BASSETERRE, St. Kitts (Reuters):
During the World Cup warm-up matches in St. Vincent this month, sheets of mathematical calculations were solemnly distributed in the media box between every session.
Even though the sky was clear and the sun was shining the Duckworth-Lewis tables for rain-shortened matches were there just in case storms suddenly swept in from the Caribbean Sea.
By the time the teams had redistributed themselves throughout the West Indies for the first round group matches the numbers did not seem quite so superfluous. Heavy showers began to delay and interrupt matches and the formula was first used in the Group D match between Pakistan and Ireland.
Duckworth-Lewis, the work of two British academics, was first introduced at the Champions Trophy 10 years ago.
It has since been used to calculate the target of a chasing team when a game has been interrupted by floodlight failure, crowd disturbances, a sandstorm (Rawalpindi), snow (Durham) and sun (Derby).
Some method of deciding the result, with a draw not an option, has been needed since limited overs cricket was introduced in the 1960s.
The first solution was the simplest. If a match was interrupted the team with the highest average runs per over played was declared the winner. It was, though, intrinsically unfair in that teams score their runs at different rates throughout an innings with the early overs usually yielding the fewest runs.
LUDICROUS TARGET
At the 1992 World Cup in Australia and New Zealand, a decision was made to set the target of the team batting second by taking away the lowest-scoring overs of the side batting first.
The result was the ludicrous semi-final between England and South Africa when the latter, playing in their first World Cup, needed 22 from 13 balls. A 12-minute downpour adjusted the target to 22 runs from seven, and finally 21 from one.
Frank Duckworth, the honorary editor of the British Royal Statistical Society Journal, was listening to the radio back in England.
"I recall hearing Christopher Martin-Jenkins on the radio saying 'surely, someone, somewhere could come up with something better'," he told the BBC. "And I soon realised that it was a mathematical problem that required a mathematical solution."
Based on historical analysis Duckworth and Tony Lewis discovered, for example, that a team that had batted 20 overs without losing a wicket would have scored 22.1 per cent of its total runs, and a team losing four wickets would have tallied 45.1 per cent.
DEFINITE TARGET
The Duckworth-Lewis formula was invented, calculating a team's target when the overs had been reduced by estimating its remaining batting resources.
The system was first employed in a match between England and Zimbabwe. England would have won under the old strike rate rule, but they lost on Duckworth-Lewis. Four years later it was formally adopted by the ICC. Its singular virtue, despite the mystification often expressed in commentary boxes, is that it can give a definite target at any stage when a match is shortened.
The most controversial application came in the 2003 World Cup when South Africa thought they had beaten Sri Lanka. However, the South Africans had misread the target, the match was in fact tied and the hosts failed to qualify for the second phase. The fault did not lie with Duckworth-Lewis but the South Africa management and as a result Shaun Pollock lost the captaincy.
"No one likes it when the result of a game has to be settled by the mathematicians," said ICC general manager David Richardson. "Cricket, by its nature, is unpredictable and fortunes can fluctuate extravagantly during the course of a match.
"However, if one is forced to find an answer to the question 'who is winning' during a match then the Duckworth-Lewis method gives you as fair a method of doing so as you are likely to get."
