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.
.


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65 Responses



  1. ffutures said,

    February 13, 2010 at 1:04 am

    I have the same birthday as my niece’s husband. My nephew and one of my grand-nephews have the same birthday. I can’t produce a three times coincidence, but there are only 365.25 days in the year, none of this stuff should be surprising.

  2. annoyingmouse said,

    February 13, 2010 at 1:16 am

    My mum and sister have the same birthday. Funnily enough that’s typically less about the statistics of coincidence and more about the doubling of the gift costs!

  3. MrNick said,

    February 13, 2010 at 2:24 am

    Most people don’t realise that because so many things happen all the time that there are bound to be extraordinary coincidences just in the normal course of things.

    My father who was in the Polish army was wounded on the first day of the German attack on 1st September 1939. Years later he visited the spot and got into conversation with a German who was there. Comparing experiences thay came to the conclusion that the German had probably shot my father all those years before.

    Unusual? Yes. Significant? No.

    Nick

  4. Andy Graham said,

    February 13, 2010 at 7:22 am

    I’m God, and so is my dad. We’ve always thought that was quite a coincidence.

  5. twistor59 said,

    February 13, 2010 at 8:01 am

    Andy Graham: Are you Jesus ? And do you have a wispy friend called Casper ?

  6. natsils24 said,

    February 13, 2010 at 9:18 am

    I share my birthday with my older cousin and my younger 2nd cousin. I just thought it was unfortunate that my 21st was ruined by the birth of my baby cousin! I really don’t understand why newspapers love these stories so much, does it actually mean anything in real life, 3 children sharing a birthday? I think not. If you look hard enough for a cool spooky pattern…well you might just find one and write a story in the Express!

  7. dkbnz said,

    February 13, 2010 at 9:33 am

    “it’s out by an order of magnitude”

    I understand why you said this (they used three terms where they should have used two) but strictly it’s out by two and a half orders of magnitude (log 365 = 2.566…).

  8. mus said,

    February 13, 2010 at 9:57 am

    what dkbnz said.

  9. Mark Baker said,

    February 13, 2010 at 10:06 am

    What, doesn’t everyone count in base 10? (er, that would be 365 for those of you using base ten)

  10. Dr Jim said,

    February 13, 2010 at 10:16 am

    What a coincidence that you should be talking about birthdays when today is my sister’s birthday, my step-mother’s and my first cousin’s.

    Off to buy a lottery ticket.

    Disclaimer: Actually, no, I’m not really off to buy a lottery ticket, and I deplore anyone who says to get one when a stroke of luck happens; while I note the coincidence, I don’t actually believe there is anything cosmic in it.

  11. Andy_Ward said,

    February 13, 2010 at 10:22 am

    Quite a while back, I remember The Sun running a story about roulette. Someone decided to walk into a casino at 11pm on the 11th of the month and put £11 on number 11. It won, leading The Sun’s lottery correspondent to announce that that odds against this were “millions to one”.

  12. Dorm said,

    February 13, 2010 at 10:43 am

    With regards to winning the lottery, a good way of explaining the odds to people is to get them to pick a number between 1 and 14 million. Then get someone else to do the same. The chance that these numbers are the same is the same chance of winning the lottery.
    (not strictly true as humans are not perfect random number generators, but it gets the point across)

  13. md1364 said,

    February 13, 2010 at 10:57 am

    Regarding luck and the lottery, to buy a ticket after something lucky has happened could be seen as bolting the stable door after the event. Better to foresee the luck coming and buy the ticket when one feels lucky, that could be problematic if, for example, the luck you had coming was to be narrowly avoid being hit by falling masonry which lucky event you traded for a win (which could be only 4 numbers therefore £8.63) and died the same day by being struck by that lump of concrete.
    Maybe I have too much time on my hands!

  14. TrubbaNot said,

    February 13, 2010 at 11:10 am

    “Everyone I meet is stunned when I tell them three of my kids were born on the same day.”

    Which implies she has more than three children, so surely the probability that three of them share the same birthday is higher than 1 in 365×365?

  15. dvavasour said,

    February 13, 2010 at 11:17 am

    Given the amount of money the lottery distributes for good causes, surely it would be a huge disservice to educate the GBP on small probabilities?

  16. Maybug said,

    February 13, 2010 at 11:24 am

    My brother and I were due on the same date, though he was premature so we don’t share a birthday.

    Distressingly we worked out that this was nine months after my Dad’s birthday, and now we can never un-work it out.

  17. wijjy said,

    February 13, 2010 at 11:28 am

    If you want a real coincidence try the Bulgarian lottery, the same numbers drawn on two consecutive weeks.

    news.bbc.co.uk/1/hi/8259801.stm

  18. SelphieB said,

    February 13, 2010 at 11:45 am

    Re the lottery, I tell people to pick numbers 1,2,3,4…etc, for however many numbers they have to choose. The reaction is that those numbers will never win, but of course they have the same probability as any other combination.

  19. daniel said,

    February 13, 2010 at 12:17 pm

    SelphieB: the problem with that advice is, given the large likelihood that several other people are following the same logic, their win would be significantly lower than if they selected numbers using some other arbitrary process…

  20. SteveGJ said,

    February 13, 2010 at 12:38 pm

    Some trite article in the Express on a matter of no importance whatsoever is one thing. The really, really worrying thing is when this sort of misunderstanding of statistics hits the court system.

    This type of mistake was made over the conviction of Sally Clark (who died in 2007) when Sir Roy Meadows stated in court that the odds of odds against two cot deaths occurring in the same family was 73,000,000:1. This was making the observation that in affluent, non-smoking households the odds of any one child dying of cot death was about 8,500:1. Of course if you’ve already had one cot death in the family, then the odds of the next one would have been 8,500:1. Only if Sally Clark’s name had been picked in advance would the odds have been 73,000,000:1. If there were 5 million such two-child families in the UK then there is a small, but still significant, chance that one may have suffered the cot deaths of both children. Then, of course, there is the assumption that the events are completely random and that there are no factors such as genetics, environment or lifestyle that were involved. Of course he had already accepted that this could be a factor, albeit at a rather broad level, by using the odds of a cot death among a particular afluent sub-group of the population. Something which allowed him to produce this inflated 73,000,000:1 figure.

    The strange thing is that, in the case of Sally Clarke, the defense’s expert witnesses had made all these points and the verdict of the jury appears still have to be swayed, at least in part, by this 73,000,000:1 claim. Unfortunately due to this country’s ridiculous laws on prohibiting research into how juries come to their verdicts (not even allowed anonymously), then we cannot know what the deciding factors were. At least with non-jury triels a judge has to provide a reasoned statement for the decision.

    Any peer-review of this evidence by any half-qualified statistician would have instantly brought to light these issues. Unfortunately, due to the confrontational nature of our criminal system, and the treatment of expert evidence as either for the prosecutions or against, then the jury is often left with gauging the relative credibility of the witnesses, and not the evidence itself. This then becomes justice as drama, not justice by reasoning.

    The Sally Clarke case is by no means the only example. Ben himself has highlighted cases where convictions have been gained when somebody has been unlucky enough to have been associated with events which are statistically very unlikely for any one individual, yet almost inevitable over a large enough population. (That’s without the sub-group problem – it’s possibly to construct endless statistically unlikely, yet still possible scenarios, and inevitably some of those will occur).

  21. kkbundy said,

    February 13, 2010 at 1:31 pm

    This happens all the time. People are forever assigning unnatural importance to the smallest of coincidences. It’s the basis of religion. My mother, born again and loving it, constantly finds proofs in the miracles of god. If she has prayed for someone in the hospital and that person recovers, god healed them. No doubts about it. Our family has had several deaths lately, but those were all gods plan, even the ones where a relatively young person suffered greatly and died after nearly recovering. God wanted it that way. God needed that man in heaven. Why? Was he building a deck? But let some one’s sore ankle turn out not to be broken and it’s her prayers that did it. Praise Jesus

    To further the battle against this type of superstition, I’ve started an Atheist Bible study at blessedatheist.com/. With it I am trying to point out the complete absurdity of a literal bible interpretation using as much humor as I can. I figure that I can best fight their young earth creationism and other bad science by crawling inside their world and poking it with sticks. And let me tell you, I’m having a great time. That book is hilarious!

    Anyway, if you read the bible, you see that many of the stories in it contain this same element of random chance being taken as divine interference. Jacob on the way to another town states that if he survives this journey safely he will believe in Yahweh forever. That’s all it takes? I demand better proof. But humans seem hardwired for this mystical belief. We are pattern recognition machines, and we are going to pick out patterns, even if they are not there.

  22. matthewoconnor said,

    February 13, 2010 at 2:42 pm

    My parents share a birthday in February. Me and my sister were born on the same day in November. You do the (disgusting) maths.

  23. Jeesh42 said,

    February 13, 2010 at 2:53 pm

    @wijjy, there’s no such thing as a “real coincidence”. And the Bulgarian lottery thing is a lot less *special* than you might think at first: blog.revolution-computing.com/2009/09/a-coincidence-occurred-film-at-11.html

  24. Jeesh42 said,

    February 13, 2010 at 2:57 pm

    @SelphieB, in fact (over a period of several zillion years) the numbers 44-49 are going to get you more money. As someone else pointed out, people are not good random number generators and tend to go for lower numbers in the lottery. Therefore, if 1-6 came up, chances are you would have to share your winnings with more people, so less for you.

  25. Mijin said,

    February 13, 2010 at 4:58 pm

    Another thing is of course that the mother is aware of the other sibling’s birth dates, and this awareness may have some effect on when she goes into labour, shortening the odds further.

  26. walks with tench said,

    February 13, 2010 at 6:58 pm

    And another thing of course is that her old fella might only get lucky on his birthday; ie once a year,and on the same night (like it or not!). Thats gonna shorten the odds a bit.

  27. ignoranceisalearnedbehavior said,

    February 13, 2010 at 7:18 pm

    I’m so glad that the writer is the health correspondent for The Express.

  28. matthewoconnor said,

    February 13, 2010 at 7:38 pm

    walks with tench: may I refer you to post number 22.

  29. walks with tench said,

    February 13, 2010 at 8:15 pm

    ah!

  30. toumai said,

    February 13, 2010 at 9:47 pm

    I was born on my father’s birthday. Both my children were due around the same time of year. People kept saying, “Wouldn’t it be lovely if they shared your birthday?” I kept replying, “I can think of things I’d rather be doing on my birthday.”

  31. iamjohn said,

    February 13, 2010 at 10:59 pm

    This has nothing to do with birthdays. However, I just saw on QI a debate about the optimum amount of alcohol. Fry said between 21 and 30 units because that range lived the longest, but curly-haired Alan said that statistic could have been skewed by associated life-style factors. Hoorah for Alan, but he was then shot down and dismissed. I will forgive Steven this once.

  32. iamjohn said,

    February 13, 2010 at 11:22 pm

    Sorry, I meant to say 21 to 30 units per week, and I also meant Stephen, not Steven. Otherwise I meant what I said.

  33. andy22 said,

    February 14, 2010 at 8:52 am

    What if the mother has sex on the same day each year for three years. She is highly likely to have the baby on the same day of the year each year.

  34. plonk said,

    February 14, 2010 at 9:03 am

    I was thrilled when I found out that I share the birthday of Richard Dawkins. I was happy for a second until I realised it has no meaning at all. But since Keira Knightley has the same birthday, there has to be some magic in it! Maybe we are soulmates… with Keira, that is.

  35. DanielDWilliam said,

    February 15, 2010 at 10:34 am

    I have two brothers who have exactly the same birthday as each other AND three Uni mates who have exactly the same birthday as each, exactly one week after mine.

    What are the chance of three people who know each other being born on the exactly the same day?!? Exactly a week after someone who has two brothers who were born on exactly the same day?!?

    My mother and sister’s birthdays are exactly a week apart.

    My best mate and I often get drunk together at exactly the same time as our partners.

    If any one would like to buy my lottery ticket from me for £100,000 I’m happy to sell it to them. I personally guarantee it. It’s a winner.

  36. neuro_chelle said,

    February 15, 2010 at 11:34 am

    Wow! What are the chances I would be reading this today, when yesterday was my own birthday!

    Those coincidences just keep coming…

    ;)

  37. neuro_chelle said,

    February 15, 2010 at 11:46 am

    Did I mention that my mum and stepdad share the same birthday? And 2 of my 3 best friends from school shared a birthday – which is also my brother-in-law’s birthday? Ahhhh stop it, this is all too spooky!!

  38. neuro_chelle said,

    February 15, 2010 at 11:54 am

    Ah, sorry to post a third time but just thought of something else! In follow-up to SteveGJ’s post, a member of my family almost had his children taken off him (permanently and irreversibly) by social services, purely due to a statistic. Shockingly, the stat was that a head injury his youngest had suffered was of a type that carried a 1:100 chance of NOT being due to child abuse. ONE IN A F**KING HUNDRED!!!! I couldn’t believe it. It was only after observing him with his kids in his own home for a month that they realised he wasn’t hurting them. I’m no longer a big fan of the child protection procedures in this country, needless to say. Absolutely shocking.

  39. MostlySunny said,

    February 15, 2010 at 2:36 pm

    my friend and her brother share the same birthday – her mum likes to remark “I am a girl of regular habits” – heh

  40. milttina said,

    February 15, 2010 at 4:53 pm

    My friend’s husband and I share the same birthday and our mothers shared a hospital room when we were born.

    I also share a birthday with Hitler. One more reason not to believe in astrology.

  41. richardelguru said,

    February 15, 2010 at 5:27 pm

    @ milttina. I’m afraid we’d have to know more about you and about your plans for the Sudetanland before we could accept that :-)

  42. jdc said,

    February 15, 2010 at 6:13 pm

    Re the stopping/starting watches coincidence: Richard Dawkins used this example in Unweaving The Rainbow. (He also used the example of the death of Richard Feynman’s wife and the clock that stopped when she died.) There’s a wee summary on ipedia.

    I noticed an interesting coincidence yesterday and, having noticed this one coincidence, I then seemed to notice more and more little coincidences – presumably I was just more aware of these minor coincidences due to having been thinking about coincidence. If I hadn’t picked up on the coincidence that was initially interesting, I doubt I’d have even noticed the others.

  43. Jeremy said,

    February 16, 2010 at 12:34 am

    I’m afraid having three children born on the same date doesn’t impress me much.

    I know a couple who have three children born on the same date … and in the same year, too!!

  44. Jake said,

    February 16, 2010 at 1:47 am

    Even the revised figure for the three births is not accurate, since that still assumes that the events are independent. That’s an untenable assumption. Consider that each of these conceptions could be occurring on the married couple’s anniversary night. That’s just a quick example; the point is that there are myriad potential reasons for these births to be occurring close together in time. Each day of the year does not have an equal chance of being a birthday, and there is good reason to suspect that this is reasonably constant across year/within a couple. In other words, there are a number of possible “third variables” which would violate independence.

  45. Jake said,

    February 16, 2010 at 2:33 am

    Looking back over the responses, it looks like a couple people already hinted at this. Oh well.

  46. thepoisongarden said,

    February 16, 2010 at 9:39 am

    The thing about lottery winnings which hasn’t been mentioned is that no one’s birthday falls on the 32nd of the month (or higher).

    As has been said, we’re rubbish at picking random numbers and many people just use ‘my birthday, Aunt Agatha’s birthday, the day the dog nearly ate the budgie’.

  47. huey said,

    February 16, 2010 at 11:50 am

    there was a story in the news recently about a woman who found 6 double yolks in a carton of eggs. this was described as odds of 1 in a trillion! leaving aside the fact that i instantly remembered finding 4 double yolks once, I went into m&s the next day, and found on the shelves “double yolk eggs” which you could buy, and yes they were all double yolkers. apparently young chickens lay larger eggs which more often than not have double yolks.

    daily mail fail www.dailymail.co.uk/news/article-1247872/Woman-finds-double-egg-yolks-box-beating-trillion-odds.html

  48. huey said,

    February 16, 2010 at 11:55 am

    found a picture. on the guardian website no less.

    image.guardian.co.uk/sys-images/Lifeandhealth/Pix/pictures/2010/02/02/double_yolk_eggs.jpg

  49. Johnnie said,

    February 16, 2010 at 1:36 pm

    Great article, but obviously just an excuse to get a Goldie Lookin Chain reference in. Which is fine.

  50. Dr Spouse said,

    February 16, 2010 at 3:12 pm

    Surely by the “rules” of luck, if you have three children born on the same date, you have had your luck for the year, and should avoid buying lottery tickets, and of course, walking under ladders, and spilling salt.

  51. 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?

  52. 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…

  53. 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!

  54. milttina said,

    February 17, 2010 at 7:41 pm

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

  55. 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.

  56. 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!

  57. Andy_Ward said,

    February 20, 2010 at 1:18 pm

    lol, I didn’t notice it was comment 11

  58. 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?

  59. 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.

  60. 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?

  61. 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.

  62. 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.

  63. 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…..my 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!!

  64. 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.

  65. 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….

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