Ben Goldacre, The Guardian, Saturday 13 February 2010
Often one data point isn’t enough to spot a pattern, or even to say that an event is interesting and exceptional, because numbers are all about context and constraints. At one end there are the simple examples. “Mum beats odds of 50 million-to-one to have 3 babies on same date” is the headline for the Daily Express on Thursday. If that phenomenon was really so unlikely, then since there are less than a million births a year in the UK, this would genuinely be a very rare event.
Their number is calculated as 365 x 365 x 365 = 48,627,125. But in reality, of course, it’s out by an order of magnitude: one in 50 million are the odds of someone having 3 siblings sharing one particular prespecified birth date that the editors of the Daily Express sealed in an envelope and gave to a lawyer 50 years ago. In reality there is no constraint on which day the first baby gets born on, so after that, the odds of two more babies sharing that birthday are 365×365=133,225. And they might even be a bit lower, if you two feel friskier in winter and have more babies in the autumn, for example.
Then there is the context. Living on your street, hanging out with the people from work, it’s easy to miss the sheer scale of humanity on the planet. In England and Wales there were 725,440 births last year. From the ONS Statistical Bulletin “Who is having babies” 14% were third births, and another 9% were fourth or subsequent births. So there are 102,000 third children born a year, 167,000 third or more-th children, and if we include the rest of the Kingdom there are even more, so on average, three shared birthdays will happen once or twice a year in the UK (although to be written about in the Express it would need to be a birth within a marriage, making 55,000 chances a year, or once every two years)
When you forget about numerical constraints, all kinds of things can start to look spooky: in a group of 23 people, there is a 50% chance that two of them will share a birthday, because any pair of birthdays on any date is acceptable. When you forget about numerical context things can look weird too: if Uri Geller gets a nation in front of the telly to tap their broken watches against the screen, and ring the call centre if the watch starts ticking again, with viewing figures of a few million, there will be more excited calls than the switchboard can handle.
If you turned to your friend and said: “you know, a lot of funny things have happened to me, quite unexpectedly, over the course of a lifetime, but let me take a moment to specify right now the one thing that would seriously freak me out, over the next 12 hours, which would be if my dog trod on the trigger to my gun, and accidentally shot me in the face”, and then your dog shot you in the calf, that would be weird. So “Dog Shoots Man” was a big story in America this week, to the delight of headline writers. But here’s “Dog Shoots Man In The Back” from Memphis in 2007, another in Iowa only two months later, and my own personal favourite: “Puppy shoots man: dog put paw on gun’s trigger as owner tried to kill him”.
Guns don’t kill people, puppies do. The world is a really big place.