Guns don’t kill people, puppies do

February 13th, 2010 by Ben Goldacre in bad science, evidence, numerical context, statistics | 65 Comments »

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.

If you like what I do, and you want me to do more, you can: buy my books Bad Science and Bad Pharma, give them to your friends, put them on your reading list, employ me to do a talk, or tweet this article to your friends. Thanks! ++++++++++++++++++++++++++++++++++++++++++

65 Responses

  1. Francis Xavier Holden said,

    February 17, 2010 at 4:21 am

    My wife has the same birthday as Mick Jagger although she is much younger. She thinks it is a spooky omen.

    But Mr SnootyPants Jagger thinks he is above it all and despite her many emails, letters and presents over the years he still refuses to acknowledge her and make a date for dinner..

    Can’t he see the odds?

  2. bluecat said,

    February 17, 2010 at 7:57 am

    My parents had their first three children at 18-month-less-2-days intervals. I thought it was an amazing coincidence until I realised the relationship between our births, the timings of school holidays and half terms, and my father’s career as a teacher.
    My partner has four children. The second was born on the second of the month, the third on the third, and the fourth on the fourth. Unfortunately the eldest messed up this extraordinary and significant conjunction and prevented them getting their pictures in the paper by being born on the 4th of July.
    Incidentally, anyone born on Christmas Day or Boxing Day may have been an April Fool’s joke…

  3. Jazz said,

    February 17, 2010 at 5:28 pm

    I think what would be more interesting is if there was a day in the year where no one was born, ever, except for one single human being
    “PERSON SHARES BIRTHDAY WITH NO ONE!” the headline will read. Actually even that sounds boring!

  4. milttina said,

    February 17, 2010 at 7:41 pm

    @Bluecat – And many people born in Feb. are prom babies.

  5. postmodernslavepoet said,

    February 18, 2010 at 7:56 am

    I couldn’t help noticing that Andy_Ward’s comment about the coincidence of 11s reported in the Sun was, spookily enough, comment number 11.

    11 is of course a most mystical and lucky number. Some older people amongst you may remember that the nations involved in the Great War all stopped fighting at the 11th hour of the 11th day of the 11th month. Wikipedia says this happened in 1918 but they probably got it wrong and it must have happened in 1911. Surely this was the coincidence to end all coincidences.

    Further proof about the power of 11, (should any further proof really be needed), comes from a woman I know who has 11 children all born on the same date in successive years. Mind you, by trade, her husband was a master precision grinder.

  6. toni49 said,

    February 19, 2010 at 11:53 am

    An uncle of mine had a habit of pointing out what he termed 50:50:90 events – ones that statistically were 50:50 chance, but he noticed that they happened 90% of the time (needless to say these were always unwanted events). When I suggested that if they happened that often, surely in was the 50:50:10 events that are worth pointing out, it took him less than a week to conceed that he doesn’t “always” pick the slowest queue in the supermarket!

  7. Andy_Ward said,

    February 20, 2010 at 1:18 pm

    lol, I didn’t notice it was comment 11

  8. Beanzy said,

    February 22, 2010 at 1:58 pm

    My mum, older brother and younger brother share the same birthday. We never thought it was more than 1 in 365 chance as they all had to be born on some day of the year and one day’s as good as the next. Surely it’s just that the random occurrence of three in one group happening just happened to our particular group?

  9. dropoutboogie said,

    February 22, 2010 at 3:22 pm

    I used to think it was incredible that I had two best friends with my birthay, as well as knowing several other people that shared the date, until upon meeting yet another person born on the same day of the year, he pointed out to me that our birthday was almost exactly 9 months after valentine’s day. I’ve never looked at my parents the same way.

  10. Shn said,

    February 22, 2010 at 7:36 pm

    My brother and I were not just born on a shared day of the year, but also the exact same birth date! Can your precious science explain THAT, eh?

  11. Martin said,

    February 23, 2010 at 1:37 am

    Dropoutboogie, sharing (or having similar) birthdays with friends isn’t that unlikely. With pre-natal and post-natal support groups there are often groups of children born close to each other.

    Even without that, once at school children with similar birthdays may stick together as, within a single year group, the children born in August will be almost a full year younger than children born in September. The September/ October kids will be that much bigger.

  12. johnnye87 said,

    February 23, 2010 at 7:33 pm

    The idea of buying a lottery ticket to cash in on a stroke of luck reminds me of a Jasper Fforde comic novel where the heroine used a jar of mixed grains as an early warning system for a baddie with entropy-manipulation powers – if they sort themselves into improbable patterns, watch out.

    …it’s better than it sounds, honest.

  13. adamb said,

    March 1, 2010 at 6:46 pm

    Our daughter was born on the same day (21st August, a truly auspicious day) as my wife and I were married. Ok it was by C-section but of course it is still an utterly tremendous coincidence (no-one need know it wasn’t a natural birth). It doesn’t end there… parents were married on that same day too!! And – gosh this is truly unbelieveable….the series of coincidences…..!! my father’s parents were married on that exact same date! According to the Daily Mirror, this is a one-in-almost 18 billion chance event!!

  14. martinz said,

    March 6, 2010 at 5:49 pm

    The glaring error is the factor of 365. The likelihood of clustering is hard to quantify, but could be very big: suppose you read ‘Outliers’ and were successful in planning to have kids in the couple of months pre school admissions? Could easily be a factor of >10.

    However did anyone spot the other obvious simple mathematical error, even assuming independence? The woman in question actually has *four* kids. So the probability in increased by another factor of four (4 ways of choosing 3 from 4). So we are down from 1 in 50 million to about 1 in 34,000.

  15. NickCooper625 said,

    March 16, 2010 at 5:57 pm

    My wife’s sister has the same birthday as my mother. Two of my brothers have birthdays on consecutive days (close enough?!).

    I was born on 21 September 1966. In my youth, it was only after I had already developed an interest in the works of H.G. Wells that I discovered that he was born on 21 September 1866. I do not, of course, claim reincarnation….