Draft:The Clark Curves (for Calculating Curtailed Cricket Contests)

Background The farce at the 1992 cricket world cup semi-final in Australia, when South Africa was asked to score 22 runs from 1 ball to beat England, was, no doubt, the trigger for many entrepreneurs to come up with a better solution for dealing with rain interruptions in cricket matches. One suspects that South Africans were more motivated than most. The Clark Curves was one such solution and was first presented to the United Cricket Board of South Africa (Brian C Basson) in 1993. Over the next 2 years correspondence ensued and in 1995, the UCBSA held a press conference in Cape Town to announce that it would be using a methodology devised by Cape Town schoolboy, Wayne Dorego. This spurred Clark to be more active in promoting his ideas and a meeting at the UCBSA soon persuaded Ali Bacher and Raymond C White to accept Brian Basson’s proposal to use the Clark Curves instead. Incidentally, there was nothing wrong with young Wayne’s concept, nor his calculations (they were very similar to Clark Curve 2) but they would only have addressed a fraction of the rain interruptions that occur. The “legal” details of how the Clark Curves are applied during cricket matches is provided by CricInfo in the link and readers are referred to that website for technical information. This entry is designed to give the background, philosophy and differences with other methods.

A 50 over cricket match has an almost infinite number of permutations and a 20 over game can also produce a sizable number. There is, therefore, no “right” answer to what happens when it rains. There are a few “good” answers and several “bad” ones. The Clark Curves were the official rain interruption methodology in the 1995 England Tour of South Africa. Mike Atherton was England’s captain and stated that he was very happy to use the system, but the only interruption was when the lights failed in Bloemfontein but the break wasn’t long enough for an intervention. Soon after, however, there was a triangular series between South Africa, India and Zimbabwe and it rained in the match between Zimbabwe (batted first) and India. When it rained in the second innings India’s target was revised. Sachin Tendulkar, India’s captain, was not interested in how the target was determined he said “Just tell me how many I need to get and I’ll get it.” And he did! Andy Pycroft (Zimbabwe) was far more interested in the calculation and declared himself happy with the revised target, although they eventually lost. Subseqentially, Sri Lanka, Australia and Pakistan all played under South African playing conditions using the Clark Curves. Nobody complained about the targets or results that the system came up with, there were no headlines on the sports pages and there was never any necessity to write lengthy explanations justifying the numbers.

Analysis

Although it is mentioned on the CricInfo website, it is believed important to detail the analytical foundation for dealing with rain interruptions. Although what follows is thought to be blindingly obvious, it has never been documented elsewhere to our knowledge.

A Timeline of the 6 possible interruptions in a cricket match

6 scenarios have been identified: at the beginning, during or at the end of each innings (x2) Each of these scenarios needs to be addressed differently. There can be multiple scenatio 2 and scenario 5 situations and 1 stoppage may be both a type 3 and a type 4 scenario in which case both sets of rules must be applied. It is well known (from the television “worm”) that the progress of a cricket innings is non-linear.

Clark Curve 1 is a representation of what a typical (statistically smoothed) worm might look like. This curve is used for scenario 2, 3, 5 and 6 calculations. A second, Clark Curve 2, represents how scores might be reduced if the number of overs is reduced (in advance). This is used in calculations for Scenarios 2, 3 and 4. It is important to note that, in the Clark Curve methodology, the exact shape of each of these curves is unimportant. They may vary from season to season, country to country, venue to venue etc. It should also be clear that different curves will apply to 50 over v 20 over games. This is in contrast to the DLS where the very methodology is based on the shape of the curve and fudge factors (G50) are applied to cater for the differences listed above. The DLS also uses only 1 curve to cater for both the CC1 and the CC2 calculations.

Wickets

It is important to take wickets into consideration in many of the scenarios and the Clark methodology does that. Andrew Samson, the UCBSA’s statistician at the time, came up with a number of “wicket ratios”. For wickets 3 to 9 the average ratio of the score at the fall of the wicket to the final total was calculated for a range of South African limited over matches. Again, the data itself is not fundamental to the methodology and different applicants may use different data. It was decided that the data relating to the fall of the first 2 wickets was too variable and the impact on the final score of little significance for the purpose for which it is used. Similarly, other applicants may feel differently or have better data. This does not affect the methodology. Once we have the wicket ratios they are applied to determine whether or not a team in scenario 2, 3 or 6 would have been able to reach the specified target with the wicket resources available. There are 2 fundamental differences between this methodology and the DLS: firstly, wickets are “taken into consideration” means that in many circumstances the number of wickets that have fallen is “considered” to be normal in the context of the innings and no adjustment is made to the number of runs. Only in exceptional circumstances i.e. when too many wickets have fallen, is it believed necessary to make an adjustment. In contrast DLS makes an adjustment on every occasion. Secondly, wickets are not taken into consideration in Scenario 5. This is believed to be the right approach for a vast number of situations in contrast to DLS whose use of wickets in this scenario is believed to be a “double whammy” i.e. sets higher targets where more wickets are lost and vice versa. This has the potential to end in a 22 runs in 1 ball type situation. The Clark method allows for a team to self correct once it returns to the field after losing too many wickets (trying to achieve a target???) before a rain delay. There are, however, a number of (extreme) possibilities arising out of Scenario 5 where the Clark solution (as applied in 1998) could have altered the balance of the game. A solution was being worked on and would have been applied in 1999 had the ICC not imposed the DLS on South Africa. This solution used the innovative approach of reducing the “resources” that are available to a team as the overs are reduced i.e. reducing the number of available wickets. Whilst this is a controversial concept, the UCBSA had decided that this was the best of all the (unsatisfactory) alternatives. For example, Team 2, chasing 250 runs to win reaches 91 for 2 after 20 overs. If rain stops the match at that point Team 2 wins. If, however, they were 91 for 6 they would lose. What happens, however, if the sun comes out and they can bat for another 5 overs. Ignoring the number of wickets for the moment, the Clark method would reduce the target to 128 i.e. they would have to score another 37 runs to win. This is easier to achieve than the 159 they would have had to get if hadn’t rained. To even up the “balance” we could reduce Team 2’s available wickets by, say, 3. If they’d been 91 for 2 they would still have 5 wickets in hand with which to score 37 runs in 5 overs and should (still) win. If, however, they had been 91 for 6 they would now have only 1 wicket standing and getting 37 runs in 5 overs is going to be a challenge and they will probably lose – the “balance” of the game has been maintained and it remains a fair cricket contest. The DLS solution in these circumstances is to set a (ridiculous) target in the latter case (22 runs in 1 ball?!) and the contest is effectively over.

Unresolved Problems

The scenario described above (and hundreds of thousands like it) are a nightmare for anybody trying to create a “fair” target and a watchable cricket contest. It is believed that the Clark Curves method is a reasonably flexible system and can be adjusted to suit the needs of the authorities i.e. “If you don’t like the solution I have proposed, what do you want to happen (in Scenario 5) and we’ll adjust the rules and the data to meet your needs.” What is described above, whilst still complex, is believed to be about as simple a solution as can be achieved. A computer program was created (in 1995), when the system was in operation in South Africa, but results and targets could still be worked out manually from the data provided. In today’s world with artificial intelligence and big data it would be possible to take into account the differences in the shape of the curves for teams batting first v batting second; the actual abilities/form of the batters and bowlers still to perform; the dampness of the playing surface; the difference in the characteristics of the venue’s pitch; the size of the boundaries depending upon whether the batters were left or right handed; the lighting conditions; what the umpires had had for lunch etc. The problem with this approach is that it would be difficult to verify that the computer has come up with the “correct” result – we all know how many bugs there are in computer software systems. But none of this is necessary because what we are dealing with is a sporting contest and there are only 2 possible outcomes: either Team 1 wins or they lose! Alternatively, we just need to know what the revised target is. If a simple method says it’s 249 and artificial intelligence comes up with 251 who cares?! It’s the ludicrously wrong answer that we need to avoid. Perhaps we should apply 5 different methods and take the average!

References

Administrative, Financial and Playing Conditions 1995.1996, United Cricket Board of South Africa

Administrative, Financial and Playing Conditions 1996.1997, United Cricket Board of South Africa

Administrative, Financial and Playing Conditions 1997.19986, United Cricket Board of South Africa