Our Non-ability to Misunderstand Statistics of Rare Events

Posted to Statistics  |  Nathan Yau

The DiceCory Doctorow from The Guardian writes about our inability to understand the statistics of rare events. We obsess so much over the near-impossible probability that something could happen that it clouds our vision of more probable events.

The rare – and the lurid – loom large in our imagination, and it’s to our great detriment when it comes to our safety and security. As a new father, I’m understandably worried about the idea of my child falling victim to some nefarious predator Out There, waiting to break in and take my child away. There’s a part of me who understands the panicked parent who rings 999 when he sees some street photographer aiming a lens at a kids’ playground.

But the fact is that attacks by strangers are so rare as to be practically nonexistent. If your child is assaulted, the perpetrator is almost certainly a relative (most likely a parent). If not a relative, then a close family friend. If not a close family friend, then a trusted authority figure.

Says Doctorow, such misunderstanding is why we gamble in casinos and why we have to wait in long security lines at the airport. We see piles of money and terrorist attacks when ultimately, the chances that you’ll win a jackpot or pass over violence is much less likely – near impossible – compared to losing all of your money and losing valuables to a curious luggage handler.

If there’s one thing the government and our educational institutions could do to keep us safer, it’s this: teach us how statistics works.

Amen to that.

[Thanks, Jan]

8 Comments

  • Getting into Black Swan territory. Currently reading the book, and sheds light on the casino issue in a bit more detail – well worth it.

    It does make you reconsider the use of visualization as a “this is how it is and will be” tool of analysis and prediction. But then again, it’s pretty difficult to account for those rare events.

  • the opinions expressed in the article would only be valid in a theoretical world.

    let’s adress 3 paradoxes he mentions: a guy going to Vegas thinking he can win big, a parent who panicks at the slightest menace to their child, and the paradox of a false positive where a test that work 99% of the time to detect a condition that happens once on a million cases actually gives misleading results 9999 times on 10000.

    guy goes to vegas:
    mathematically, if one plays indefinitely they will lose an infinite amount of money. but this can’t happen as one’s lifespan and resources are limited. on the other hand if one wins big, which has admittedly very small chances of happening, they could get more money than they ever could earn in a lifetime. and until they actually spend their betting money, they enjoy the hope of winning which has a non-null value.
    In other words: you spend a limited amount of money, which you accept to lose, and you get a chance to win an unrelatedly high amount of money. Is that such a bad deal? If one had an infinite amount of time and money at their disposal, then gambling could only yield negative results, but such is not the case.

    For the panicking parent, the same reasoning apply in the opposite direction. Losing a child has an infinite cost, even though it has a low chance of occuring (unfortunately higher than winning at the lottery but still), while taking all possible precautions has a non-null cost. while such precautions could seem excessive and unjustified, they make sense in the face of the unbearable possiblity of letting your child be harmed. Again if one felt comfortable with the idea of putting a price tag on a child’s life, there could be a treshold where it would be rational to stop. That’s the difference between the real world and a hypothetic model.

    finally the example he gave is not too convincing. it is inaccurate to say that this test gives erroneous results 9999 times out of 10000; because it also gives correct results for 990000 people…

    I’m a mathematician that gambles now and again. and loses more often than not. but that’s ok

  • Doctrow writes “In other words, in the effort to find the terrorist needles in our haystacks, we’re just making much bigger haystacks.”

    Sounds to me like its Doctrow who needs to learn how statistics works. Data mining or any other diagnostic procedure allow us to calculate a posterior probability of an event which may be much higher than the prior probability, suggesting whether or not we should investigate further–we may have a much SMALLER haystack.

    As one statistician said about our detractors: “There are liars, outliers, and out-and-out liars.” And lots of folks who should have taken TWO semesters of statistics, and passed with better than a C.

  • As an economist and political scientist, I would add one thing:

    Maybe we gambling because what we care is not about the expected value, since we receive more “utility” to high gain than to middle or low gain. So, we indeed are rational people, even if we gamble. In other words, even knowing statistics, I can gamble and being a rational man.
    That’s what we’ve learned a long time ago with St. Petersburg Paradox, isn’t it?

  • As Jerome points out, the potential for infinite loss, as with a child, destroys the theoretical argument. Also, as Ishikawa warned us: always suspect the data. In the case of danger to children, catastrophic data and ‘skinned-knee’ data have been lumped together for the benefit of groups advocating one thing or another. Accepting this egregious distortion as a foundation for argument calls the whole point of the article into question. One suspects it was written by a childless person.

  • I definitely wasn’t expecting this. It’s like our very own statistics lesson going on here. Nice. Thanks everyone for taking the time to teach about bringing the real world into theories!

  • We gamble because it’s a controlled format for taking risk which is necessary for some people to feel that they are living a complete life. In a world where our risks are being increasingly mitigated, partaking in the minor (to most people) risk of losing some money adds missing adrenaline to a lot of people’s lives.
    Personally, when I gamble (which is not very often), I figure out how much I can lose and try to make that last as long as possible while having fun and then compare that cost to other forms of entertainment (movies, concerts, vacations, etc…). If you’re savvy, you can entertain yourself with gambling much more effectively than through other means.
    Airbags anyone?

  • Thomas –

    The few times I’ve been gambling, I’ve invested a few bucks in a roll of coins, and budgeted that to last the time I planned to spend before gorging on the $4.99 buffet. $10 of quarters gives you a lot of sensory overload, with the lights, bells, sirens, and coins spilling into the loose metal cup. My lastgambling escapade was over ten years ago. I travel to Atlantic City every year for a conference, and haven’t felt the need to gamble since the time in Tahoe where I lost, let’s see, $20 between my wife and me.

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