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# How the Duckworth-Lewis-Stern method works

An explanation of the basic principles behind how targets and par scores in rain-affected games are decided

S Rajesh
08-Jun-2017

## How does DLS work?

The DLS (Duckworth-Lewis-Stern) method works on the principle that a batting team has two resources in hand when starting an ODI innings: 300 balls, and ten wickets. As the innings progresses, these resources keep depleting, and eventually reaches zero when a team either plays out all 300 deliveries, or loses all 10 wickets.
When, due to any reason, the batting team loses overs, they are denied the opportunity to make full use of their resources. Targets are hence revised in a way that is proportional to the amount of resources available to each team.
The rate at which these resources deplete isn't uniform across the overs, but varies depending on the scoring patterns of ODIs (calculated from studying matches over several years). At any point, the resources lost due to an interruption depends on:
• number of overs lost
• stage of an innings when the overs are lost
• wickets in hand at the time of the interruption
Losing overs in the later stages of an innings will usually impact a team more than losing the same number of overs earlier in an innings, as those overs are more productive, and teams have less opportunity to recalibrate their targets than if overs are lost early in the innings. A team which is already six down after 20 overs will have lesser to lose from a 10-over interruption, than a team which is, say, only two down at that stage. That is because in the first case, the team has already lost a huge chunk of their batting resources by the dismissals of six top-order batsmen. A team which is only two down can better capitalize on the last 30 overs than a team which is six down. However, the system doesn't take into account the specific batsmen who have been actually dismissed, or those who are still to bat.

## Do wickets lost after the interruption impact the chasing team's target?

No, they don't. According to DLS, a team exhausts its entire resources either when it is bowled out, or when it plays the full quota of overs. So, a score of 300 all out in 48 overs is the same as a score of 300 for 6 in 50 overs (in a 50-over game). What matters, though, is the number of wickets lost at the time of the interruption: the fewer the wickets lost, the greater is the opportunity cost of the overs lost for the batting team. A team which is only three down after 40 overs is likely to score more than a team which is eight down, and that is reflected in the targets that DLS sets.

## Why does the target for the team batting second sometimes reduce after an interruption in the first innings, even though both teams have the same number of overs?

Sometimes, when the team batting first has lost several early wickets, a reduction of overs is beneficial to them. For instance, if a team is 80 for 6 after 20, they will benefit from a reduced game. If 20 overs are lost and they finish on 140, DLS will readjust the 30-over target for the chasing team to 121. That is because the team batting first had already lost a huge chunk of their batting resources before the interruption, and would probably have been bowled out well before 50 overs anyway. The chasing team, however, have been denied the opportunity to bat up to 50 overs to chase a relatively low score. To redress that balance, their target is reduced to 121.
Another example: in the second game of the 2017 Champions Trophy, for instance, Australia's 46-over target stayed at 292 (New Zealand made 291) after a four-over loss when New Zealand were 67 for 1 in 9.3. Had they been 67 for 4 and then finished with the same total, Australia's target would have come down to 284.
Hence, if the batting team senses that rain is imminent, the smart thing to do would be to keep wickets in hand, to ensure they maximize the benefits of DLS.

## What is the difference between par score and target score?

Par score is the total that a chasing team should have reached - when they are 'X' wickets down - at the time of an interruption; target is the revised score that a team is required to get after an interruption. In a nutshell, par scores are calculated before an interruption, while targets are calculated after an interruption. The target is one fixed number, while the par score changes according to the number of wickets lost.
For instance, the Champions Trophy match between Australia and Bangladesh match which was recently washed out, the par scores for Australia after 20 overs were 41 for 0, 48 for 1, 58 for 2, 69 for 3, 84 for 4 and so on. If the interruption had happened at 20 overs and no further play was possible, Australia would have been declared winners for exceeding the par score corresponding to the number of wickets they had lost. If they hadn't, Bangaldesh would have won.
If it had rained during the innings break, leaving Australia with only 20 overs to bat, then their revised target, with all ten wickets in hand, would have been 109 in 20 overs.

## How do net run rate calculations change in matches where DLS comes in?

In matches affected by DLS, the score for the team batting first is taken as the par score at the time of the interruption (if no further play is possible), or as one run less than the target (in case a revised target is set). Thus, in the case of the Australia-Bangladesh match, if Australia were one down at the time of the interruption at 20 overs, then Bangladesh's score for the purposes of NRR calculation would be 48. If Australia had been set a target of 109 in 20, then Bangladesh's score would be taken as 108 in 20.
The logic behind this is simple: the NRR of the winning team should always be greater than zero, and higher than the losing team in that game. Else, there could be situations where the winning team could be ahead of the par score, but have a run rate lower than the end-of-innings rate of the team which batted first. For instance, Australia, at 50 for 1 after 20, would have been ahead of par, but their run rate of 2.5 would have been below Bangladesh's innings run rate of 3.66. That wouldn't make cricketing sense. Adjusting the score of the team batting first ensures that the team which wins the game always has a positive NRR for that match.

S Rajesh is stats editor of ESPNcricinfo. @rajeshstats