# First Night: Duckworth-Lewis: The odd couple getting even with the weather

### Andrew Longmore meets a double act in their element as head-scratching game goes on

CRICKET'S LATEST double act arrived, joined at the hyphen, looking a little flustered. By executing the cricketing equivalent of splitting the atom, Frank Duckworth and Tony Lewis have gained a belated celebrity. Their previous interview had run late. Their apologies were profuse. "I'm a bit dehydrated," says Duckworth, heading off in search of a glass of water. Thirsty work this show business.

The routine is well rehearsed now. It is like the old Monty Python sketch. Do you want the five- or 10-minute explanation? Duckworth-Lewis in a nutshell. Their composure was not helped by an error in the guide to the D/L method (not even Hobbs and Sutcliffe were abbreviated to H/S) presented to the media. Cue mathematical consternation. Not quite a glitch in Fermat's Theorem, but enough of a cock-up on the eve of the method's debut in the World Cup to warrant a few furrowed brows.

It is 11.12 on the opening morning of the 1999 World Cup and an underpopulated Lord's is suffering its first shower of the tournament. Not a moment was lost to rain in the first World Cup in England 24 years ago, the commentator helpfully informs us. One record gone then. But if the prevailing weather of the past fortnight is extrapolated - the mathematical lingo is catching - to the next five weeks, you can forget Warne and McGrath, Lara and Tendulkar, Walsh and Ambrose, the most quoted partnership will be two village cricketers from west Lancashire.

So, let's get the easy bit out of the way. D/L for innumerates. The key is a table of figures resembling logarithms which calculates the "resources" left to the side batting in the event of rain. Resources are the number of overs received and the number of wickets left. You don't need to know the figures, just the principle. The brilliance of the D/L method, the difference from the umpteen unworkable predecessors, is that it translates an imponderable set of circumstances into the precise language of mathematics and it does so in a formula which can cope with an almost infinite number of variables.

Above all, it maintains the integrity of the sport. At any given moment, the balance of the match can be interpreted by a set of stats. "It's the best method by a long way," Steve Waugh, the captain of Australia, said. "You are rewarded for taking wickets. I can't work it out, but I think it's a very good system."

The team who go into the rain interruption in control of the game should emerge from it in the same position; cricket is not reduced to the sort of absurdity which cost South Africa any chance of reaching the final of the 1992 World Cup. Though 12 of the last 13 balls were lost to rain, South Africa's target was reduced by a mere one run, leaving them to score 21 off the last ball. It is no coincidence that one of the method's chief sponsors, David Richards, chief executive of the International Cricket Council, was then head of the Australian Cricket Board, which took much of the flak. In the aftermath, Richards appealed to mathematicians the world over to come up with a better system. Down in the West Country, the considerable grey cells of Dr Frank Duckworth were already at work.

Duckworth, 59, is editor of the Royal Statistical Society's house journal and has the greying, unruly hair to prove it. As a cricket lover he had long been perplexed by the anomalies of the rain laws and had begun to fill the backs of envelopes with informal outlines of a mathematical solution. He delivered a paper entitled "Fair play in foul weather" to the RSS conference in Sheffield in 1992.

A copy of the paper found its way on to the desk of Tony Lewis, a lecturer in management science at the University of the West of England in Bristol, stirring the curiosity of another cricket lover and unwittingly triggering an unlikely friendship. Only two years later did Frank Duckworth and Tony Lewis, one small and livewire, the other dark-haired, more circumspect, not unlike his namesake, the former England captain and BBC commentator, meet in person. By then, a delve back into the archives of one-day internationals had given the pair enough confidence to alert the top brass at the old Test and County Cricket Board. But there was still work to be done.

"I was going on holiday to Hawaii with my wife," Duckworth explains. "September 1995 it must have been. On the plane out there, I felt I'd cracked it. When I got there, I faxed Tony. He said, `Yes, but...' but by the end of an exchange of faxes, we felt we had the completed formula." The problem then, as many British inventors have found, was persuading the establishment. "It's one thing to have a good idea, quite another to sell it. Our biggest achievement has been to sell it." So what were the eureka moments? Listening on the radio to England v Zimbabwe at Harare, 1 January, 1996, the first international application of D/L perhaps?

"There were two," Duckworth says. "One was an ICC meeting chaired by Clyde Walcott, who was a childhood hero of mine. Tim Lamb had just become chief executive of the new England and Wales Cricket Board and he spoke very positively about it and Ali Bacher said he wished South Africa had used it in that 1992 semi-final. The other was when the ECB decided to adopt it for the following season. That's when we came out, shook hands and went down the pub to celebrate." Equally significantly, the pair had found common interests outside cricket.

"I don't think it would have worked if we'd not got on so well together," adds Lewis, 57. "We found totally coincidentally that we have a lot in common. We live five miles from each other and went to schools which were deadly rivals in Lancashire. Both of us love cricket but have never exactly been great players."

"Tony," says Duckworth, "is more user friendly, he has to sell it to people. I tend towards the scientific purist method. I'm the theorist, he's the practitioner. But we both have respect for each other. If there's a disagreement, the truth will out." The problem is that the truth comes wrapped in some incomprehensible logarithms. Last year, Middlesex learnt from their car radios that the victory they had left Canterbury with had been Duckworth-Lewised into a one-run defeat. It was not the method, it was the communication. Fair it might be, say the critics, but how can cricket, a game already shrouded in mystery, whose beauty lies in its infinite variety, be so subjected to the rigours of the anorak brigade?

"Indecipherable, one paper called it," says Duckworth. "They spelt it wrong too. People call it a `whim'. We would like people at least to try to understand it before saying it's incomprehensible. You don't have to be particularly numerate, no more so than filling in a tax form which everyone has to do now. You don't need a university degree and you don't need to be computer literate."

If D/L have a good World Cup, there will be no stopping their conquest. Only Australia and Sri Lanka have yet to sign up. It is thoroughly appropriate that the land which brought you cricket and rain should supply the solution to their unhappy alliance. "Not the best, but the most recognised thing I've ever done in my life," says Duckworth. Cricketing and academic. Next month, Lewis will present the method to a conference in China.

"Our way is not perfect, but it works about 99.5 per cent of the time." If a side scores a six off every ball of its 50 overs before rain, D/L could technically require the opposition to score more than six runs a ball to win. "Personally," says Duckworth. "I wouldn't mind if it didn't rain all tournament." A sentiment that everyone can understand.

The Duckworth-Lewis Method

IF matches are rain-affected the Duckworth-Lewis system is used to reset targets. The system is based on the percentage of resources (overs and wickets) a team have left. For example, with 50 overs and 10 wickets remaining, a team have 100 per cent of their resources left. The table below illustrates the percentage of resources at other selected stages of an innings.

50 100 83.8 49.5 26.5 7.6

40 90.3 77.6 48.3 26.4 7.6

30 77.1 68.2 45.7 26.2 7.6

20 58.9 54.0 40.0 25.2 7.6

10 34.1 32.5 27.5 20.6 7.5

PERCENTAGE RESOURCES REMAINING

The procedure for working out targets is as follows:

1 For each innings calculate the resource percentage lost by interruption and therefore deduce the resource percentage still available.

2 If team B have less resources than team A, calculate the ratio of the resources available to both teams. Team B's revised target is calculated by scaling down team A's total by this ratio.

3 If Team B have more resources remaining than Team A, calculate the amount Team B's resources exceed Team A's. Calculate this as a percentage of 225 (the average score in 50-over one-day internationals). This gives the extra runs to add to Team B's target.

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