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Monday, June 20, 2011

Why V Jayadevan(VJD) rain rule is better than The Duckworth-Lewis (D/L)

Exit D/L, enter VJD?

Srinivas Bhogle, Monday, June 20, 2011
I hear that the ICC has invited V Jayadevan to Hong Kong on June 27 to present his VJD rain rule to reset targets in rain-interrupted ODI matches. So is ICC preparing to reopen the D/L vs VJD rain rule question? I hope so. I also hope ICC gives the VJD rain rule a fair hearing this time. Last time I got the impression that the umpire raised his finger even before he heard the appeal.

So what's this VJD vs D/L debate all about? I've done this comparison earlier, but there's no harm in revisiting the question again a decade later. So here we go.

Mathematician vs engineer

The Duckworth-Lewis (D/L) approach to design rain rules was to make a deep study of the ODI scoring pattern, write down mathematical equations that accurately model this pattern, and then build a system that faithfully implements this model. You could call this the 'mathematician's way'.

The Jayadevan (VJD) approach was to start with a system that does the job, test this system to discover flaws or weaknesses, and progressively improve the prototype till it starts delivering good results. You could call this the engineer's way.

It is easy to guess that the mathematician will win the early rounds in the contest. But, as the process evolves, the engineer will start gaining ascendancy. The mathematician is now constrained by his equations while the engineer has the freedom to improvise and improve.

I have watched the D/L vs VJD tussle with interest. D/L easily won the first round: the idea of using the combined resource percentage to reset ODI targets was elegant - even beautiful! Even more admirable was how D/L used par scores to solve the problem of multiple interruptions in the middle of ODI innings - which is really the crux of the rain rule problem.

Jayadevan's early forays were less successful. He started with the clever idea that he must somehow marry the 'norm method' to the 'most productive overs' method. Both methods were promising, but both had failed because they were incomplete. Could their marriage work?

Jayadevan's earliest trials had severe deficiencies: he had problems handling multiple interruptions, and he still hadn't worked out a way to handle a first innings interruption. It isn't well known that Jayadevan got a lot of guidance from Frank Duckworth in those early days. But Jayadevan was a quick learner, and soon developed routines to handle these worrying interruptions using the original D/L idea of a par score.

With these corrections, VJD was ready to challenge D/L! Both methods had resource tables, and both had a way to reset targets in all possible interruption situations. Jayadevan's calculation routines were however harder, especially for multiple interruptions. Both D/L and VJD only required easy arithmetic after reading off values from a table, but the D/L calculation was appreciably simpler and more intuitive.

Jayadevan's advantage in those early contests was that his model was aligned better to real match scenarios; for example, the VJD model recognized that scoring rates are higher in the first 15 overs, and drop off once field restrictions are lifted. The D/L model couldn't accommodate this scoring pattern - their equations assumed that scoring rates kept rising monotonically as the overs depleted. In other words, D/L always expected teams to score less in the 6th over than in the 16th.

Early worries for the mathematician

The D/L method was used in the 1999 World Cup in England. It was largely successful even though some former players, notably Geoff Boycott, didn't like the idea that Team 2 sometimes had to score many more runs than Team 1, in the same number of overs, to win.

The first worrying sign about D/L became visible in the 1999 World Cup, but few noticed it. In a group match against Sri Lanka, India scored a mammoth 373 batting first, with centuries by Sourav Ganguly and Rahul Dravid. Chasing 374, with an impending threat of rain, Sri Lanka collapsed rather quickly for 216. Almost nobody realized that if Sri Lanka had batted cautiously to reach about 120 for no loss after 25 overs, and the match had then been washed out, Sri Lanka would have won by the D/L method even though they needed to score at the ridiculously high rate of 10 an over for the next 25 overs to win the uninterrupted game. This is a tough ask even in a 2011 T20 game!

Why did D/L set such an absurdly low target? An informal explanation is that D/L was still giving a much higher weight to 'wicket lost' than 'overs remaining' at this stage. As the overs remaining depleted to 25, the D/L response continued to be: "But they still have all ten wickets intact!" And why was D/L responding this way? Because deep down D/L had assumed that the average maximum score in ODI matches is just about 250. The D/L equations had failed to anticipate such a high Team 1 score!

The VJD method faced no such constraints. It reckoned the Sri Lanka needed to score 150/0 in 25 overs (30 runs more than D/L) if it had to win against India's 373 in 50 overs.

Soon there was a second worrying sign. Inspired by what Sanath Jayasuriya and Romesh Kaluwitharana did in the 1996 World Cup (and Mark Greatbatch earlier in the 1992 World Cup), most ODI teams began to exploit the field restrictions in the first 15 overs to significantly accelerate their scoring rate. This was a big departure from the D/L model's assumption that later overs always yield more runs: teams were now scoring more in the 5th over than the 16th over when they were supposed to score less!

When queried, Duckworth-Lewis shrugged off this concern. They argued that the gain from an early batting slog was compensated by the greater probability of losing wickets … and so it was still even-steven. The D/L argument was probably valid in batting conditions that favoured new ball bowlers. But trying bowling at high noon in Mumbai's Wankhede Stadium with a hard ball and unprotected boundaries!

Once again VJD was in a better place, because it had already factored in the probability of an early slog in the first 15 overs. Why didn't the D/L model anticipate this scoring pattern? They didn't because such a pattern didn't exist when they wrote down their equations … and they couldn't change their equations easily now because they were so mathematically 'proper' and unyielding.

Soon a third worrying sign appeared on the radar. In a 2000 Durban ODI against New Zealand, the D/L method set South Africa an absurdly high target of 153 in 32 overs, in response to New Zealand's 114/5 in 32.4 overs, i.e. nearly 40 runs more! While D/L insisted that this target was reasonable (and it helped that a rampaging Lance Klusener scored 41 runs in just 18 balls to win it for South Africa), the real reason was a weakness in the algorithm to calculate D/L targets that was used those days.

In the D/L method when Team 2 had fewer resources than Team 1 (R2 < R1), the reset target was obtained by using the scale-down ratio R2/R1. However when Team 1 had fewer resources (can happen if Team 1's innings in the ODI match is curtailed), i.e. when R2>R1, the target reset rule didn't use the scale-up ratio R2/R1! Instead it needed a construct involving a work-around: multiple (R2 - R1) by the average score in an ODI innings (called G50; initially G50 was assumed to be 225, then 235) and add this increment to Team 1's score. In low-scoring matches, like the Durban ODI, this increment becomes unacceptably excessive.

The G50 work-around always baffled me. Why would two accomplished professors not choose to use ratios both to scale up and scale down the combined resources? My best guess is that is what they intended...but then found that their model wouldn't allow it (in certain cases a scale-up set absurdly high targets!)

The VJD method had no such inhibitions; it could scale up or down almost with impunity because it wasn't shackled by mathematical equations having nice continuity properties. No wonder it made Duckworth-Lewis and other experts studying the method very suspicious! Surely there must be some discontinuity - and, therefore, some inconsistency - somewhere? Indeed this was one of the reasons why the ICC expert rejected the VJD proposal in a 2004 review.

The moment of reckoning

The 2003 World Cup in South Africa provided the next stern examination of the D/L method. With many rain interruptions, the D/L method had to be used frequently. There were a few glitches, none more tragic than the hosts being eliminated because they read the D/L table wrongly…but the real test would be the Australia-India final!

In the final of the 2003 World Cup, in reply to Australia's staggering 359/2, India had reached 145/3 in 23 overs, with Sehwag in top gear, and rain looking very likely. As it turned out, it didn't rain…but what if India had reached 157/3 at the 25-over mark, and the skies had then opened up to end the match? India would have become undeserving winners of the 2003 World Cup by the D/L method!

This result convinced Duckworth-Lewis that it was time to rework their method (there is little doubt that if India had won, the D/L method would have received an instant burial). It would appear that D/L successfully persuaded ICC to accept a computer-based method…at least for the big international matches. It was decided that the existing (manual) D/L method would continue as the 'Standard Edition', while the computer-based method would be called the 'Professional Edition'.

So how was the 'Professional Edition' different? As their 2004 JORS paper reveals, Duckworth-Lewis added additional variables to their mathematical model that would let them 'straighten' their curves; the more Team 1 scored, the straighter the D/L curves would become. In cricketing terms, 'straightening' a curve is like 'giving more weight to overs remaining than to wickets lost'. After all if Team 1 scores 500, Team 2 will be more concerned about scoring off every ball than about preserving wickets.

'Straightening' a curve also requires 'regenerating' the D/L table based on Team 1's final score. So while the Standard Edition continues to have one D/L table for all situations, the Professional Edition generates a new D/L table for every Team 1 score.

The mathematician fights back

The D/L Professional Edition was indeed a good recovery vehicle. Let us see how the Professional Edition (PE) addresses the three worrying signs that we mentioned earlier.

The first worry - relating to D/L setting 'well-below-expected' targets if Team 1 hits up a well-above-average score - was completely addressed; indeed the primary motivation in devising the computer-based PE was to solve this vexing problem. As an example, PE would have set Sri Lanka a target of about 150/0 in 25 overs if it had to defeat India's 373 in 50 overs in that 1999 World Cup match at Taunton. [Curiously enough, this was exactly the target set by the VJD method in its original version!]

The second worry - about the D/L model not being aligned to the observed high scoring pattern at the beginning of an ODI innings - still remains a weakness; but it got partially alleviated because of the introduction of the modified 10+5+5 power play scheme. The availability of a 'floating' batting power play has transferred some of the slogging fury to later in the innings, and that helps D/L - because the method is better equipped to deal with the end-innings slog than the early-innings slog.

Finally D/L reports that, with the introduction of the PE, both scale-ups and scale-downs of the combined resource percentage ratio (R2/R1) are now possible and the G50 construct is now no longer needed. I have not been able to verify this claim because it is so hard to gain access to the D/L PE (and why is that so?), but it must be true because the ICC website explicitly says so. But I would be curious to know if this is always so, especially in application of the D/L PE to T20 matches (about which I will talk a little later). I also wonder why D/L chose to get rid of G50 after consistently defending it in the early years. (And when did this happen? An example in the 2004 JORS paper, which introduced the D/L PE, still used the G50 work-around!)

But the engineer is still ahead!

When I asked Jayadevan to react to the D/L Professional Edition he said something rather surprising: "After the introduction of the PE, I note that the D/L and VJD targets are now much closer. But doesn't that imply that the old D/L gave poorer targets than VJD?"

ICC's permission to allow computer-based rain rules proved to be a godsend for Jayadevan too because his target calculations were rather tedious to do manually, especially in cases with multiple interruptions. Jayadevan also used the opportunity to re-draw his own target curve, to further improve the VJD target when Team 1 piles up a huge score.

It would be correct to say that neither the D/L nor the VJD target is now simple back-of-the-envelope arithmetic. Both methods exploit the extra computing power available to effect internal corrections; the case of multiple interruptions when Team 1 is batting is especially treacherous and requires an iteratively convergent procedure.

The VJD and D/L methods that we now see have thus migrated from back-of-the-envelope calculation to black-box computation. An interactive menu requires the end-user (scorer or third umpire?) to simply enter the match details…and the computer provides the target score!

The last straw?

With the advent of T20 cricket the D/L vs VJD battle is being played out all over again in 20-over matches. The data we have so far indicates that the D/L and VJD targets overlap even better in T20 than in ODI. So if ICC opts for VJD in ODIs, they can easily use the same rain rule in T20 matches.

The VJD method has already been used extensively in the now defunct Indian Cricket League (ICL). In fact, it was reported that IPL4 too would use VJD; but BCCI developed cold feet at the eleventh hour and reverted to D/L.

How do the VJD and D/L methods deal with T20 targets? Unlike D/L, the VJD formulation doesn't explicitly keep track of the number of overs remaining; it only looks at the percentage of overs remaining. This is an advantage because one can always 'pretend' that the VJD ODI tables are in fact also the VJD T20 tables. With D/L it is harder to carry forward the pretence; so D/L is obliged to assume that a T20 match is actually an ODI match limited to 20 overs for both sides.

To be honest, all this assuming and pretending is convincing no one. The simple truth is that the current D/L method simply doesn't model T20 matches well enough, and you don't need Paul Collingwood or Stephen Fleming to tell you that. From all accounts, T20 is a very different sort of animal. I remember writing a comment with Rajeeva Karandikar in which we suggested that a 'shrunken trouser' D/L approach might work better than a 'cut trouser' D/L approach. But, in reality, neither approach works too well.

It's time to give Jayadevan a chance

The Duckworth-Lewis method has had a long and chequered innings. But every product or discovery has a timeline, and I believe D/L's time is up.

They don't play ODI cricket the same way now as in 1997. Aggregates, and therefore strike rates, have risen appreciably. Power plays with field restrictions now strongly impact batting style, playing strategies have changed and are continually evolving, the minimum number of overs each side must bat has been reduced from 25 to 20 overs, and T20 cricket is influencing ODI cricket in ways we still haven't fully fathomed.

In simple terms, the script of limited overs cricket has changed. So the solution must also change. Our recurring theme in this narrative has been that the mathematical premises underlying D/L's curves are no longer tenable; and even the less curvaceous Profession Edition doesn't look too pretty after its poor T20 performance. ICC's love affair with D/L now has to end.

It should have ended in 2003 itself after D/L was badly exposed in the World Cup final - especially since the VJD alternative was by then available. But ICC contemptuously dismissed VJD without even a hearing, let alone a trial.

All the data and evidence we have suggests that VJD will perform very well in ODI matches, and marginally out-perform D/L in those difficult 'corner' cases. Even if VJD occasionally proves embarrassing, let us not forget how often D/L has taken ODI cricket to the edge of the precipice.

ICC has been unbelievably kind to the D/L method for almost 15 years. It would be fair to give the VJD method a chance at least for the next two years.

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