Cricket has a problem no other major sport has to solve. When rain shortens a limited-overs match, the two sides have not had the same opportunity, and somebody has to decide what a fair target would have been. For a long time the answers were bad.
What came before
Early methods adjusted the target by run rate: if the chasing side lost a quarter of its overs, it chased three-quarters of the runs. That ignores wickets entirely, and it is far easier to score at eight an over for ten overs with all ten wickets standing than it is across fifty.
The method that replaced it was worse. The Most Productive Overs rule removed the chasing side's target runs from the lowest-scoring overs of the first innings, on the theory that this was symmetrical. It was not, and it produced the moment that ended it: a World Cup semi-final in 1992 in which a rain break left South Africa needing 22 from 13 balls, and the recalculation reduced that to 21 from 1. The chase was over before it resumed.
The idea behind DLS
Frank Duckworth and Tony Lewis, two English statisticians, started from a different premise. A batting side does not have overs. It has two resources, overs remaining and wickets in hand, and both matter, and they interact.
Ten wickets and fifty overs is 100% of the available resource. Ten wickets and twenty-five overs is not 50%, because a side batting twenty-five overs with all its wickets can attack from the start. Two wickets and twenty-five overs is much less than either, because the resource that lets you use overs aggressively has already gone.
Duckworth and Lewis built a table of resource percentages for every combination of overs remaining and wickets lost, derived from what teams have historically scored from those positions.
How a target is set
Three steps.
- Work out what percentage of resources the first side actually used.
- Work out what percentage the second side will have available.
- Scale the first innings score by the ratio between them, and add one.
If both sides had the same resources, the target is unchanged. If the chasing side has fewer, the target comes down, but by less than a run-rate calculation would suggest, because the wickets are worth something. If the chasing side has more resources, which happens when the first innings was interrupted, the target goes up.
That last case is the one that surprises people. A side bowled out for 180 in a rain-shortened first innings can find the opposition chasing 220, and the arithmetic is right: the first side batted knowing it had less time, and the second gets more.
The Stern revision
The S was added in 2014, for Steven Stern, the Australian statistician who took over maintaining it. The original tables were built on scoring patterns from an era when 250 was a good ODI total. Scoring rates rose sharply, particularly at the end of innings, and the model had to be re-fitted to match. It continues to be updated as the game changes.
What it does not do
DLS makes no attempt to model who is playing, what the pitch is doing, or which specific bowlers are left. It is a historical average across a large sample, applied to a single match, and it will occasionally produce a target that looks unkind to one side.
The defence of it is comparative rather than absolute. Nobody claims it is perfect. It is better than every alternative that has been tried, and it is transparent, because the tables are published and anyone can check the arithmetic.
Matches decided this way are recorded in our archive with the result as officially declared. You will find them across the ODI and T20 records, usually noted as a win by a runs margin under the method.
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