Duckworth-Lewis Calculation Graphs for Different Duration Matches

I think one the best things to have happened to cricket in 1990s was the development of a rule to update the target score should there be an interruption and team batting cannot have full set of overs. Even more remarkable was that ICC who has a reputation for choosing wrong options always, accepted this rule. This rule was devised by two statisticians Frank Duckworth and Tony Lewis and appropriately named after them.

According to Duckworth and Lewis, cricket is about using resources (overs and wickets) to achieve a target set by an opposition who batted first. Therefore, in case of an interruption, both overs and wickets should be considered. 

Exact D-L calculations often become very cumbersome. Thus, in absence of sophisticated computer, most teams in small league and friendly matches devise some ad-hoc rule. Here I show the graphs that can be used to estimate the modified target after an interruption. Originally the D-L method was developed for 50 overs matches, but usually in small leagues and friendly games, matches are shorter, therefore I estimated the D-L calculations for 20,30,40 and 50 over games.

How to read and use the graphs

x-axis is number of over remaining. The different colors of the lines refer to number of wickets fallen. So estimate the scaling factor to update the target, you need to know how many overs have been bowled (i.e. x-axis), how many wickets of the team batting second have fallen, color of the line. Corresponding to the number of wickets fallen and over bowled, y-axis give a fraction, by which you have multiply the original target to get the updated target.

Imagine, you are playing a 40 over game and set a target of 220, and rain stops the play at 25 over and the team chasing has lost 6 wickets. What should be D-L score of the team batting second to win the game? So we draw a vertical line at 15 over, and find out where does it cross the green line, from that crossing draw a horizontal line and find out what value it corresponds to on the y-axis. In this example we get 43.6 on y-axis. This means that the opposition should have scored 56.4 % runs i.e.  220 *(100 - 43.6) = 123 runs. This number would go up if they had lost one more wicket, to 142 and so on.

Enjoy your own simplified graphical D-L update rule, but I do wish that your games go on uninterrupted...

right arm over

Arvind