Duckworth-Lewis-Stern Method: How Rain Rules Work in Limited-Overs Cricket
The Duckworth-Lewis-Stern (DLS) method is the mathematical formula used to calculate revised targets in limited-overs cricket when rain interruptions reduce the number of overs available. Developed by statisticians Frank Duckworth and Tony Lewis (with later refinements by Steven Stern), DLS replaced the simpler 'run rate' method in 1997 and became the standard ICC-mandated rain rule. DLS factors in wickets remaining as well as overs — unlike the old method which only adjusted for overs lost.
DLS background: before DLS, cricket used simple 'run rate' calculations for rain-affected matches. The problem with simple run rate: if a team batting first scored 250 from 50 overs (run rate 5 per over) and rain reduced the second innings to 40 overs, the target was revised to 200 (40 × 5). But this ignored wickets: if the team batting second still had 10 wickets, they could bat more aggressively with 10 wickets in 40 overs than the team batting first had with 10 wickets for 50 overs. The old method gave an unfair advantage. The 1992 World Cup semi-final (England vs South Africa) — where South Africa famously needed 22 runs off 1 ball after a rain reduction — exposed how broken the old system was. DLS (then D/L) replaced it in 1997.
Resources Concept
DLS core concept — resources: DLS is built around the concept of 'resources.' Each team has 100% resources at the start of their innings: the combination of wickets remaining and overs remaining. As overs are bowled, resources decrease (fewer overs remaining). As wickets fall, resources decrease faster (fewer wickets means the batting team is more vulnerable). The key insight of DLS over the old method: resources are a function of BOTH overs and wickets, not just overs. A team with 20 overs remaining and 10 wickets has significantly more resources than a team with 20 overs remaining and 5 wickets — they can afford to bat more aggressively because they have more 'insurance.' DLS quantifies this relationship precisely using empirical data from thousands of matches.
How DLS Calculates Targets
How DLS works in practice: when rain interrupts a match and overs are reduced, the DLS method calculates the percentage of 'resources' each team had available for their innings. If Team A batted a full 50 overs (100% resources), scored 250, and then rain reduced Team B's innings to 40 overs from the start (Team B's starting resources are less than 100% because they have fewer overs), DLS calculates Team B's target proportionally to their available resources. If Team B has 85% of the resources Team A had, their target is 85% of 250 = 213. When Team B has already started batting and rain interrupts mid-innings (say they have batted 25 overs and scored 120 with 6 wickets remaining — resources already used), DLS calculates the remaining resources and adjusts accordingly. The calculation is always done by the official DLS software — umpires don't calculate it manually.
Criticism of DLS
Criticism of DLS: despite being vastly superior to pre-1997 rain rules, DLS has been criticised in specific circumstances. (1) Very short matches (fewer than 5 overs) — DLS results in these ultra-short matches can seem arbitrary because the statistical basis (based on full-match data) may not reflect the extreme variability of 5-over games. (2) High-scoring powerplay situations — if a team has hit 100 runs in the powerplay and rain interrupts at over 6 with 10 wickets, DLS may set a target for the remaining team that feels unduly generous. (3) Match outcome disagreements — teams sometimes feel the DLS target was unfair when they just missed it or just exceeded it by one run. The ICC continues to refine DLS — Steven Stern (who joined as third developer in 2014) updates the underlying data model regularly to reflect the evolution of batting and bowling standards in the T20 era.
Frequently asked questions
What is the DLS method in cricket?
The Duckworth-Lewis-Stern (DLS) method is the mathematical formula used to set revised targets in limited-overs cricket (ODI and T20) when rain or other interruptions reduce the number of overs available to one or both teams. DLS was developed by statisticians Frank Duckworth and Tony Lewis in the 1990s and adopted as the ICC standard in 1997 (replacing the flawed 'run rate' method). The method calculates a 'resources' percentage for each team — factoring in both overs remaining AND wickets remaining — and uses the resources ratio between the two teams to set a fair revised target. For example: if Team A had 100% resources and Team B only has 85% resources (due to overs being cut), Team B's target is set proportionally lower. DLS is now the universal rain rule in international limited-overs cricket.
How is a DLS target calculated in cricket?
DLS target calculation: the official DLS calculation uses tables (derived from a statistical model of thousands of ODI and T20 matches) that assign a 'resources remaining' percentage to every combination of overs remaining and wickets remaining. When rain interrupts a match: (1) The referee's DLS software records Team A's final score and the resources they used; (2) If Team B's innings is shortened (either before they bat or during their innings), the software calculates their available resources; (3) The target is adjusted based on the ratio of resources: if Team B has 80% of Team A's resources, their target = Team A's score × (80/100). If Team A had fewer overs (due to rain in the first innings), they may have scored with fewer resources than 100% — the DLS software accounts for this in the calculation. The actual calculation requires the official DLS software; umpires do not calculate it manually.
Why was the DLS method introduced in cricket?
The DLS method was introduced in 1997 to replace the flawed 'run rate' calculation that was used for rain-affected matches before it. The old method only adjusted targets based on overs remaining — ignoring the crucial variable of wickets remaining. The problem: a team with 10 wickets and 25 overs remaining has far more resources than a team with 5 wickets and 25 overs, but the old run-rate method treated both situations identically. This created systematic unfairness. The most dramatic failure was the 1992 World Cup semi-final where the old 'most productive overs' rain rule left South Africa needing 22 runs from 1 ball — a mathematically impossible target caused by a flawed calculation, not cricket. Duckworth and Lewis developed their resource-based model to properly account for both overs and wickets remaining. After refinement and testing, it was adopted by the ICC as the universal rain rule.