Friday, July 06, 2012

How to toss a coin


The Americans have a simple, if sometimes brutal, method of selecting their athletes for the Olympics. There is a trial, sudden death; the first three are chosen, past performance counts for nothing.

But nobody had foreseen the snag – or if they had, they had failed to put in place Plan B.

What happens if two (or more) competitors tie for third place?

So there was a scramble to work something out when exactly that happened this year. The two athletes involved were offered a choice: run it off or toss a coin.

Cricket seems to have managed all these years to have matters, such as who bats first, decided by The Toss without further explanation or instruction (except that it must take place outside, not in, the Pavilion). But we live in anxious, litigious times, so USA Track & Field provided detailed guidance.

First, the coin must be a ‘United States Quarter Dollar coin with the image of George Washington appearing on the obverse hub of the coin and an Eagle appearing on the reverse hub of the coin. Each athlete shall inspect the coin to ensure the obverse and reverse hubs of the coin reflect the images of George Washington and the Eagle, respectively’.

So my first question is: what happens if, upon inspection, the image of George Washington is found to lie upon the reverse hub, & the Eagle upon the obverse hub of the coin?

The toss itself must be carried exactly as prescribed: ‘the USATF representative shall bend his or her index finger at a 90 degree angle to his or her thumb, allowing the coin to rest on his or her thumb. In one single action, the USATF representative shall toss the coin into the air, allowing the coin to fall to the ground’.

If the coin falls wholly or partly on its edge, the toss is to be repeated.

There is more detail (nearly 400 words in all), but my concern is whether this protocol,  interferig as it does with the law of error by removing some of the sources of random variation in the tossing of a coin, upsets the assumptions on which the theory of a 50:50 chance for heads or tails is based.

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