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Duckworth-Lewis-Stern (DLS) Calculator

🌧️ Cricket rain rule — revised targets, par scores & resource percentages

Simple DLS Target

Rain reduces Team 2's overs — most common scenario.

Team 1 Score

Team 1 Overs Allotted

Team 2 Overs (Original)

Team 2 Overs (After Rain)

Team 2 Wickets Lost at Interrupt

Par Score at Current Point in Team 2's Innings

Enter Team 2's current state to see if they are ahead or behind DLS par.

Current Score

Overs Remaining

Wickets Lost

Par Score Tracker

Is Team 2 currently ahead or behind DLS par? Live check.

Team 1 Final Score

Team 1 Overs

Team 2 Total Overs Available

Team 2 Current Score

Overs Remaining

Wickets Lost

Team 1 Innings Interrupted

When rain also affects Team 1's batting innings.

How this works: Team 1 loses some overs mid-innings. The resource they lost due to interruption is subtracted from their full-innings resource to get the adjusted Team 1 resource percentage. Team 2's target is then calculated against this adjusted baseline.

Team 1's Innings

Team 1 Final Score

Team 1 Overs Allotted (Original)

T1 Wickets at Interruption

Overs Remaining Before Interrupt

Overs Remaining After Resumption

Team 2's Innings

Team 2 Overs Available

T2 Wickets if Interrupted (else 0)

DLS Resource Percentage Table

Resource % for all overs remaining (1–50) × wickets lost (0–9).

Values computed from the simplified DLS exponential model: R(u,w) = Z₀[w] × (1 − e^{−b·u/Z₀[w]}), b = 0.0765. Full-innings (50 overs, 0 wickets) ≈ 100%.

Formula Quick Reference

Resource Percentage

R(u,w) = Z₀[w] × (1 − e^{−b·u/Z₀[w]})

u = overs remaining, w = wickets lost, b = 0.0765

Target (T2 resources ≥ T1)

Target = T1 Score + (R₂ − R₁) × G50

G50 ≈ 235 (par innings score for a 50-over match)

Target (T2 resources < T1)

Target = T1 Score × (R₂ / R₁) + 1

Proportional reduction — most common rain-stop case

Z₀ Values (by wickets lost)

0W:55.7 · 1W:50.0 · 2W:41.6 · 3W:33.6 · 4W:26.2

5W:19.5 · 6W:13.9 · 7W:9.1 · 8W:5.4 · 9W:2.4

What is the Duckworth-Lewis-Stern (DLS) Method?

The Duckworth-Lewis-Stern (DLS) method is the official mathematical system used by the International Cricket Council (ICC) to determine fair revised targets in limited-overs cricket matches interrupted by rain, bad light, or any other cause. It replaced the older and frequently criticised "highest scoring overs" (HSO) method that had been used since the 1970s.

The method was invented by two English statisticians, Frank Duckworth and Tony Lewis, and first published in 1998. It was adopted by the ICC for all One-Day Internationals in 1999. In 2014, Australian statistician Professor Steven Stern took over the method's maintenance and applied refinements to better handle high-scoring Twenty20 and ODI matches — giving rise to the "Stern" addition to the name: DLS.

The most famous catalyst for its creation was the infamous 1992 Cricket World Cup semi-final between England and South Africa. South Africa needed 22 runs off 13 balls when rain interrupted play. Under the old rain-rule, when play resumed they needed 22 runs off just 1 ball — a manifestly impossible task. The absurdity of the result prompted the search for a fairer system.

How DLS Works

The central insight of the DLS method is that a batting team's ability to score runs depends on two resources simultaneously: the number of overs remaining and the number of wickets in hand. A team with 30 overs remaining and all 10 wickets is in a very different position from a team with 30 overs remaining but only 3 wickets left.

The DLS method assigns a resource percentage to every combination of (overs remaining, wickets lost). A team starting a full 50-over innings with all wickets intact has 100% resources. As overs are consumed and wickets fall, the resource percentage decreases. When rain interrupts play, we compare the resource percentages available to each team and adjust the target accordingly.

Key Principles

Resources depend on both overs remaining and wickets in hand — not just overs.
The target adjusts proportionally based on the ratio of resources each team had available.
If Team 2 has fewer resources than Team 1, the target is scaled down proportionally.
If Team 2 has more resources (rare, but possible in some T1 interruption scenarios), the target is increased by a G50 factor (≈235 runs, the par score for a 50-over innings).

The DLS Formula

The resource percentage for a given state (u overs remaining, w wickets lost) is computed using an exponential decay model:

R(u, w) = Z₀[w] × ( 1 − e^{−b × u / Z₀[w]} )

where b ≈ 0.0765 (ODI/50-over format constant)

Z₀ Values (Asymptotic Averages by Wickets Lost)

The Z₀ value for each wicket count is the asymptotic average — the maximum resource percentage achievable at that wicket count with unlimited overs. It represents how much scoring potential remains at that level of wickets.

Wickets Lost	Wickets Remaining	Z₀ Value	Interpretation
0	10	55.7	Full complement — highest scoring potential
1	9	50.0	One wicket down
2	8	41.6	Two down — resources falling faster
3	7	33.6	Three down — middle order exposed
4	6	26.2	Four down
5	5	19.5	Five down — lower order dependent
6	4	13.9	Six down — tail batting
7	3	9.1	Seven down
8	2	5.4	Eight down — last pair batting
9	1	2.4	Nine down — last wicket standing

Note: The Z₀ values do not sum to 100 — they are used within the exponential formula, where the full 50-over, 0-wicket resource R(50, 0) ≈ 53.6 is normalised to 100% by the software. Our calculator normalises automatically.

Worked Example

Scenario: Team 1 scores 250 in 50 overs. Rain interrupts Team 2's innings after 20 overs when they have lost 3 wickets. Play resumes with 15 overs remaining (i.e., the total available overs to Team 2 is 35). What is the DLS target?

Step 1 — Calculate Team 1 Resource (%)

Team 1 batted their full allotment (50 overs, 0 wickets lost at the start):

R(50, 0) = 55.7 × (1 − e^{−0.0765 × 50 / 55.7}) ≈ 53.60
Normalised T1 Resource ≈ 100%

Step 2 — Calculate Team 2 Resource (%)

Team 2 has 15 overs remaining and 3 wickets already lost:

R(15, 3) = 33.6 × (1 − e^{−0.0765 × 15 / 33.6}) ≈ 10.82
Normalised T2 Resource ≈ (10.82 / 53.60) × 100 ≈ 20.19%

Step 3 — Compare Resources

T2 resources (≈20.19%) < T1 resources (100%) → use the proportional scaling method.

Step 4 — Apply Target Formula

Target = T1 Score × (T2 resource / T1 resource) + 1
Target = 250 × (20.19 / 100) + 1
Target = 50.47 + 1 ≈ 52 (rounded up to nearest whole number)

Note: A real DLS calculation would use the full professional tables, but this demonstrates the methodology correctly. Use the calculator above for precise values using the standard Z₀ parameters.

Common DLS Scenarios

Scenario	When it applies	Calculator Tab
Rain stops before Team 2 bats	Match shortened — Team 2 gets fewer overs from the start	Simple Target
Rain during Team 2's innings	Team 2 has already batted some overs; remaining overs reduced	Simple Target
Live par score check	Is Team 2 currently on track to win or lose on DLS?	Par Score Tracker
Rain during Team 1's innings	Team 1 also lost overs — adjusted T1 resource used	Team 1 Interruption
Multiple interruptions	Rain stops play more than once — recalculate at each stoppage	Team 1 Interruption

Frequently Asked Questions

What is the Duckworth-Lewis (DL) method in cricket?

The Duckworth-Lewis (now DLS) method is a mathematical formula used in limited-overs cricket to recalculate a fair target score when rain or other interruptions shorten a match. It accounts for both the overs remaining and the wickets in hand as scoring "resources," and adjusts targets proportionally based on the resources available to each team. It replaced fairer-sounding but flawed older methods and has been the ICC standard since 1999.

Why was the DLS method introduced?

The most notorious example occurred in the 1992 World Cup semi-final between England and South Africa. South Africa needed 22 runs from 13 balls when rain stopped play. The "highest scoring overs" rule in use at the time reduced the revised target to 22 runs from 1 ball — making the task mathematically impossible. This absurdity prompted Frank Duckworth and Tony Lewis to develop a resource-based model during the 1990s. Their formula was officially adopted by the ICC in 1999 and refined by Professor Steven Stern in 2014.

What is a resource percentage in DLS?

A resource percentage represents the proportion of scoring potential a batting team has remaining at any given point in their innings. It depends on two factors: the overs still to be bowled and the number of wickets remaining. A team at the start of a 50-over innings with all 10 wickets has 100% resources. As overs are used and wickets fall, resources shrink. The DLS method ensures each team's revised target reflects the resources they actually had available.

How do I calculate a DLS target?

First, compute resource percentages using R(u,w) = Z₀[w] × (1 − exp(−b × u / Z₀[w])) where u is overs remaining and w is wickets lost. Normalise both team's resources relative to a full 50-over innings. Then:

• If T2 resources < T1 resources: Target = T1 Score × (T2% / T1%) + 1
• If T2 resources ≥ T1 resources: Target = T1 Score + (T2% − T1%) × G50, where G50 ≈ 235

Our calculator handles all of this automatically — just enter the match details and click Calculate.

What happens when both teams' innings are interrupted?

When Team 1's innings is also shortened by rain, their effective resource percentage is adjusted downward to account for the overs they lost. The resource "lost" by Team 1 is calculated as R(overs_before_interrupt, wickets_at_interrupt) − R(overs_after_resumption, wickets_at_interrupt). This lost resource is subtracted from Team 1's full-innings resource. The resulting adjusted Team 1 resource % serves as the baseline for calculating Team 2's DLS target, ensuring both teams are treated fairly. Use the "Team 1 Interruption" tab in our calculator for this scenario.

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