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In Cricket, Why does the Batsman get the Benefit of the Doubt in close-call decisions by the Umpire?


I heard a cricket commentator on BBC Radio4 long-wave ask this question in 2010, and his co-commentator said rather stoically that this was just the way the game had traditionally always been played. However, although I'm no expert at cricket, I felt there was a mathematical answer which would explain the situation more clearly, so here goes:

In a game of cricket, there's quite a lot going on, but there is a particular piece of the game which is crucial, and that is the part where the bowler bowls the cricket ball in the direction of the wicket and the batsman defends the wicket and sometimes decides to whack the ball with the bat so that it's going to take a while to get it back, during which the batsman may score some runs. That event, the bowling and batting, is sometimes known as a "ball", and there are six of them in an over. It seems simple, that there's a contest between two people, the bowler and the batsman, and that it would be like a joust, where it would be equal, and therefore that any judgements made would have to be equal.

However, here's why it's not equal: The bowler and the batsman are doing quite different things, and the whole game of cricket is not a sequence of such events in an equal way. Most notably, if a decision made by the umpire is "close", the consequences of getting it wrong are quite different for the batsman and the bowler. Instead of it being like a competition between two knights on horseback having a joust, where both have a lance and a shield and both are trying to unhorse the other, it's more like a competition between a cheetah and a gazelle, where the cheetah stands to gain some lunch or not, whereas the gazelle stands to live another day or to die.

Therefore in close-call decisions, it's better for the umpire to give the benefit of doubt to the batsman.

To put some numbers on this, supposing the batsman is likely to score about 40 runs on average, and at each ball there is a one in 50 chance of being "out". If only 10% of the situations have any doubt about whether to call "out", then it is more realistic to put those doubtful cases in favour of the batsman.

Another situation in which an unequal judgement is applied towards fairness is in criminal court cases where a jury has to decide if the defendant is guilty or not. If the evidence is 50:50, the defendant should be acquitted, because it is better that a guilty person is set free than it is that an innocent person is jailed. Again, it is the difference in severity of the consequences which makes the bias justified.