December 12, 2005

Probability neglect

Nice term in one of the Sunday papers: probability neglect, the tendency to consider the consequences of something happening, but not the probability. So fear of child abduction, for example, is much more pronounced than it was thirty years ago, even though the risk hasn’t changed in that time. People are much more worried about things which are very unlikely to happen, but which would be dreadful if they did, than things which are relatively common but less serious.

But why does probability neglect happen? It’s partly a psychological thing; imagining something happening and how we would feel about it is easy, natural, intuitive, but thinking about probability is difficult, mathematical, unfamiliar. And it’s also partly a media problem; we have much more news reporting now than we did, say, thirty years ago. There were no 24 hour news channels then, only a small number of TV channels, and no internet. The news machine is voracious, and so when there is an accident or a disaster or any sort of human tragedy, it is reported and analysed endlessly. This makes us think that events which are actually very rare happen frequently, and perversely, events which are relatively common are under-reported precisely because they’re not news.

As an exercise in trying to make myself think about probability, I went and found some statistics relating to the riskiness of different modes of travel. Before you read on, what’s the safest way to travel? How much safer do you think it is to travel by car than to walk? A bit? A lot? Is a train safer than a plane?

The best numbers I could find were fatalities per billion passenger kilometres for 1999, and they look like this:-

Mode of transport Deaths per billion passenger km
Air 0.02
Boat 0.3
Rail 0.9
Car 2.8
Pedal cycle 41
Pedestrian 49
Motor cycle 112

(It was a bad year for rail fatalities because of the Ladbroke Grove crash which killed more than thirty people; rail fatalities are normally less than half this figure.)

The trouble is, if you worry irrationally about things, then rational argument is by definition unlikely to change your mind. If you’re a parent, it’s extremely difficult to think probabilistically about your children; if you sleep with a baseball bat by your bed for reassurance, you’re not going to be swayed by figures showing that burglary is in decline. The best we can hope for, I think, is to understand that we’re often irrational and try to remember that now and again.

*Update 13th Dec*: I’ve since discovered this fascinating list of the odds of dying of just about anything (PDF) which reassures me that there are at least some things which are both unlikely and largely ignored. My odds of dying by being confined to or trapped in a low-oxygen environment, for example, are vanishingly small, and as if that weren’t good news enough, I hardly ever worry about it!

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  1. For various reasons, deaths per billion passenger km is not necessarily the most useful statistic to look at. In fact, it's quite a weird statistic. I certainly wouldn't conclude that walking is less safe than driving because the number of km people drive is much higher than the number people walk. Comparing the driving / motorcycle / train stats is probably fair, comparing the cycle / walk stats is probably fair, but the other comparisons are meaningless. How about comparing based on the probability of death per hour of walking / driving / etc. Or the probability of death on any given driving / walking trip. And so on.

    But I agree with your general point that people don't understand risk. I remember the day after the London bombing arguing with someone that it would probably be much safer for them to take the tube even if they knew there was going to be another bombing at some point in that week than it would be for them to drive instead.

    13 Dec 2005, 01:28

  2. Mathew Mannion

    You could also argue that deaths per hour would be a misleading statistic as well – because the air deaths would probably shoot up on a massive scale, probably overtaking rail I'd imagine, and the slower ones would be taken down, so it'd imply that it's safer to walk or cycle, which is probably inaccurate. If you walked a billion kilometres then you're far more likely to die than driving a billion kilometres

    13 Dec 2005, 09:42

  3. Chris May

    if you walked a billion kilometres then you're far more likely to die than driving a billion kilometres

    Of old age, I expect :-)

    13 Dec 2005, 11:58

  4. Mathew Mannion

    In fairness, that would probably polute the statistics… It'd have to be a fair test…

    13 Dec 2005, 12:17

  5. This whole irrational fear of flying really bugs me as well, I just don't get it. For the sake of comparison, here are the figures for deaths per billion hours of travel (I've made assumptions about the speed of travel for each mode of transport)

    • Boat: 15
    • Air: 20
    • Rail: 108
    • Car: 280
    • Pedestrian: 294
    • Pedal cycle: 1230
    • Motor cycle: 11200

    I could well have worked this out incorrectly, but I think it is about right.

    13 Dec 2005, 15:36

  6. A more useful statistic would be to multiply the deaths ppkm by number of kilometres travelled in a typical year, and dividing by 1 billion. Then you've got the relative probability of being killed while doing any of these activities in a typical year, although the numbers would (I think?) bear no mathematical relationship to the actual probability.

    13 Dec 2005, 16:16

  7. I am slightly appalled by the NSC list. Good to see no radiation deaths in 2002 but the odds of dying from hot tap water versus venomous spider are interesting!

    13 Dec 2005, 16:18

  8. Mathew Mannion

    Am I right in reading those extra statistics in thinking that there's a 229–1 chance of dying in the US from falling to your doom in your lifetime? Scary.

    13 Dec 2005, 16:34

  9. The motorcycle stats do of course include:

    1. retarded 40 year old car drivers who buy 200mph superbikes and kill themselves on the first corner (that actually happens very often, the biggest cause of bike accidents is simply not going round a corner properly due to excess speed and a lack of skill);
    2. riders of weezy powerless defenceless scooters, with only the absolute minimum of training;
    3. chavs on stolen trail bikes;
    4. people who get hit by random motorway rubble in Barcelona (there's simply no excuse for that kind of stupidity).

    14 Dec 2005, 15:59

  10. Air and space transport accidents: 5,704–1
    Intentional self-harm by firearm: 218–1

    Don't worry about dieing in a plane crash, you're 25 times more likely to shoot yourself in the head, and as they don't allow guns on planes, I think you'll be pretty safe

    14 Dec 2005, 16:07

  11. Mathew Mannion

    Surely the far more scary statistic is that 1 in 115 people will kill themselves, and 1 in 35 will be involved in some kind of accident?

    14 Dec 2005, 16:14

  12. Matthew Sperrin

    Of course, the main thing that makes these statistics meaningless is they're all just averages. I'd say my chance of dying by shooting myself is fairly close to zero, whereas I imagine it would be somewhat higher for a manic depressive soldier…

    22 Dec 2005, 18:29

  13. Colin denRonden

    I have stats for road deaths per 100 million vehicle kms travelled in Great Britain in 2000 as being 0.7. Anyway, all this depends on the significance of what you’re measuring. If you’re God its absolute number of deaths. If you’re an underdeveloped country with few cars or roads its deaths per number of vehicles or km of roads. For testing efficiency of government measures in developed countries its deaths per km travelled.

    04 Dec 2007, 01:28

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