Tuesday, 10 July 2012

Average



Life must be quite difficult for First Class cricket umpires. Lots of tricky judgments to be made as to whether batmen may or may not be out, and whether or not the light is suitable for play. But surely no decision can be trickier than the requirement of the England & Wales Cricket Board that they assess the pitches according to a six point scale: 6 very good, 5 good, 4 above average, 3 below average, 2 poor, and 1 unfit. That is correct – no ‘average’. I understand that it is just possible that an umpire, who as a child saw the Oval in its heyday, might decide that he never these days gets to see a pitch that he can in conscience describe as very good; I understand that it is just possible that the standard of groundsmanship may have improved to a point where he never sees an unfit one. But even with my limited statistical knowledge I find it difficult to envisage a situation where nothing is ever average. Surely, by definition, the majority of them will be average.

I’m sure my mathematical friends will point out that whilst this will be true of the modal average, the mean average will probably compute out to a non integer figure between 3 and 4, so that every pitch will indeed be either over or under that figure. But I cannot believe that human beings, which many umpires are, will read it in that way. Week after week they will see pitches that are, in every human sense of the word, average. Perhaps any pitch that is average must be graded as above average, rather than below, on the principle that the groundsman gets the benefit of the doubt.

This could easily be passed over if this were an example confined to cricket. But I have worked in a school where one was expected to assess students on the three point scale: excellent, good, unsatisfactory. The theory of management was that anyone who wasn’t good was letting the side down; my personal view was that that if someone wasn’t unsatisfactory that was good enough for me. But why the horror of the word average?

I was once asked by an educational psychologist to assess various pupil behaviours as to whether they were displayed less than average, average, or more than average by an individual. This is not too difficult in the case of behaviours such as “chatters in class” or “fiddles with pen”. But one of the behaviours was “attempts to strangle other pupils”. So what is the average for that behaviour?

Never having had a student attempt manual strangulation I assume the modal average is nought. So less than average must be a minus number. What does this represent? Making positive efforts to revive a pupil strangled by someone else?

The mean, assuming that this behaviour has occurred at some time in some place, is of course slightly above nought. So every non-strangler could be rated as less than average. You cannot however attempt to strangle someone on 0.0004 of an occasion. Either you do or you do not. So any actual strangler is going to rate as more than average. Therefore noone would rate as average.

Which brings us to First Class umpires….