According to David J. Hand, author of the engaging The Improbability Principle, there are five strands contributing to the Improbability Principle: the Law of Inevitability, the Law of Truly Large Numbers, the Law of Selection, the Law of the Probability Lever and the Law of Near Enough. The Improbability Principle, Hand succinctly, is: Extremely improbable events are commonplace. In 1866, the British mathematician Augustus De Morgan wrote, “Whatever can happen will happen if we make trials enough.” Hand summarizes this as: Someone, somewhere, at some time won a lottery twice, and he provides several examples, along with an account of a man who survived seven strikes by lightning. Perhaps, though, this is not quite amazing; Roy Sullivan, a park ranger in Virginia, no doubt spent a great deal of time outside in all kinds of weather.
No doubt most people have experienced what we like to call amazing coincidences. The first chapter chronicles a series of such of events involving the actor Anthony Hopkins and the George Feifer novel The Girl From Petrovka. Something less amazing, but nevertheless an odd coincidence, occurred when I started reading chapter 2. Hand quotes a verse from the book of Proverbs: “The lot is cast into the lap, but its every decision is from the Lord” — a passage I had read the evening before.
Basically, probabilities and chance are counterintuitive. We tend to underestimate high probabilities and overestimate low ones. The birthday problem is a delightful example of this. What is the lowest number of people who must be in the same room to make it likelier than not that at least two of them have the same birthday (day and month, not year)? The answer is a surprisingly small 23.
There are also other underlying principles at work. We tend to ignore evidence that does not support our theories (and indeed, our political views), emphasizing only that which does. We can also cherry-pick our data. Painting bull’s-eyes around arrows you shot into a door would qualify as selection bias.
As Hand writes, “The Improbability Principle tells us that events which we regard as highly improbable occur because we got things wrong. If we can find out where we went wrong, then the improbable will become probable.” I am reminded of the story of two gentlemen in a Dublin pub drinking to the amazing coincidences that keep piling up as they recount their early lives. When another patron asks what’s going on, the bartender points out that the O’Reilly twins are getting drunk again.
If you wish to read about how probability theory can help us understand the apparent hot hand in a basketball game, superstitions in gambling and sports, prophecies, parapsychology and the paranormal, holes in one and multiple lottery winners, you will enjoy this book. The statistician Samuel S. Wilks (paraphrasing H.G. Wells) said that “statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” With that laudable goal in mind, The Improbability Principle should be (in all probability) required reading for us all.
John A. Adam reviewed this book for the Washington Post.