Scoop Review of Books

Rolling the Dice

The Improbability Principle: Why incredibly unlikely things keep happening by David Hand (Bantam Press, $39.89)
Reviewed by C P Howe

Who hasn’t heard a relative, a colleague, or a journalist comment on an unlikely event? Perhaps someone wins the lottery two weeks in a row. Or the financial markets crash twice in ten years. Or – in the case of my parents – they see a car with their initials on the number plate. Isn’t that incredible! What a co-incidence!

These are the kinds of things David Hand takes a close look at in The Improbability Principle and he does a great job for the general reader. Although some of the maths will be a stretch – and some almost inaccessible – to non-mathematicians, it doesn’t distract from the story he’s telling.

It turns out that his Improbability Principle is ‘not a single equation, but a collection of strands’ and Hand walks us through them – he calls them ‘laws’ – together with other material about probability and chance.
There are plenty of examples showing just how hard it is to know what is going on in the world around us, and he explains carefully the real chances of a particular event happening, whether it is an event we think should be uncommon but is in fact highly likely, or a perceived co-incidence that can be explained simply by the maths of probability.

Hand looks first at the way unusual things seem to happen more often than we’d expect, explaining how humans simply cannot comprehend how large truly large numbers are. He shows that rather than be surprised at rare events, we should be surprised if they did not happen. He likes to use dice and lotteries as examples; for the latter, he does some quick calculations and easily demonstrates how an ‘unusual’ result, like someone winning twice, or the same numbers coming up two weeks in a row should, in fact, be expected.

He then turns his attention to the way people interact with events, and here he is less convincing. People tend to select results that meet their expectations, or are willing to accept as the same results that are not. He drops in some wonderful and entertaining examples, including the man who painted targets around his arrows after he had fired them – the law of selection – and a very funny passage from Dickens: ‘circumstances that tallied with wonderful exactness; such as Barbara’s father having been exactly 4 years and 10 months older than Kit’s father; and one of them having died on a Wednesday and the other on a Thursday’ – the law of near enough.

Hand also identifies a further law – the probability lever – about how minor shifts in circumstances or events can change probabilities so much that the highly unlikely becomes almost certain, and uses examples from financial market crashes over the last century to demonstrate it.
He doesn’t go far enough in linking events that are unusual, or appear unusual, with people’s perception and reaction to those events. While he touches on it in places – for example, our tendency to see patterns or causality where there is just randomness – his lack of expertise in psychology and behaviour starts to show as the book progresses. In particular, he misses several opportunities when discussing rare events to illustrate a typical human response. If 1, 2, 3, 4, 5, and 6 came up in the lottery it would be headline news. The chances of 12, 17, 35, 23, 9 and 41 coming up are exactly the same, but the reaction would be quite different. Why do people think and react to such events in the way that they do? Hand leaves out interesting discussions he might have included about public scientific and mathematical literacy.

He is undoubtedly well-read. The quotations at the beginning of each chapter, and the references listed by chapter at the end of the book, leave us in no doubt he has looked far and wide for his material. And he has credentials – Emeritus Professor of Mathematics at Imperial College London, amongst other things. And yet I found him using examples to explain probability and improbability that he really should have left alone.

The first involves sports. Hand shows that three or four baskets in a row, or multiple home runs, should be expected in any long run of random events. This is the same explanation he gives about rolls of dice, or specific sequences of digits occurring in numbers such as pi. I can see what he is getting at, but there is something very wrong with his sporting examples. Success in sport is not random. If Irene van Dyck has the ball the probability she will score is well over 90%, and it has nothing to do with chance. Hand misses the presence of one of his own laws – the probability lever. Actual success also depends on form on the night, and the opponents. And scoring, or any other kind of success, has a psychological effect which immediately influences performance. There is a wealth of research available on players being ‘in the zone’ or ‘on a roll,’ which Hand fails to note.

The second troubling example involves literature. Hand says, ‘Shakespeare aficionados will know [he] appeared fond of alliteration (my italics,)’ and goes on to quote a study showing that alliteration in Shakespeare occurs no more frequently than would have happened by chance. Shakespeare ‘might as well have pulled his words out of a hat.’ Clearly Shakespeare chose his words very deliberately. He didn’t appear fond of alliteration – he was fond of it. Alliteration may well occur in his works at the same frequency as it would have at random, but it hardly needs saying that Shakespeare’s placing of alliteration, not to mention his careful use of many other figures of speech, is about as far from random as you can get.

These two irritating and inappropriate examples, although only a small part of the book, detract from what is otherwise a very successful and entertaining attempt to explain unlikely events, our often irrational responses, and the chances of said events happening to you or me. I recommend The Improbability Principle, but I recommend pairing it with The Elements of Eloquence by Mark Forsyth to counter any doubts you might have about the randomness or otherwise of figures of speech, and a decent sports psychology text (such as D J Collins, ed., Performance Psychology: A practitioner’s guide) if you need convincing that sporting success and winning streaks have anything to do with chance.

Acknowledgement: The review copy of The Improbability Principle was provided by Scoop Review of Books.