How does the Duckworth-Lewis-Stern (DLS) method works in cricket?

How does the Duckworth-Lewis-Stern (DLS) method works in cricket?

The whole cake represents 100% of the cake. Now cut the cake into four pieces. Three pieces together will represent 75% of the cake, two pieces will show 50% while only one piece will represent 1/4 or 25%.
Now, imagine a batting side in ODI format. At the start of the innings, they have 50 overs to play and 10 wickets in hand. This 50 overs+10 wicket is 100% of the ‘resources’ they have. If they have 0 overs left to play or all their 10 wickets have been taken, then they are left with nothing. Hence, 0 overs left to play or 0 wickets in hand shows that the batting side has 0% of the resources.
Now here the main thing starts.
  • How are scores adjusted according to DLS system?
Let us say there is a match between Australia and England. Australia scored 250/10 runs in 50 overs in the first innings. England was at 190/5 in 40 overs when rain interrupted the match. The rain is so much that no further play is allowed and the winner has to be decided by the DLS method.
Now according to the run rate method, it might look that Australia should win the match because they had a run rate of 5 (250/50) than 4.75 (190/40) of England but this is not the case. It is unfair because this doesn’t take into account that England still has 5 wickets left and the pace of batting won’t be the same in the last overs. This is where the DLS system helps.
DLS system uses a formula to take into account the over remaining and also the number of wickets they have in hand. This is the chart,


Now England was at 190/5 in 40 overs which means they lost 5 wickets and still have 10 overs in hand. In this table, look for 5 wickets lost and 10 overs remaining, and it will lead to the number 26.1. This means England still have 26.1% of their resource (overs+wickets) remaining.
26.1% is the resources left with them. So how much resources (overs+wickets) did they consume? It is 100–26.1=73.9. This means in reaching 190/5 in 40 overs, they consumed 73.9% of their resources (overs+wickets).
Now Australia had scored 250 in 50 overs by utilizing 100% of the overs. So now the adjusted score will be 73.9/100 multiplied by 250. This is to see how much Australia would’ve scored had they consumed the same amount of resources that England used (73.9%). So 0.739*250=184.75 which means Australia would’ve scored 185 runs with the same resources as England. England was at 190/5 so according to DLS method, England has won the match.
Had England been at 190/6, the adjusted score would’ve been 193 runs. Had England been at 190/7, the adjusted score would’ve been 205 runs. You can check this yourself from the table. As the wickets increased, the adjusted score increased and hence in rain prevailing conditions, team tend to focus more on losing minimum wickets.
Example 2
Imagine it is India VS NZ. India scored 300 runs in 50 overs but before the start of the second inning, rain starts. Due to rain, the second inning is reduced to 45 overs. What will the adjusted score be?
Now the DLS method needs to account for the reduced overs. NZ has 10 wickets but now they have only 45 overs. So search the table for 45 overs left and 0 wickets lost, it will lead you to the number 95. This means that NZ has 95% of its resource available now.
India had earlier scored 300 by using 100% of the resources. So what would India’s score be if they also had 95% of the resources like NZ? It will be 95/100 multiplied by 300. Hence 0.95*300 gives 285 runs and hence 286 runs will be the target for NZ now.
If the first innings had utilized 100% of their resources then you simply, multiply the resources used or resources available percentage of the 2nd team with the score of the first inning to get the adjusted score.
  • If you have to judge the winner if the rain stops the match fully, then you use the resources used percentage.
  • If you have to adjust the score which has to be chased now then you use the resources available percentage.

Now, what if the rain had interrupted the first inning too and the first team didn’t use 100% of their resources? What if they only played for 30 overs? In that case, you simply calculate the resources utilized by Team 1 from the same table the same way you used for Team 2 earlier and then you simply use the formula,
Adjusted score= Team 1 score * Resource % with Team 2/Resource % with Team 1
Bingo!
If Resource % of Team 2 is more than Resource % of Team 1, then the fraction value will be more than 1 and the adjusted score will become greater than the first inning score and hence often you see in reality too that the adjusted score is sometimes greater than the first inning score.

This is the whole foundation of the method. Nowadays, the officials use more formulae and data which isn’t available to the public and is available only as a software but the basic logic behind the method is the same as mentioned in the answer.

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