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June 23, 1998

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When it pours, they reign!

Sridhar Ramesh

Discussion group
What makes the perfect rain rule? You tell us ...
The recently concluded Singer Akai Nidahas Trophy in Sri Lanka drew the attention of the average cricket fan to the problem of selecting rain rules for curtailed one-day matches.

As is the norm, eyebrows were raised, criticism amply levelled, and the matter inevitably laid to rest at the end of it all. To put this piece in context, think back to when India was playing New Zealand in the league phase, with the tournament very much alive.

The match, as such, was a one-horse race. Azharuddin won the toss and promptly inserted New Zealand, for his bowlers to restrict them to a modest 219 for 8 in 50 overs. Powered by the now-customary Tendulkar blitzkrieg, India got off the blocks strongly and was coasting at 131 for 2, two balls into the 25th over when it all happened. That is to say, it rained.

A look at the score-card suffices to gauge India's dominance. Yet, we are told, India was on the verge of defeat courtesy those convoluted rain-rules. Lending dignity to the ridiculous, one might add that India would have needed 147 in 25 overs to win the match. India owed it to the rain gods to have chosen to bestow their grace before the 25th over could be completed.

This naturally cues us into examining the rules governing stoppages of play.

A brief history of rain-rules

Rain rules have probably been part of the one-day game even before rain made its debut. One recalls India salvaging a solitary win during the 1982-'83 tour of Pakistan on the basis of a rudimentary rain-rule. Ironically, the rules may have gone from bad to worse over the years.

The first ever rain-rule was simple. If rain or bad light were to curtail the first innings of a one-dayer, a certain number of overs were deducted from each side's quota. If it happened during the second innings, the team batting second was required only to get as many runs as the first team had scored at a similar stage. Further, a minimum of 15 overs per side was stipulated as the requirement for a decision.

For instance, the India-Pakistan match referred to above was awarded to India since they had scored 193 in 27 overs, which was more than Pakistan's score of 175 at that stage. Pakistan went on to add a further 77 off the next 6 overs, boosting their overall run-rate, but to no avail. The slog over phase was simply ignored.

The slip showed. Soon, the rule was amended to take into account the first side's overall run-rate. The team batting second had to score at a better run-rate than the overall run-rate of the first team to win the match, the number of overs being immaterial beyond the 15-over minimum requirement.

This rule was an improvement over the first, but inadequacies remained. The second team had fewer overs, and all their wickets in hand, to get the required runs.

A further improvement was sorely needed, as for a brief period in the early '90s, chaos reigned. There was even an India-Pakistan match in Sharjah in '91 in which the umpires disallowed Indian appeals for light because they were unsure of the rain-rule in force.

The 1992 World Cup in Australia, which adopted the bizarre "highest scoring overs" rule, imparted more than its fair share of notoriety to rain rules by turning in a slew of verdicts that were dubious, at best. Rain rules appeared to have regressed. The situation called for the ICC to step in and enforce a uniform rule for all international matches. Fairness, in addition to uniformity, is what one might have hoped for. Yet, six years after that World Cup, rain rules are not uniform. Worse, they are, sometimes, palpably unfair.

Pick a card, any card

As of today, there appear to be up to four different sets of rain-rules on the prowl. The recent India-New Zealand match apparently came under the jurisdiction of the ICC 1995 Rain Rule for Limited Overs Internationals , which follows a naive scalar adjustment of the target. Thus, a team batting second which finds 20 overs knocked off its innings due to rain ends up having to score 76% of the original target (assuming the first team batted the full 50 overs) to win.

Naive, because it doesn't seem to care when the interruption occured. Most teams chasing a total of 250 or thereabouts do not plan on getting 76% of that score by the 30th over. The threat of imminent rain thus puts this additional pressure on the team batting second, as was possibly the case in an India-Sri Lanka league match played in the same recent tournament.

Now, this rule might work well if rain interrupts play prior to the completion of the first innings or before the start of the second, but anybody who has read his Murphy well will tell you that such a thing never happens.

The Australian rain rule is a minor improvement over the '92 World Cup rule, in that it deducts from the "highest scoring overs" total, a fraction of 0.5% for each over lost. The highest scoring overs rule meant that a team batting second, whose overs were reduced to 30, say, from the original 50, would face a target equal to the number of runs scored by the team batting first in their 30 highest scoring overs. Not highest scoring contiguous block of 30 overs, mind you, but an over here, a couple there, and so forth. The amendment only reduces the target a further 0.5% for each over lost. While this in in some sense different from the ICC 1995 rain rule, it is not necessarily better.

On the one hand, the timing of rain-interruptions are still blissfully ignored. Secondly, considering only the highest scoring overs makes little sense, since thereby, a team that bowls first gets unduly, unfairly penalized for bowling maiden overs. This is exactly what happened in the '92 World Cup in a match between India and Australia. India was chasing 238 in 50 overs for a win when, halfway into their innings, rain stopped play briefly. On resumption, the Indians were informed that 3 overs were docked but since they had bowled a maiden and two other overs at 1 run apiece, only 2 runs were deducted from the target. The asking rate suddenly shot up and, gallantly as India fought, they could only come within 2 runs of victory.

Clark-Samson and Duckworth-Lewis rules

Entering the realm of cerebral rain rules (fortunately, even those exist), we have the Clark-Samson rules in force for limited overs internationals in South Africa and the Duckworth-Lewis method in vogue in England.

Both these rules recognize that the timing of a rain stop is vital to determining the nature of revision required for the target. They also take into account the wickets lost by the batting team, should rain terminate their innings prematurely. Sensible, because being 150 for 2 in 35 overs is not the same as 150 for 7, if you were chasing something like 230 in 50.

A first look at each of these rules reveals how much they resemble each other. For instance, if the target of a team batting second is 220 in 50 overs and rain terminates play after 25 overs, the winning totals as per Clark-Samson would be 98 for 2, 98 for 3, 110 for 4, 133 for 5 and so on.

As per D-L rules, the targets would be 87 for 2, 98 for 3, 111 for 4, 125 for 5, and so forth.

Strikingly similar. Yet, the philosophies are somewhat different. The Clark-Samson rule performs two projections of the score of the team batting second. The first is a runs-based projection from the Clark Curve. A score of 98 runs after 25 overs projects to a total of 220 in 50. A score of 110 in 25 projects to 247, and so forth. The second is a wickets-based projection - from the Samson solution - whereby a score of 98 for 2 or 98 for 3 projects to 253. 110 for 4 goes to 220. The original target must be less than or equal to the minimum of these two projections.

Love Clark, love Samson too

Consider the case of a team chasing 210 for a win in 50 overs. Assume they opt for an early onslaught and reach a score of 145 for 6 off 25 overs when rain washes out play. This is a Type 6 stoppage as per Clark-Samson rules, where the run-rate projects to 326 in 50 overs. But that's the good news; the bad news coming from Mr. Samson is that the wickets-based projection is 205, which falls short of the original target of 210.

Scanning the spectrum of possibilities, we arrive at the opposite problem. Consider a team chasing 210 in 50 overs but opting for a steady start. Assume they reach 90 without loss in 25 overs when it rains, and no further play is possible. The Clark projection is 202, while the Samson projection is 232. The team batting second loses again, but this time to Mr. Clark. In Case A, the chasing team only had to score 65 runs off 25 overs with 4 wickets in hand. In Case B, the team had to score 120 off 25, but with all 10 wickets in hand. In either of these cases, one would expect them to get those runs more often than not. But the Clark-Samson rules demand a tight adherence to a not-too-flashy-not-too-thrifty style of play; thus a team is not offered the option of planning the run-chase to suit its strengths.

The Duckworth-Lewis rule, despite its ominous nomenclature, is far less schizophrenic. The key is to consider the two resources - viz., 1) overs remaining, and 2) wickets in hand - in combination. A single projection is made based on this combination. Thus, a team chasing 210 and losing 6 wickets after 25 overs needs to have scored only 137 for a win. Applying these rules, the team in Case A considered earlier wins its match, and so does the team in Case B. To intensify the pitch for Duckworth-Lewis, it may be noted that the tables of resource percentages have been arrived at based on a statistical survey of limited overs matches actually played. No thumb rules passed off as "digital" technology. So, accusations of unfairness, arbitrariness, or bias, would be baseless.

Room for improvement?

To the purist, the best rain-rule is still a poor substitute for a completed match. There is popular opinion in favour of a) replaying matches, and b) splitting the points regardless of the position. While option (a) is no doubt attractive, tightly scheduled tournaments do not always allow for this. Option (b) is too conservative, yet not altogether devoid of merit. Consider, for instance a closely contested match where a team chasing 250 in 50 overs, loses a couple of early wickets but consolidates to reach 126 for 3 in 30 overs. Assume that the batsmen at the crease have been around for 10-15 overs and are all set to up the tempo. Rain at this point kills their chase. On the other hand, if they had reached 127 for 3 in 30, they would win. A little unconvincing, considering that 20 overs remained to be bowled and a team that could get 123 runs in those 20, with 7 wickets in hand, would just as likely get the 124th too.

This may be suitably altered by allowing an "uncertainty region" around the projected score. Let us say that a team with 126 for 3 in 30 overs may score between 230 and 265 runs in 50 overs. From statistical studies, the width of this uncertainty region may be determined to the 90th percentile or so, depending on the fairness vs decisiveness trade-off sought. If the uncertainty region encloses the original target, a tie or draw may be awarded.

The width of this region would naturally increase with the number of overs that remain to be bowled. After all, a team that has played 48 overs would provide a better estimate of its final score than a side that has played 30.

This uncertainty belt might even assist in jettisoning the 25-over minimum requirement for a match to be deemed complete. The current thinking is that it takes no fewer than 25 overs to determine, with reasonable accuracy, the projected total of a batting side. With the uncertainty factor, matches could be decided even before 25 overs are bowled in the second innings if the relative performances warrant such a decision.

Consider one such incident that occurred recently - the final of the Benson and Hedges Cup between Essex and Leicestershire at Lord's on July 11, 1998. Since rain washed out play on the first day with Leicestershire at a precarious 36 for 6 off 16.5 overs, the match was resumed the following day and formalities completed.

Imagine if this were a league match with no provision for the extra day in case of a washout. Though Essex had not bowled the minimum of 25 overs, it would not be unfair to Leicestershire to award the match to Essex for their convincing performance. Applying the Duckworth-Lewis rule, the Leics had used up 63.63% of their resources. The projected total, would therefore be a paltry 57 runs. Even allowing for the uncertainty introduced by their having to play a further 33 overs, the final total could be predicted to lie in an interval of, say, 37 to 107, with a fairly high confidence level.

In layman's terms, the Leics would be extremely hard-pressed to attain a total greater than 107 off 50 overs, given the paltry resources at their disposal. So, it would make absolute sense to declare Essex the winner then and there, and far less sense to split points.

Conquering the elements seems rather difficult - cricket matches might have to be played in domed stadia for that. The alternative is to mitigate their menace. The selection of a good rain rule might do just that, but the search is far from complete.

And beware of the bad rain rule, for having one of those is worse than having no rain rule at all.

Mail Prem Panicker

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