It is a scenario familiar to any cricket fan: a match is building to a thrilling climax, the skies darken, and the rain begins to fall. The players rush from the field, leaving a contest hanging in the balance. In these moments of meteorological frustration, a complex mathematical formula often becomes the star of the show. This is the Duckworth-Lewis-Stern method, or DLS, the system used to reset targets in rain-affected limited-overs matches. But what is this mysterious calculation, and how does it actually work? BBC Sport's Ask Me Anything team delves into the origins and mechanics of one of cricket's most debated topics.
The Problem Before the Solution
Before the DLS method, cricket used far cruder systems to adjudicate rain-affected matches. The most common was the Average Run Rate method, which simply compared the run rates of the two teams. This approach was notoriously unfair, as it heavily favoured the team batting second. A team chasing 250 from 50 overs, for instance, could be left needing 150 from 25 overs—a much higher required run rate—if rain intervened. This system ignored the fundamental advantage of knowing a precise target and having wickets in hand as a resource to be spent aggressively. The cricketing world needed a more statistically robust solution.
The Statisticians from the North
Enter two English statisticians: Frank Duckworth and Tony Lewis. Duckworth, a consultant statistician from Lancaster, and Lewis, a lecturer from the University of the West of England, were both avid cricket fans who saw the flaws in the existing system. They began working on a new method in the 1990s, one based on a revolutionary core concept: that a batting team has two resources with which to score runs – its remaining overs and its remaining wickets.
They analysed decades of scoreboard data to create a statistical table that quantified the percentage of these combined resources remaining for a team at any point in an innings. The method was first used in a professional match in 1997 and was officially adopted by the International Cricket Council (ICC) in 1999. Reflecting on their creation, Tony Lewis once explained its philosophical underpinning, stating: "We wanted a system that was fair to both sides, one that replicated as closely as possible the outcome that would have occurred had there been no interruption."
How the DLS Method Actually Works
At its heart, the DLS method is about resource percentages. Before a match even begins, each team is considered to have 100% of their resources available (50 overs and 10 wickets). As the innings progresses, this percentage depletes. The method uses a published table or a computer program that calculates the exact resource percentage for any combination of overs left and wickets lost. When rain interrupts play, the system calculates the resources each team had at its disposal, and the target for the team batting second is adjusted accordingly.
For example, in a simple scenario:
- Team A bats first and scores 250 runs using 100% of their resources (50 overs).
- Rain then shortens the match before Team B bats, reducing their innings to 40 overs.
- With 40 overs and 10 wickets in hand, Team B has, for instance, 85% of their resources available.
- Team B's new target is therefore 250 x (85% / 100%) = 213 runs.
The calculation becomes more complex with multiple interruptions, but the principle remains the same: it's all about the balance of resources lost by each team. The system is designed to be progressive, meaning the later a wicket falls, the more costly it is in terms of resource percentage, accurately reflecting the strategic reality of one-day cricket.
The Stern Revision and the Modern Game
As the game evolved, particularly with the advent of T20 cricket where scoring rates are significantly higher, it became clear the original Duckworth-Lewis model needed updating. In 2014, Australian professor Steven Stern took over the custodianship of the method, which was subsequently renamed the Duckworth-Lewis-Stern method. Stern's key contribution was to refine the underlying data, basing the resource percentages on scoring patterns from a more recent and expansive set of matches, which better accounted for the aggressive batting seen in the modern era. He noted the shift in the game's dynamics, saying: "The original D/L tables were based on 50-over cricket from the 1990s to the early 2000s. The game has changed, with higher scoring rates, especially in the first half of an innings, and the rise of T20."
Common Misconceptions and Criticisms
Despite its statistical rigour, the DLS method is often misunderstood and criticised by fans, players, and pundits alike. A frequent complaint is that it sets seemingly impossible or unfair targets, particularly in T20 cricket where a team may be asked to score an exceptionally high number of runs from a very short number of overs. However, this is usually a feature, not a bug. The method recognises that a team with all ten wickets in hand can take more risks and achieve a higher run rate than a team that is already several wickets down. The system is designed to put the chasing team in a position that is as difficult as it would have been had the full innings been played.
Other points of contention include:
- The perceived complexity and "black box" nature of the calculation, which can be opaque to viewers.
- The impact of a late-innings interruption, which can drastically change a target just as a chasing team is getting comfortable.
- The fact that the par score (the score the batting side needs to be level) is often different from the target score, leading to confusion.
DLS in the Wild: A Famous Example
One of the most dramatic illustrations of DLS was the semi-final of the 2015 Cricket World Cup between South Africa and New Zealand. Batting first, South Africa posted a formidable 281/5 in a 43-over rain-affected innings. Using the DLS method, New Zealand was set a target of 298 from 43 overs—a revision that confused many. The calculation, however, was based on South Africa having their innings interrupted twice, losing more of their resource percentage than New Zealand did from a single interruption. The match was ultimately decided on the penultimate ball, with Grant Elliott hitting a six to seal New Zealand's victory, a finish that, while heartbreaking for South Africa, was deemed a fair reflection of the contest by the DLS parameters.
Conclusion: An Imperfect but Necessary Tool
The Duckworth-Lewis-Stern method remains an integral, if controversial, part of modern cricket. While no mathematical model can perfectly replicate the unpredictable drama of a full cricket match, DLS provides a far more equitable solution than any of its predecessors. It acknowledges the strategic interplay between overs and wickets, and its continual evolution under Stern ensures it adapts to the changing nature of the sport. As long as rain clouds loom over cricket grounds, the complex calculations of DLS will continue to be a source of fascination, debate, and, most importantly, a method to ensure a fair result can be found when the weather refuses to play ball.