Duckworth-Lewis

Team batting first- Team A
Team batting second- Team B

This is something many of you know and many of you don't. Almost all cricket fans are aware of the Duckworth-Lewis term but almost all are not aware of the way it is calculated. 

      It is a method adopted by the ICC officials to fairly calculate the runs to be scored by the Team-B if the overs of the team batting second are reduced due to any interruptions. 
      In case, the match is abandoned after the team batting second has played some overs, then this method is used to calculate the amount of runs that should have been scored by Team-B, and then the winner is declared accordingly.
        This method was devised by two English statisticians, Frank Duckworth and Tony Lewis. Resources are the essence of this theory. This method is calculated on the basis of amount of resources available for Team-B after the match is interrupted. The resources are calculated and accordingly judgement is given. 
 

Percentage total resources remaining reference table (D/L Standard Edition)

Overs remaining	Wickets in hand
	10	8	6	4	2
50	100.0	85.1	62.7	34.9	11.9
40	89.3	77.8	59.5	34.6	11.9
30	75.1	67.3	54.1	33.6	11.9
20	56.6	52.4	44.6	30.8	11.9
10	32.1	30.8	28.3	22.8	11.4
5	17.2	16.8	16.1	14.3	9.4

 This is the table where resources available are already calculated in percentage.

Situation 1- Team-A completed their innings and Team-B's innings is reduced by some overs.

Example- 

Team-A scored 231 runs for the loss of 4 wickets in 50 overs.
Match is interrupted and team-b has only 30 overs to play with 10 wickets in hand.

Now, According to the standard edition of D/L method,
S x R2 / R1

Where,
R2= Resources available to Team-B
R1= Resources available to Team-A
S= Runs scored by Team-A

Calculation:
231 x 75.1 / 100 = 173.481
That means, Team-B has to score 174 runs to win in 28 overs. 

Situation 2.Team-A has completed their innings and Team-B has played a part of their innings when the match was abandoned.

Example
Team-A has scored 270 in 50 overs. Team-B scored 240 with the loss of 6 wickets in 45 overs when the play was abandoned. 

Calculation:
#Amount of resources lost by Team-B= 14.3 % (Table)
#So, Total resources left for Team-B = 100-14.3= 85.7%

Therefore, according to the formula,
S x R2 / R1:

270 x 85.7 / 100= 231.39

So, Team-B had to score 232 at the end of 45 overs to win the match, having scored 240, wins the match.

Situation 3- Team-A has completed their innings. Team-B has played a part of the innings when the match was interrupted. The match is started with reduced overs for the Team-B.


Example:
Team-A has scored 270 runs after 50 overs. Team-A scored 70 runs for the loss of 2 wickets in 20 overs when the play was stopped. The play was resumed and the overs were reduced to 40 overs for Team-B.

Calculation:
#Amount of resources available to Team-B after interruption= 30 overs and 8 wickets . That equals to 67.3% (Table)
#Resources available to Team-B after reduction in overs= (40overs-20overs) 20 overs and 8 wickets= 52.4% (Table)
#Resources lost= 67.3% - 52.4% = 14.9%
#Total resources available to Team-B= 100% - 14.9% = 85.1%

Therefore, 
270 x 85.1 / 100 = 229.77
Team-B has to score 230 runs to win the contest in 40 overs.

This method was first used in a match between Zimbabwe and England in which, Zimbabwe won by 7 runs.
       This method has faced many criticisms based on its accuracy and based on its calculation but it is still believed to be a fair method which provides statistically fair calculations.
       ICC uses the professional edition of this method, in which, the formula is the same but the resource percentage is different which the ICC has not disclosed publicly.