 had no interruption in its innings, so had 100% resource percentage available to it. But, it is not the case with Team 2.
Team 2 innings: Resource (in per cent) available at start of innings: 100%
After 40 overs, Team 2 has: 10 overs and 5 wickets left
From the table, resource (in per cent) left at suspension of play: 27.5%
As play is abandoned all the remaining resource are lost.
Hence, resource (in per cent) available for Team 2 innings: 100 - 27.5 = 72.5%
Team 2 has less resource available than Team 1.
To give the target, now Team 1 score must be scaled down by the ratio of resource: 72.5/100
Team 1 scored 250, so Team 2's target: 250 x 72.5/100 = 181.25
For competitions commencing April 1999, the next lower whole number, in this case 181, is the score to tie, or the 'par score' for the match situation at the stoppage.
As there will be no further play, the winner is decided according to whether or not the par score has been exceeded.
In this example, with 199 runs on board, Team 2 has exceeded the 'target' by 18 and so are declared the winners by 18 runs.
Scenario 2:Interruption to Team 2 innings
Example: A match has been shortened to 40 overs per side even before it commenced. Team 1 has scored 200 runs from 40 overs and Team 2 has lost 5 wickets while scoring 140 runs in 30 overs. Play is suspended and 5 overs are lost. What is Team 2's revised target?
Team 1 innings: At the start of 40 overs, resource (in per cent): 90.3%
Team 2 innings: Resource (in per cent) available at start of 40 over: 90.3%
After 30 overs, Team 2 have: 10 overs and 5 wickets left.
From table, resource (in per cent) left at start of suspension: 27.5%
5 overs are further lost, so when play resumes, only 5 overs are left.
From table, resource (in per cent) left at resumption of play: 16.4%
Hence, resource lost: 27.5 - 16.4 = 11.1%
So, resource available for Team 2 innings: 90.3 - 11.1 = 79.2%
Team 2 has less resource available than Team 1. To give the revised 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': 200 x 79.2/90.3 =175.42.
This rounds down to 175 to tie with a revised target of 176. This means, Team 2 require 36 more runs to win from 5 overs with 5 wickets in hand.
Scenario 3: Interruption to Team 1 innings
Example: In an ODI, Team 1 has lost 7 wickets in scoring 190 runs in 40 overs from an expected 50 when extended rain leads to Team 1 innings being terminated and Team 2 innings is also restricted to 40 overs. What is the target for Team 2?
As the teams' inning are in different stages withr 10 overs having been lost, they represent different losses of resource.
Team 1 has lost 7 wickets and has 10 overs left when rain stopped play.
From the table, one can see that the premature termination of their innings has deprived Team 1 of 20.6% resource percentage they had remaining. Having started with 100%, they have used 100 - 20.6 = 79.4%.
Which means, Team 1 has had 79.4% resources available for their innings.
Now, Team 2 will also receive 40 overs. With 40 overs left and no wicket lost, one can see from the table that the resource percentage available (relative to a full 50 over innings) is 90.3%.
Team 2, thus, has 90.3 - 79.4 = 10.9% greater resource than Team 1 had. 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]
So, one needs to add 190 + 24.53 to get 214.53, Rounding down gives 214 to tie and Team 2's target as 215 in 40 overs.