The story so far: Rain had played spoilsport at the 2019 International Cricket Council (ICC) cricket World Cup England and Wales, washing out a number of matches, including India’s clash with New Zealand. As wet weather continued to affect games, the Duckworth-Lewis-Stern (DLS) method came to feature prominently at the tournament.
What is the DLS?
The Duckworth-Lewis-Stern or DLS method (as it is now known) is a mathematical system employed to calculate target scores and reach outcomes in rain-shortened limited-overs matches. Devised by English statisticians Frank Duckworth and Tony Lewis and originally named after them, it was first used in 1997. Australian academic Steve Stern updated the formula, becoming its custodian ahead of the 2015 World Cup; his name was added to the title.
Why is it needed?
Having a reserve day in place for a limited-overs match and resuming proceedings the following morning would seem ideal, but logistical and scheduling challenges mean this is not always feasible. And so the game’s administrators have for long laboured to find the fairest way of settling rain-affected one-dayers. When a match is interrupted by inclement weather, and one or both teams do not get their full quota of overs, an outcome has to be reached in the time available after the resumption of play. What any calculation is doing is trying to adjust a target score according to the reduction in overs. Any number is an estimate: there is no one right answer. What the ICC has tried to do is arrive at a formula that takes into account as many parameters as possible, and properly reflects the efforts of both teams. The DLS method, which has been updated a few times, is generally considered the most accurate system used in international cricket.
Why were older methods discarded?
When ODI cricket was first played, Average Run Rate (ARR) was used to calculate targets. Here, the chasing side simply had to match the opponent’s run rate. For example, if Team A scored 200 in 50 overs, at a run rate of 4, and if Team B’s innings was reduced to 30 overs, then the total to overcome would be 120. But this method did not take into account wickets lost, or the fact that it was easier to maintain a good run rate over a lesser number of overs. So if Team A made 200 in 50 overs batting first and Team B was 100 for nine in 20 overs when rain ensured no further play was possible, the latter would be declared the winner. So the ARR method was inherently biased towards the team batting second.
Australia came up with an alternative to the ARR ahead of the 1992 Cricket World Cup, called the Most Productive Overs (MPO) method. This involved reducing the target by the number of runs scored by a team in its least productive overs, equal to the number of overs lost. For example, if Team A made 250 in 50 overs and Team B’s innings were reduced to 30 overs, then the total to beat would be the total number of runs Team A scored in its highest-scoring 30 overs. Here, Team B had genuine cause for complaint because the best 20 overs its bowlers had sent down were ignored. For argument’s sake, if Team B had bowled 20 maiden overs and conceded 250 runs in the other 30 overs, then its 30-over target would still have been 251. So Team B was being penalised for bowling too many low-scoring overs. Clearly, this method tended to favour the side batting first.
Its flaws were famously highlighted during the 1992 World Cup semifinal between England and South Africa. Chasing England’s 252, South Africa was 231 for six and needed 22 off 13 balls when rain stopped play for 12 minutes. Two overs were lost and so the two lowest-scoring overs — yielding one run in total — in the England innings were struck off. This meant that the target was reduced only by one, and South Africa had 21 runs to score off one ball (the scoreboard incorrectly flashed 22 that day). This farcical end to the game prompted the search for a better method.
Years later, Duckworth told the BBC in an interview that this incident had inspired him to come up with a solution. He said, “I recall hearing [cricket journalist] Christopher Martin-Jenkins on the radio saying ‘surely someone, somewhere could come up with something better’ and I soon realised that it was a mathematical problem that required a mathematical solution.”
How does the DLS method work?
Neither the ARR nor the MPO methods were able to factor the match situation into their calculations, failing to take into account the wickets a team had left. The DLS method addresses this issue, considering both wickets and overs as resources and revising the target based on the availability of those resources. At the start of an innings, a team has 100% of its resources — 50 overs and 10 wickets — available. The DLS method expresses the balls and wickets remaining at any point as a percentage. How much is a wicket or a ball worth in percentage terms? This is calculated according to a formula that takes into account the scoring pattern in international matches, derived from analysis of data (ODI and T20, men and women) from a sliding four-year window. On the first of July every year, a new year’s worth of data is added; so the DLS evolves as scoring trends do.
The rate at which resources deplete is not constant over the course of innings: the curve is exponential, with that resource percentage falling faster as more wickets are lost and more balls are consumed.
The DLS method sets targets (and decides outcomes) by calculating how many runs teams should score (and would have scored) if the resources available to both sides were equal. To calculate a target, the formula may simply be expressed thus: Team 2’s par score = Team 1’s score x (Team 2’s resources/Team 1’s resources). In international cricket, the resource values (which are not publicly available) are obtained from a computer programme.
The DLS method also allows for the fact that a team batting before a rain interruption would have batted differently had it known the game was going to be truncated. Of course, the weighting of wickets and overs is based on a formula, and there can be no universally perfect weightage, simply because the method cannot make qualitative measurements of individual batting abilities. It was long felt that under the D-L method, teams chasing big totals were better off keeping wickets in hand when rain was around the corner even if it meant scoring at a lower rate. Steve Stern felt he had improved on the D-L method in this regard by adjusting the formula to reflect changing realities in high-scoring ODIs and T20 matches.
An older version of the DL method (called the D-L Standard Edition), meant to be used where computers are not available, applies pre-calculated resource values of a chart. Where upward revisions are required (when the first innings are interrupted), a quantity called the G50 — the average total score in a 50-over inning — is used as a reference. For matches involving ICC full member nations, G50 is currently fixed at 245. However, the Standard Edition is not used in international cricket.
Are there alternatives to the DLS method?
V. Jayadevan, an engineer from Kerala, devised an alternative in 2001, but it was never adopted by the ICC. The VJD method, as it is known, is used in Indian domestic cricket, though. Mr. Jayadevan has continually argued that the DLS method is statistically inconsistent and that his system produces superior results.
