When he was 14, Persi Diaconis packed a fresh deck of cards and a spare pair of socks into a knapsack and ran away from home to become a magician’s assistant. He spent the next few years as an apprentice with Dai Vernon, whose sleight of hand was so smart, so sharp, he even beat Harry Houdini, who famously claimed he could pick any magic trick on the third go, until Vernon fooled him seven times in a row.
They used to call Vernon “the Professor”, and now they do Diaconis, too. Because that is what he is. The Mary V Sunseri professor of statistics and mathematics, to be exact, at Stanford, where he has been continuing his lifelong study of chance and probability.
Diaconis made his name studying card shuffling, but he has also done a lot of work on the one part of a cricket match no one ever really stops to think about. The coin toss. “When was the last time anyone watched the coin toss or really focused on it?” says the head of the Big Bash, Kim McConnie.
Which is why, this season, captains in the Big Bash will not be tossing coins but bats, “specially weighted to make sure it is 50-50”. They will be calling “hills or flats”, just like children playing backyard cricket. McConnie says: “We’re making it much more relevant to families, we are creating a moment which is much more fitting with kids.”
Which bit of gimmickry may or may not be related to the fact Cricket Australia have hired M&C Saatchi to run a campaign called “It’s Your Game” that is supposed to repair the damage done to their public reputation by all that sandpapering. Unfortunately, Diaconis does not seem to have done any work on the dynamical bias in cricket bats. But he has done a whole lot of it on coin tosses. Which, of course, are “as close to a random phenomena as I know”. Until he proved that, actually, they are not. Rather, Diaconis says, “coin tossing is a deterministic process” that depends on how hard you flick and fast it travels.
Boil down his elegant mathematics into language we can get away with here in the sport section and he found that, more often that not, a coin will land the same way up as it was when you tossed it. It works out as the odd one out of every 100 tosses. That is if you catch the coin in your hand. Let it land, and another set of forces come into effect. Especially if the coin has a bevelled edge. Diaconis calls it “edge bias”. He first learned about it from a magician who used to shave coins down so they would always fall his way around. Diaconis says it is possible to find coins that will fall tails up eight times out of 10.
There is a tactic, then, a trick to it that will tip the odds ever so slightly in your favour. Always call the side that is facing up at the start. And if it lands, it helps if you have already seen which way it is inclined to fall. Which is a new ruse, even in cricket, where there is a history of people coming up with cunning ploys. WG Grace is supposed to have called “the lady” when he knew the Queen was on one side and Britannia on the other, while Saleem Malik had an entire repertoire of tricks. According to Dickie Bird, when Pakistan were playing against New Zealand, instead of calling heads or tails Malik “jabbered away in Pakistani” which meant his opposite number “had no idea whether he’d won the toss or lost it, was batting or fielding”.
After that, they started making the match referees go out to watch the toss. Which was why when Malik memorably won by calling “bird” in a Test against Zimbabwe, someone was there to make him take it again. In the end, all this made little difference. Malik is one of the rare captains whose record is exactly 50-50, 12 Tests, 12 tosses, six wins, six losses. There tends to be more variation to tossing than you might think. Len Hutton, for instance, was a useless tosser. It’s true. There have been a few but Hutton was the very worst. He won seven tosses out of 23 Tests, which is the lowest win rate out of every captain who led in at least 20 Tests.
Hutton, however, was not nearly so bad at it as Joe Root is good. He has won 18 out of 24, so he is calling three out of every four. He is tied with Lindsay Hasset as the best tosser in the history of Test cricket. At which point, when you do start look at this ritual a little closer, it begins to seem a little odd that the game lets blind luck and “dynamical bias” play such a large part.
Especially when, as a new bit of analysis by Sidharth Monga over on Cricinfo shows, the coin toss has become so important. “There has been a clear and consistent dip,” Monga writes, “in the win-loss ratio of sides fielding first in Test cricket.”
This year, the team who have lost the toss have only won nine Tests out of 43. A decade ago, it was 19 out of 47, a decade before that, 19 out of 45. Maybe they would have better luck with those “specially weighted” bats or, failing that, the toss might be scrapped altogether.
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