Cricket Duckworth-Lewis-Stern Calculator

What Is the DLS Method? The Duckworth-Lewis-Stern (DLS) method is the mathematical formula used in limited-overs cricket to calculate a revised target score when weather interrupts play. It was developed by Frank Duckworth and Tony Lewis, two British statisticians, and was first used in international cricket in 1997. The method was updated and renamed to include Steve Stern, who took over as the custodian in 2014. Before DLS, rain rules were often perceived as unfair. The “most productive overs” rule at the 1992 World Cup is the notorious one: a twelve-minute rain break turned a gettable South African chase into more than twenty runs off a single ball, and that scoreboard is a large part of why DLS exists.

The Core Concept: Resources The DLS method treats a team’s available “resources” as a combination of overs remaining and wickets in hand. At the start of an innings: 100% resources (all overs, all 10 wickets). As overs are bowled or wickets fall, resources are consumed. The resource table is calculated from historical data on scoring patterns.

How a Revised Target Is Calculated When Team 1’s innings is complete and Team 2’s is interrupted: Team 2’s target is adjusted based on the percentage of resources Team 2 has available vs. what Team 1 had. If Team 2 has more resources than Team 1: their target is increased beyond Team 1’s score. If Team 2 has fewer resources: their target is reduced proportionally. Formula: D/L Target = Team 1 score × (Team 2 resources / Team 1 resources) + 1 run

The resource curve this calculator uses

Duckworth and Lewis published the shape of the curve even though the exact table is proprietary. Resources remaining decay exponentially with overs left:

Resources(overs left, 0 wickets) = (1 − e^(−0.0324 × u)) ÷ (1 − e^(−0.0324 × N))

where u is overs remaining and N is the full innings length. For a 50-over innings that gives:

Read the top row across and the counterintuitive part of DLS falls out. A side that has all 50 overs but has already lost five wickets holds only 64% of a full innings, and at seven down it is 42%. Wickets are resources in their own right, which is why a team eight down does not get a target anywhere near the one they would have had batting deep. Read a column down instead and you see why sides accelerate: the last ten overs are only about a third of the innings by resource, so the early ones carry more weight than their share of the overs suggests.

The 0-wicket column above is close to the official ICC figures, within about half a percentage point. The wicket columns are a flat multiplier and are the rougher part: real DLS makes wickets matter less when few overs remain, and this model applies the same discount throughout. Expect a few percentage points of drift in the wicket columns, most of it late in an innings with many wickets down.

G50, and why it is not used here

G50 is the expected total for a team using all its resources, around 245 runs in ODI cricket. DLS only needs it when Team 2 ends up with more resources than Team 1 had, which happens when Team 1’s innings was cut short and Team 2’s was not. This calculator handles the ordinary case, where Team 2’s innings is the one interrupted, so the target scales directly off Team 1’s actual score and G50 never enters it.

Why DLS is used

It accounts for the differing value of wickets and overs at different stages of an innings, which no run-rate rule can do. It is used in all ICC-sanctioned ODI, T20I and domestic limited-overs cricket. The standing criticism is that it can still produce odd results in very short matches, which is part of why a result needs at least 20 overs per side in an ODI and 5 in a T20.

This calculator is an approximation

The exact DLS resource tables are proprietary to the ICC. The curve above is a published approximation of the same shape, and it lands close on common scenarios. Official match targets are always produced by ICC-certified software, so treat this as a way to understand a target rather than to dispute one.