03 Apr

Despite being an average club cricketer from Lancashire, Tony Lewis (on the right in the picture) became one of the most famous names in the game as one half of the double act who pioneered the revolutionary Duckworth-Lewis method of readjusting targets in rain-hit one-day matches.

Lewis, who died on 2 April, aged 78, was a lecturer in management science at the University of the West of England when a copy of a paper produced by Frank Duckworth, of the Royal Statistical Society, attracted his interest.

The paper, entitled ‘Fair play in foul weather’, was produced in 1992 and outlined the basic thoughts behind creating a fairer system to decide one-day cricket matches. Lewis had his own ideas on how to develop the concept and the two began to work together on a method that would first be used in international cricket in 1997, soon becoming a fundamental part of the professional game, broadly accepted by players and spectators alike, even if only a few understood the mathematics behind it. “I can’t work it out,” Steve Waugh, the former captain of Australia, said. “But I think it’s a very good system.”

In the 1990s, existing systems for settling rain-affected contests were inadequate. The average run rate method reflecting how quickly a team was scoring, but took no account of how many wickets had been lost; the most productive overs method disproportionately favoured the team who had batted first.

The crisis point was reached in the 1992 World Cup semi-final between England and South Africa. South Africa needed 22 from 13 balls when rain stopped play, but when the teams returned to the field, the revised target was 21 runs from one ball. Duckworth recalled radio commentator Christopher Martin-Jenkins saying, ‘Surely someone, somewhere could come up with something better,’ ” Duckworth said. “I soon realised that it was a mathematical problem that required a mathematical solution.”

He set about working on a solution that revised a target while maintaining the balance of the game and, in Tony Lewis, Duckworth found a willing accomplice. Duckworth was described as the theorist in the partnership, Lewis as the practitioner. The two found that they had much in common, having attended nearby schools by the Lancashire coast. “I don’t think it would have worked if we’d not got on so well together,” Lewis said. “Both of us love cricket, but have never exactly been great players.”

The mathematics of their method is based on an exponential decay relationship which sought to take account of the different scoring rates at different points of a one-day innings and the wickets lost and overs remaining at the batting team’s disposal. Their calculations were based on the study of thousands of one-day matches and the method has been updated in recent years for Twenty20 cricket and to reflect faster scoring rates in both white-ball formats.

In 2014, their creation attracted a new collaborator as the Duckworth-Lewis-Stern method, credited Professor Steven Stern, an Australian mathematician now charged with keeping the system up-to-date.

The fame of the original creators grew to the extent that there is both a racehorse and pop group named after them, but they felt a sense of pride in having made such a contribution to the game they loved. “It is very satisfying that players generally accept revised targets now as fair and that we have made a significant contribution to the history and development of the game,” Lewis said.

The Duckworth-Lewis method never claimed to be perfect, but proved to be considerably less imperfect than the other systems. And its inventors were good enough to give a mathematical estimation of its shortcomings. “Our way is not perfect,” Duckworth has said. “But it works about 99.5 per cent of the time.”

Frank Duckworth and Tony Lewis were awarded MBEs in the Queens Birthday Honours list in 2010 for services to Mathematics and Cricket.

John Stephenson


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