What is Duckworth Lewis method in cricket- par scores and when is it applied in matches?

Here is everything you need to know about the Duckworth-Lewis-Stern (DLS) method, which has already been summoned a few times at the 2022 T20 World Cup in Australia and how South Africa, historically, has found itself at the receiving end of DLS calculations and rain stoppages.

Rain has already had a significant say on some results at this year’s 2022 T20 World Cup in Australia. | Photo Credit: AFP

Following occasional rain interruptions during Round 1 and the first week of the Super 12s at the 2022 T20 World Cup in Australia, questions have been asked about the planning for wet weather at the World Cup. The tournament does not feature reserve days for the group stage - although the semifinals and final have one.

Afghanistan's fixture at the MCG was rained out for the second time in three days, with its T20 World Cup match against Ireland abandoned on Friday. Afghanistan's match against New Zealand was also washed out without a ball being bowled.

It was the second consecutive rain-affected fixture for the Ireland too, however enough overs were bowled in its game to force a result against England on Wednesday, which was also played in Melbourne.

Here is everything you need to know about the Duckworth-Lewis-Stern (DLS) method, which has already been summoned a few times and how South Africa, historically, has found itself at the receiving end of DLS calculations and rain stoppages.

WHAT IS IT

The Duckworth-Lewis-Stern or DLS method (as it is now known) is used 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.

The DLS method takes into account both wickets and overs as resources and revises the target based on the availability of those resources. At the start of an innings, a team has 100 per cent 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 which 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 an innings: the curve is exponential, with that resource percentage falling faster as more wickets are lost and more balls are consumed.

HOW DOES IT WORK

The DLS methods 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 off a chart. Where upward revisions are required (when the first innings is interrupted), a quantity called the G50 — the average total score in a 50-over innings — is used as reference. For matches involving ICC full member nations, G50 is currently fixed at 245. However, the Standard Edition is not used in international cricket.

At the receiving end

South Africa has quite often been at the receiving end of rain stoppages and DLS calculations. Below are a few instances of the same.

MATCH 1: SEMIFINAL - England vs South Africa, Sydney, 1992 ODI World Cup

RESULT: England won by 19 runs (via rain rule)

TALKING POINT: The rain interruption that prompted the rain-rule to be employed and oust South Africa from the contest. In its first-ever World Cup, the side trotted to the semifinals and was well in the hunt to clinch its target of 253 in 45 overs. Needing 22 runs from 13 deliveries, the South Africans were forced to endure a rain-break that proved to be fatal. At resumption, the side needed 21 from one delivery — turning what would have been an exciting climax to an anti-climax.

The moment brought a reanalysis of the contentious rain rule that was eventually replaced by the Duckworth-Lewis (now Duckworth-Lewis-Stern) method.

MATCH 2: South Africa vs Sri Lanka, Durban, 2003 ODI World Cup

RESULT: MATCH TIED (Duckworth-Lewis Method)

TALKING POINT: South Africa's fatal error in reading the required target as set by the Duckworth-Lewis method. This was the home team's final contest in the group stages, and it needed to win to progress to the next stage. As in 1992, rain caused South Africa pain once again.

In the 45th over of South Africa's innings, Mark Boucher had been conveyed a target of 229, but they needed to score one more run to win. As it turned out, Boucher calmly pushed the final ball of that over to leg and did not take a single. The ball before, he had hit a six. The teams couldn't return to the pitch after the interruption as the rain had got hard.

Shaun Pollock, the captain, was seen with his hands with his head in the dressing room. In front of the home crowd, South Africa had crashed out in the first round.

For Sri Lanka, Marvan Attapattu was the star - he scored 124.

MATCH 3: South Africa vs Zimbabwe, Hobart, 2022 T20 World Cup

RESULT: No result; both teams awarded one point

TALKING POINT: Following persistent rain in Hobart, the match was reduced to nine overs a side. Zimbabwe made 79-5, with Wesley Madhevere smashing an unbeaten 35 off 18 balls. Quinton de Kock then slammed 23 off the first over of the chase, before a short delay a ball later, with South Africa's target then reduced to 64 off seven overs. But heavier rain returned. With South Africa on 51-0 off three overs, umpires decided to take the players off and subsequently end the match. South Africa had reached the DLS par score at that stage. But without the game able to be reduced by two more overs, the target was not revised further and they had to settle for a no result, with each side awarded one point.