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Once lambasted as 'unfathomable' and 'arcane', the Duckworth-Lewis method for resetting targets in rain-interrupted cricket is now the international standard. ORS member Tony Lewis reports on how this came about

How we sold Duckworth-Lewis

The Duckworth/Lewis (D/L) method has now become the international standard for resetting the target in one-day cricket following interruptions which are usually due to rain but also on occasion they have been for floodlight failure, sandstorms, snow and even crowd disturbance. The D/L methodology has an OR basis (see JORS 1998 (3) pp220-227) but is simple enough to apply using nothing more than a pocket calculator and a table of pre-calculated percentages. The user does not have to understand OR to use the method; only how to perform the four operations of number - but in the correct order!

It really is very simple to apply once the method’s logic has been understood - but to hear many journalists you would be forgiven for thinking that a degree in maths is necessary. Nothing could be further from the truth, a fact that undoubtedly has ultimately led to the method’s international adoption. But it has been a long and interesting campaign to convince the cricketing world.

The early beginnings

Following the inception of one-day cricket in the 1960s the method of resetting the target due to rain interruptions was handled using average run rate. The imperfections of this method were quickly realised but, for want of something better, the approach survived for many years. After hearing many radio discussions, Frank Duckworth realised that it was not a simple problem and that it warranted a mathematical approach but he did nothing formal at the time. It was the effect of the rain-rule in use in the infamous 1992 World Cup semi-final that galvanised Frank into formulating a model to attempt to solve the problem and to provide a fairer system. In that match South Africa suddenly had to get an impossible 21 runs from one ball, when they had previously been well placed against England. Frank presented his ideas to a ‘Statistics in Sport’ session of the Royal Statistical Society’s annual conference in August that year in Sheffield. The ideas were theoretical, based on no actual data and the mechanism of target calculation required a computer. Nevertheless delegates were sufficiently impressed to persuade Frank to send his work to the Test and County Cricket Board (TCCB) in London. He managed to see Tim Lamb, Cricket Secretary at the time who, whilst recognising some of the merits of the system, had to admit that the TCCB were not then ready to use computers.

I received a copy of Frank’s conference paper from a colleague at my former institution, the University of the West of England. I was in charge of final year student projects in the Mathematics Department. It struck me that it would make a neat project for a student to obtain some cricketing data to estimate the parameters of Frank’s model and to see whether or not the method would work. The student obtained English domestic one-day data from the Cricketer’s Almanac, Wisden. When his work proved the viability of Frank’s method I felt that the project would be worth pursuing after the student’s graduation. After more data collection during the ensuing year or so and slight modifications to its application in the model I contacted Frank (who by chance lived no more than 6 miles away from me in Gloucestershire). We agreed that it might well be worth working together and for another approach to be made to the TCCB taking advantage of my university platform.

Approaching the cricket authorities

The timing of our approach was fortuitous in that the 1996 World Cup was approaching and we learnt that the International Cricket Council (ICC) was still to finalise the World Cup’s ‘rain-rule’. This helped us to secure an audience with David Richards, Chief Executive of the ICC and also Tim Lamb to present our method but, due to difficulties in arranging a time, this meeting couldn’t be held until October 1995, very close indeed to the 1996 World Cup.

Frank and I used this delay very profitably. On the way to a holiday in Hawaii, Frank had a brain wave which simplified enormously the way the method could be applied, and which meant that a computer was no longer needed to do the calculations. After an exchange of several faxes in which we discussed each other’s suggested modifications we realised that we really had cracked the problem. The model we produced at that time of the relationship between average further runs, overs left and wickets lost has not changed since.

Although in the event we were too late for the 1996 World Cup, our presentation and subsequent discussion went very well. One outcome was a recommendation that we should do some further confirmation of our results using exclusively international data. The second was an invitation to present our method to the chief executives of countries of the ICC in July 1996.

The first breakthrough and usage

This ICC meeting, with its bevy of famous former cricketers, proved to be an extremely important step in persuading countries to try out the Duckworth/Lewis method (the name we finally decided upon). After a month or two’s deliberation, a further presentation and some more discussions, almost simultaneously the cricket boards of England and Wales (ECB) and Zimbabwe decided to give the method a trial, the former for the 1997 domestic season and the latter for England’s 1996/7 tour of Zimbabwe. And close on their heels, the ICC management decided to try out D/L in the ICC Trophy competition in March/April 1997 in Kuala Lumpur where it was almost guaranteed to rain late every afternoon.

D/L had its first airing on 1 Jan 1997 when England lost to Zimbabwe, failing to achieve the D/L revised target but having surpassed the average-run-rate requirement! Although no one thought that this was an unfair result, press reaction was very mixed, it being their first exposure to D/L. Words such as ‘unfathomable’, ‘arcane’, ‘university boffins’ appeared liberally in the British press.

Reactions were similar in the early part of the 1997 ECB season when, on one wet day in June, D/L was invoked in no less than 7 of the 8 Sunday League matches. We realised that although we had achieved some success with the cricket authorities, several of whose members were sufficiently numerate to appreciate D/L’s logic, many journalists were not at the same level of understanding. We responded to direct enquiries but resolutely refused to write letters to the editor rebutting or rising to the many provocative and ignorant comments of some cricket journalists. We quickly grew a few extra layers of skin! Several readers of the broadsheet press did respond in our defence, but on their own behalf, which reassured us that serious thinkers about the game recognised the validity of the innovative features of D/L.

Nevertheless it was a learning experience for us in terms of appreciating the need to prepare explanatory leaflets, booklets and develop a web page, to assist in the dissemination of information on the method and in explaining its principles.


Following a review at the end 1997, a slight modification and substantial simplification in how the method was implemented, the ECB adopted D/L for the foreseeable future and New Zealand joined the band of converts. A further presentation to the ICC in May 1998 led to D/L being adopted for the Commonwealth Games in Kuala Lumpur, the Wills International Trophy in Dhaka and, what had been a major goal, the 1999 World Cup in England. Most other countries took their lead from this and so, in rapid succession, South Africa, India, Pakistan, Bangladesh and West Indies adopted D/L for domestic one-day matches as well as for one-day internationals (ODIs).

Although Australia and Sri Lanka were conspicuous by their absence from this list we had made several cordial contacts with the Australian Cricket Board (ACB) both during my visits to Australia for conferences and to see family, and by Frank when his holidays took him ‘down-under’. The ACB, it seemed, were in favour of using D/L - but only when it became the international standard rain-rule.

General acceptance

Another presentation in May 1999, in which we attempted to allay some doubts in certain quarters, and a successful use of D/L in the warm-up games of the World Cup, led to Duckworth/Lewis being designated the official ICC rain-rule for the next two years. It is to be used by all full and associate member countries of the ICC for both domestic and international matches. With this news we felt that we had achieved our major objectives.

And the Press? In the UK, comment is now usually neutral, which we feel, is tantamount to high praise! As it is the method which allows teams to get on with the game and let the effects of the weather be fairly compensated by D/L, if press coverage ignores D/L we can be satisfied that it is now an accepted part of the game. There is still work to be done with the press overseas which has not been exposed for as long but we hope that, learning from our experiences within the UK, the understanding and acceptance of D/L will be quicker abroad.


Developing D/L has been an absorbing, challenging and fascinating experience. We have needed to persuade cricketing authorities of the method’s virtues and its simplicity. We have undoubtedly been helped here by the numerate abilities of key personnel responsible for the method’s implementation in several countries. We have had to develop skills in communication in hitherto unfamiliar areas such as with the print media and also for radio and occasional television programmes. Such experiences, although daunting at the time, have been very rewarding. And it is very pleasing to have been involved in a project which not only has an OR basis but also has had a very practical effect on the world, albeit the cricketing world.

First published to members of the Operational Research Society in Inside O.R. January 2000