With the Ashes competition about to start, we thought it might be a good time to relate the contribution that Operational Research has made to the world of cricket. This comes through the work of one of the most famous Operational Researchers in the world – Dr Tony Lewis MBE, known as part of the Duckworth/Lewis team.

The contribution is in the area of one-day cricket. In this form of the game each team gets a limited number of overs to bat. There are many versions of this form of cricket and the number of overs that each team gets ranges from 20 to 60.

If each side gets its full allotment of overs, then there is no problem. However if one or both of the innings is affected by something like rain, then a method is needed to determine what a ‘fair’ score should be.

As limited overs cricket became more and more popular in the 1980s, various methods were adopted, however none was very successful for long. Each method eventually met a match where its flaws became apparent.

The earliest method was the simplest. Simply take the average number of runs that a team had scored, and assume that the other team had to score at the same rate in the overs that they are allowed to have.

In January 1989 Australia played the West Indies. Australia progressed at a steady rate, but were caught by rain and scored 226 runs in 38 overs – a run rate of 5.9 runs per over. Further rain reduced the West Indies innings to 18 overs. Doing the maths, this left the West Indies needing 108 runs in their overs, which of course they made easily.

This was, however grossly unfair on Australia for 2 reasons. Firstly achieving a run rate of 5.9 over 18 overs is much easier than achieving it over 50 overs (as you have more wickets to play with). Secondly as teams tend to get more runs towards the end of their allotment of overs, it was likely that Australia could well have scored at a higher rate than 5.9, especially as they had wickets in hand when rain curtailed their innings.

The net result was a change in the rules, which was adopted by the International Cricket Council (ICC).  This rule was that instead of taking a flat rate of runs scored per over, only the best overs would be counted.

This new ‘simple’ rule was tested in the World Cup semi final in 1992. In that match England were playing South Africa. England scored 252 in 45 overs. South Africa were looking very much on target with 231 runs after 42 overs and 5 balls. South Africa needed 22 runs off 13 balls which was very much possible.

Unfortunately at that point a few spots of rain caused the umpires to call a halt to the game. Although the halt was temporary, it caused the deduction of 1 over from the match to 44 overs. As the least productive over was a 0 run over, this kept the target at 22 runs, but reduced the time to get it to 7 balls. The South Africans protested, and during the protest another over was deducted, leading to the ridiculous situation of South Africa needing 22 runs off 1 ball!

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Finally the ICC agreed that the ‘simple’ methods had failed, and that a new method was needed. They first tried a method based on a parabola model created by Wayne do Rego. He analysed a large number of one day matches, and came out with a formula which calculated the expected number of runs that would be scored. Whilst this was fairer than any previous method, and it was relatively simple to apply, it ignored one of the key factors – how many wickets a team had left.

It was at this stage that Frank Duckworth gave a paper to the 1992 Royal Statistical Society conference titled “A fair result in foul weather”.  The basis of his suggestion was a slightly more complex model which took into account the number of wickets remaining as well as the number of overs left.

One of the members of the audience at that event was a lecturer from the University of the West of England, and he decided to set the creation of this model for a student project. The student in question was Julian Adams, who collected data from Wisden and duly created the model.

This was then passed this onto Tony Lewis, and he and Duckworth decided to try and convince the ICC to adopt their model.

At first the ICC was not sure about the method, especially as it took a computer to make the calculations (at a time when computers were a lot rarer than they are now) and the name “Lancastrian method” possibly didn’t help with some of the Yorkshire members. However Duckworth and Lewis managed to refine the system so that it could be applied much more easily, and following much discussion with the ICC, it was agreed that the method should be trialled.

The first group to test the method was Zimbabwe for the upcoming visit of England. After a few matches, the first rain affected match arrived – on 1st January 1997. Zimbabwe scored 200 runs in 50 overs, but rain meant that England would only have 42 overs to bat. Lewis recalls that he was driving to see his daughter on New Year’s day when he heard on the radio that a ‘new method’ was going to be used to determine England’s target. He then realised that the target of 185 that was calculated was actually incorrect – this was the target to tie and not to win. When he got to his daughter’s he contacted Duckworth, but they both agreed not to do anything and hope. Fortunately for them the error did not become apparent as England only scored 179 runs and thus lost the match. Interestingly if the average run rate system would have been used then the target would have been 169 and England would have won.

This fact caused some of the press to criticise the method – “Academic responsible for England losing” being one of the headlines. However people generally realised that the method was fair (even if it was difficult to understand).

The method was adopted for the 1999 cricket World Cup, and following a two-year full international trial, it was finally adopted as the ICC standard in 2001.  The work was still not over – many still thought that an easier method was possible, however a final competitive review in 2004 confirmed the Duckworth Lewis method as being the best.

Duckworth and Lewis have not stopped since the adoption of their method. The model is constantly refined as more and more data is created. They have adapted it for use in 20/20 matches. And they have also developed a variant version for matches with high scores.

Capgemini’s Operational Research team use similar techniques when they compare performance against benchmarks. As with one-day cricket it is easy to find a simple benchmark, however it’s important to ensure that all of the relevant factors have been taken into account – otherwise you may end up with misleading results.