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Cricket · Stats · 5 min read

DUCKWORTH
LEWIS

The rain rule that was broken for 30 years — and the two statisticians who fixed it.

1992
The disaster
25+
Years in use
2D
Resource model
DLS
Current name
01 / The Problem

CRICKET HAS TWO CLOCKS

Unlike football or tennis, cricket has two resources that both tick down simultaneously.

🕐
50
OVERS
= Time
🏏
10
WICKETS
= Lives

The same 30 overs remaining means completely different things with 2 wickets lost vs 8 wickets lost. Same time — totally different game.

Same overs left. Different universe.
Strong position
30 ov
2 wickets lost
65% resources
Under pressure
30 ov
7 wickets lost
24% resources
Tap next to see what went wrong in 1992
02 / The Disaster

MARCH 22, 1992

England vs South Africa · World Cup Semi-Final

ENGLAND 252 / 6
SA NEEDED 22 off 13 balls
South Africa were on track. 22 runs needed from 13 balls — difficult but very achievable. The crowd was electric. Then the rain came.
After rain — old MPO rule said:
21 off 1
21 runs needed off just 1 ball
South Africa were eliminated. Not by batting. By maths.
Rain rules history
✗
Average Run Rate
Ignores wickets entirely. A team 8 down treated same as none down.
✗
Most Productive Overs
Removes lowest-scoring overs — punishes strategic early batting. Created the 1992 disaster.
✓
Duckworth-Lewis (1999)
Models both resources together using real match data. No systematic failure in 25+ years.
03 / The Formula

THE RESOURCE FUNCTION

Z(u, w) = Z₀(w) × [1 − e−b(w)·u]

Tap any wicket state below to see its resource curve

u
Overs remaining
Time resource left (0–50)
w
Wickets lost
Capital spent (0–9)
Z₀
Max resource
Best case from this wicket state
b
Decay rate
How fast resources build per over
Resource % by overs remaining
Resource percentage versus overs remaining for selected wicket state.
At 50 overs: 100% At 25 overs: 75% At 10 overs: 32%
The exponential shape was fitted to thousands of real innings — not assumed. The maths followed the cricket.
04 / Live Example

RAIN HITS. NOW WHAT?

Team A: 274 all out in 50 overs
Team B: 87/2 after 20 overs when rain stops play

1
Team A's resources used
100%
Full 50 overs, started with all wickets. Complete innings.
2
Team B's resources — after rain
74.1%
34.3% already used (20 overs, 2 wkts) + 39.8% remaining (15 overs left, 2 wkts)
3
Resource gap
−25.9%
Team B has less batting potential than Team A had. Target is scaled down proportionally.
4
Revised target calculation
Revised target
204
274 × 74.1% + 1

Already scored 87 → need 117 more off 15 overs
05 / The Resource Map

TAP ANY CELL

Rows = overs remaining · Columns = wickets lost

Tap any cell to see what that match situation means in real terms.

Overs 0wkt 2wkt 4wkt 6wkt 8wkt 9wkt
50 overs · 0 wickets
100%
Perfect start
10 overs · 9 wickets
3.5%
Last wicket hanging
25 overs · 2 wickets
63%
Comfortable chase
25 overs · 7 wickets
19%
Crisis mode

5 THINGS
TO REMEMBER

The D/L story in plain language — for anyone who builds systems.

1
Measure the right thing
D/L asked "what does each team have?" not "how do we adjust the score?" Reframing the question unlocked the solution.
2
Build from data, not theory
The exponential curve was fitted to thousands of real innings — not assumed. The maths followed the sport.
3
Simple breaks at the edges
ARR and MPO work in easy cases. They catastrophically fail in edge cases — which are exactly where fairness matters most.
4
Fair ≠ equal
D/L doesn't give both teams the same target — it gives a contextually appropriate one. Fairness requires understanding situation, not uniformity.
5
Models need maintenance
D/L → DLS in 2014. Same architecture, updated data. Build systems that recalibrate without being rebuilt.