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’ was the headline for the Daily Express on Thursday. If that phenomenon was really so unlikely, then since there are fewer than a million births a year in the UK, this would genuinely be a very rare event.
The Express’s number is calculated as 365 × 365 × 365 = 48,627,125. But in fact it’s out by an order of magnitude. One in 50 million would be the odds against someone having three siblings who share one particular prespecified birth date, which the editors of the Daily Express had sealed in an envelope and given to a lawyer fifty years ago. In reality there is no constraint on which day the first baby gets born on, so after that, we’re just interested in the odds of two more babies sharing that same birthday, which are 365 × 365 = 133,225 to one. And those odds might even be a bit lower: if you two feel friskier in winter, for example, your babies might tend to be born in the autumn.
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 Office for National Statistics (ONS) Statistical Bulletin ‘Who is Having Babies’, 14 per cent of these were third births, and another 9 per cent 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. All of which means that on average – since the odds of three shared birthdays is about 133,225 to one, and there are 167,000 third births a year in England – this specific birthday coincidence will occur about once or twice a year in the UK. To be written about in the Express it would also need to be a birth within a marriage, which gives us 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 twenty-three people, there is a 50 per cent 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, then 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 twelve hours, which would be if my dog trod on the trigger of 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.