Giving the batsman the benefit of the doubt? It's in the law

On the final day of the Adelaide Test between India and Australia, Marais Erasmus consistently declined to give lbws in cases where the batsman was well forward and the height was marginal. Erasmus did give M Vijay out to a delivery that, according to the ball-tracker, was similarly high, but Vijay was deep in his crease when the ball clattered into his pads.

Many believe the idea that the batsman should get the benefit of doubt is a matter of tradition, not law. Lbw is governed by Law 36, the relevant portion of which states that the striker is out lbw if he intercepts the ball with any part of his person and "but for the interception, the ball would have hit the wicket". In this article, I will argue that Law 36 does contain within it the basis for the practice of giving the batsman the benefit of the doubt. My view, based on reading the law, is that this is not merely a matter of convention or tradition.

If you throw a ball at the stumps, exactly two outcomes are possible: the ball hits the stumps, or it does not hit the stumps. You hit or you miss. A third possibility does not exist. In order for lbw to come into the picture, it must be the case that the ball does not actually hit the stumps. The umpire has to predict what might have happened had the ball not hit some part of the batsman (typically the leg, i.e. the pad). Hence, the number of possibilities here are not the same as those in the simple case of throwing a ball at the stumps unimpeded. However, the number of possible decisions remains exactly two: out and not out.

Any prediction about what might have happened would lie somewhere on a probability distribution. In other words, there are infinitely many predictions that are possible. A value of 0 would apply if you are absolutely dead certain that the ball would miss the stumps; 1 if you are absolutely certain that the ball would hit the stumps; and any fraction in between depending on how much doubt you have. You could conclude, for example, that you are 90% sure that the ball would hit the stumps. Or you could be only 25% sure that it would miss the stumps. All of these would be maybes, some closer to "out" than others.

The law says that the batsman is out only if "but for the interception, the ball would have hit the wicket". It does not say "would have hit the wicket with a probability of at least 70%". Nor does it say, "more likely than not, the ball would have hit the wicket". For every possibility less than 100% certainty, there is some chance that the ball would have missed. In all cases other than those in which the ball would have gone on to hit the stumps, the batsman is not out lbw. Therefore, the idea that the benefit of doubt has to go to the batsman is a part of law, not simply tradition.

How might probability be established? Put another way, how does an umpire determine the degree of uncertainty?

Umpires have developed many ways of doing so. Erasmus used one such method in those lbw rulings in Adelaide. When a ball has further to travel, it can be reasonably argued that there is less certainty about where it will end up. For an umpire, this increased uncertainty has been considered significant. This holds true not just for height but also for width. When the ball is turning sharply, or when it is swinging appreciably, the possibility that it could spin or swing past the stumps is logically greater. This is why so few lbws are given off sharply turning offbreaks. Where tradition, or convention, comes in is in the consensus about these ways of reviewing lbw appeals. The tradition lies in the measuring of uncertainty, not in the conclusion reached thereafter. The conclusion is required by the law.

For an umpire standing at the bowler's end, the uncertainty may increase significantly when a batsman is well forward (or batting outside the crease and playing forward) and the impact is relatively far from the stumps. As far as the mathematical calculation of the ball-tracking system goes, the uncertainty does not increase significantly. Given a point of impact, and given a trajectory up to the point of impact, the certainty with which the ball tracker can predict the path of the cricket ball does not change significantly whether the batsman is well forward (about 8ft from the stumps) or caught on the crease (4ft from the stumps). The ICC tried to factor this notion of uncertainty into ball-tracking predictions during the 2011 World Cup with the 2.5 metre rule - which is now a 3 metre rule and was recently applied in favour of Daniel Vettori at Hamilton.

The problem is complicated by the existence of "umpire's call", which applies to all situations that are deemed to be insufficiently clearly one or the other (hitting or missing, pitching in line or pitching outside leg, hitting in line, or hitting outside the line). It is not in dispute that when the ball-tracker produces an "umpire's call" result, it is describing an lbw appeal where the batsman is less clearly out than one in which it produces verdicts of "hitting", "pitching in line" and "impact in line". Yet sometimes "umpire's call" can result in an out decision if the umpire originally gave it out.

In some respects this makes sense. It gives primacy to the original decision. In a review system this is the correct thing to do. But what does this mean for the lbw law? It amounts to the reviewer saying, "I cannot confirm or deny the original decision. I'm not sure. It could go either way. So ignore me for now." Under the letter of the lbw law, this means that there is some chance that it is not out, and therefore the decision must be "not out". "I'm not sure" can only lead to an "out" decision if "I'm not sure" is ignored.

In the absence of ball-tracking, in marginal cases such as the ones that result in "umpire's call" verdicts from ball-tracking, it is reasonable to think that a given set of expert umpires might rule differently. Some umpires may be surer than others that an lbw can be given. This is reasonable. There must always be marginal cases with a law like the lbw on which experts will disagree. While "umpire's call" in the DRS preserves the primacy of the umpire's decision, it does so by ignoring its own conclusion about the appeal. Under the lbw law, any doubt must result in a "not out".