The ‘Fightback’ In Cricket And Regression Toward The Mean

The word ‘fightback’ in cricket – often used to denote an improvement in the performance of a team – always annoyed me. Possibly this may have been because growing up I was a nervous Aussie cricket supporter, and given that the Australians had the upper hand in the majority of matches they played in, the word was seemingly most often employed by commentators cheering on the efforts of the other team. But possibly there was also a sense that a ‘fightback’ was not really that big a deal, that is a sense that it would be unusual for all 11 members of a cricket team to perform poorly.

This latter point is essentially the idea behind the concept of regression toward the mean. I like this term, because it puts a cricket team’s supposed ‘fightback’ into proper perspective. Say that a team is 4/40 – a pretty bad start to any team’s innings, and you have two batsmen who have to get off the mark out in the middle. What would you expect each of them to score? If they each scored about 40 runs, and added about 80 runs to the team total, you might be inclined to say that they had done very well, and that they had led a ‘fightback’. But really, scoring about 40 runs each is what you would expect, on average, the No.5 and No.6 batsmen to score. Now it could be that the team being 4/40 indicates that batting conditions are worse than average, and that would mean a batsman who performed at their average had actually done pretty well. Nevertheless, the point is that the anchor for one’s expectations should be what a batsman has done over his career rather than how the other batsmen have performed on any particular day.

Similarly, if a team is expected to make on average about 350 runs per innings, and they make only about 100 runs in the first innings, it shouldn’t be at all surprising that they would make substantially more than 100 runs in the second innings. Again, it’s nothing more extraordinary than a team regressing towards its mean performance. And the same applies if a batting team gets off to a considerably better-than-average start: you would expect that it is more likely than not that their performance from there on in will deteriorate, and the bowling team’s performance will improve in comparison.

Of course none of the above will seem that revelatory to cricket-watchers who have completed a course in statistics. But it’s a reminder that, during the course of a single match, when one is wondering what has been the driving force behind a supposed ‘fightback’, the answer often isn’t anything more dramatic than performance simply regressing to the mean.