Anorak's corner

Michael Vaughan is a useless tosser – literally. He’s won just 6 tosses in the 22 tests he’s been captain.

This is very improbable. I reckon (though I might be wrong - this isn't my strong suit) that the chances of being this unlucky are just 2.6 per cent; it’s a binominal distribution.

Weirder still is that this continues a long losing streak by England captains. Hussain, Atherton and Stewart all lost the majority of their tosses; complete statistics in all their glory are here. Since 1993 England’s test captains have won only 54 of 138 tosses. There’s only a 0.7 per cent chance of being that unlucky.

By contrast, England’s more upper-class captains often won the toss. Taken together, Peter May, Colin Cowdrey and Ted Dexter won 57 of 98 tosses, with May and Cowdrey being especially successful.

If we are applying conventional tests of statistical significance, this means we cannot reject the hypothesis that the coins now used in England test matches are bent. Nor can we reject the hypothesis that it’s better for English cricket for teams to be captained by Establishment figures.

Maybe this just goes to show how silly tests of statistical significance are, as Deirdre McCloskey points out.

You’re right – I don’t have a girlfriend.

Comments

[Scott Campbell at Blithering Bunny]

It would be interesting to compare the toss records between home and away series. Presumably the coins aren't bent in England. How much of the bad luck is taking place overseas?

But then, isn't it the case that the visiting captain gets to call? So how would a bent coin help then? One of the Sky commentators reckoned that the other captain puts the coin heads or tails up, depending on what is called. But can you rig a toss so easily? And why does it only happen when England are playing?

[Andrew]

There was an article recently in (I think) New Scientist, which cited a study of coin tossing that concluded that you should pick the side that is face up when the coin is being tossed, to gain some slight statistical advantage. Perhaps Vaughan and past England captains are doing the opposite.

[rw]

Isn't McCloskey's point that one shouldn't confuse statistical significance with economic (or, here, sporting) 'importance'? The former in no way implies the latter.
However, the poorness of Vaughan's tossing does seem 'important', although this is a subjective opinion about a magnitude. If one accepts this, statistical testing _is_ then useful in judging whether Vaughan is unlucky or is being cheated (or indeed has poor tossing technique).