Wringing the water out of rain-soaked scores

The author decodes the puzzling Duckworth-Lewis formula used in cricket

India had scored 119 runs for the loss of three wickets in 29 overs against Sri Lanka in the last league match in the recent tri-series in the West Indies when a downpour stopped proceedings. When the match resumed, there was time left only for Sri Lanka to bat, that too three overs less than India. What score should Sri Lanka chase? If you went by run rate, then the challenge would have been an easy 106 in 26 overs. But this would have injustice to the team whose batting was disrupted mid-way. India started the match with a 50-over batting plan and reserved its resources for use in the slog-overs - an assault that was ultimately denied to it. Lanka, on the other hand, knew from the start that it had 26 overs in which to overhaul the 4.10 target run-rate.

That is where the Duckworth-Lewis method stepped in and gave the Sri Lankans the objective of chasing 178 runs. In other words, the Lankans would have to make 59 more runs that India did not. Was this a travesty of scoring requirements? Not quite.

Two English statisticians, Frank Duckworth and Tony Lewis, wanted to avoid the anomalies inherent in methods followed in setting targets in truncated matches, like the unfair run-rate system, and came up with what is now commonly called the D/L method in 1997. The logic they injected in the system was to consider a match as the result of efficient use of similar resources by two teams. These resources, the Englishmen decided, comprised batsmen and overs in which to score runs. In other words, 100 per cent resources meant 10 wickets in hand and 50 overs to bat through. By studying how all the matches were played till then, the duo created a table of mathematically calculated available resources at each point of the innings - that is with each ball bowled and with different number of wickets remaining. The Duckworth-Lewis system aimed to determine the winner by calculating what each team would score if they had identical resources.

According to the table formulated by the two statisticians, India, in the match against Sri Lanka, used 49.4 per cent of its resources, having lost three wickets and faced 29 overs. There were 26 overs available to the Lankans to force a win. Since they had all 10 wickets but less than 50 overs to bat, they started with resources equalling 68.3 per cent of maximum, according to the table. A computer program, used in all professional matches, calculated that since Sri Lanka had more resources than India, it would need to make a higher 178 to win the match. The target was arrived at using the formula T = S + G (R2 - R1), where T is the target, S is the runs scored by the first team, G is the average score of a full 50-over innings (currently determined to be 235), R2 is the resources of the second team and R1 those of the first team.

In situations where the resources of the team batting first are more than those of the team batting second (opposite to the India-Lanka match above), the formula used is T= S x R2/R1 (target is equal to the resources of team 2 divided by resources of team 1 multiplied by the runs scored by Team 1).

When there are multiple disruptions in the first innings or in the second that require resetting of targets, the umpires, or the computers, calculate the resources used up by the teams during their time at the crease over various durations. Then either of the two formulae are applied to find the proportional score if the resources of the two team were equal.

V Jayadevan, an Indian engineer, has also come up with his VJD system to calculate scores and targets. And while a presentation on VJD was made before the International Cricket Council last year, it was decided it would continue to depend on Messers Duckworth and Lewis to make sense of soggy chaos on cricket fields.