How Are Sharks Less Dangerous than Vending Machines? An Exercise in Conditional Risk


Did you know that vending machines, not a major danger in most of our minds, are twice as likely to kill you as a shark? I heard this statistic at the new shark-and-ray touch tank of the New England Aquarium, which I try to visit weekly with my daughters. You stand at a large, shallow tank with plexiglass walls and can lay your hand in the water, gently feeling the sharks and sting rays swimming by.

The aquarium probably wants to convince visitors that sharks are not the fierce predators of Jaws fame, and thereby help protect sharks from hunting and extinction. Although I could admire this motive, the comparison always surprised me. My number sense complained that sharks simply must be more dangerous than vending machines.

However, upon looking up the risks, I found that the comparison was correct. The yearly risk (in the United States) of dying from a shark attack is roughly 1 in 250 million. In contrast, the yearly risk of dying from a vending machine accident is roughly 1 in 112 million. The vending machine is indeed roughly twice as lethal as the shark!

Why then was I still troubled by the comparison? Maybe my number sense needed a tune up, and I should just accept the statistical facts of life. I then started thinking about it using the method of easy cases. This method, along with proportional reasoning (the tool in this post about colonial-era literacy), is one of my favorite tools for developing what I like to call number-sight: the ability to see connections among (and make sense of) the myriad numbers around us.

The easiest case is often an extreme one. My own extreme case of shark-attack risk happened while teaching at the African Institute for Mathematical Sciences, in Cape Town, South Africa. The institute is right on the beach, so one day I tried learning to surf (with more emphasis on “try” than on “learn”). I soon heard whistles from the lifeguards. Because the water was packed with swimmers, I assumed that swimmers were going too far out. That’s what the whistles meant on the New Jersey beaches in my childhood. As an adult who knew how to swim, why worry? After returning to shore, I learned that the whistle was warning everyone of a great white shark that had been sighted swimming around the bay. It was probably the same shark that had bitten the leg off a surfer a few months earlier.

Don’t tell me that, while surfing in that bay on that day, a vending machine posed more danger to me than that great white shark! From this extreme case, I realized the problem with the comparison. These statistics are averaged over everyone in the United States. In most places in the U.S., such as Kansas, people are nowhere near a body of water with sharks. The comparison of the risk to a vending machine, while true as far as it goes, ignores highly relevant information—such as whether one is swimming in the same bay as a shark.

The comparison also ignores important information about vending machines. After all, how do people die from a vending machine? Vending machines are not known carcinogens. I imagine that the machine takes someone’s money and malfunctions. The customer then shakes it to free the snack, whereupon the machine tips over and crushes the hot-tempered purchaser. As the doctors say, “Don’t do that then!” Keeping cool in this difficult situation probably reduces the vending-machine death risk to zero.

This problem of implicit but essential statistical information is wonderfully illustrated in this XKCD cartoon:

(used under XKCD’s license)


Leave A Comment

Comments are moderated and generally will be posted if they are on-topic and not abusive.



View All Comments »
  1. BL1Y says:

    The really fascinating statistic is that 100% of people who try swimming with a vending machine die from drowning.

    Well-loved. Like or Dislike: Thumb up 148 Thumb down 9
    • Winner says:

      This is, remarkably, the same percentage chance you will die from shaking a shark for lost change.

      Well-loved. Like or Dislike: Thumb up 117 Thumb down 4
  2. Scott Templeman says:

    You can play with the numbers lots of ways, but there is no convincing way to make shark attacks as threatening as less sensationalist threats.
    The fact is sharks are not overly interested in us as food.

    I’d recommend folks check of the book The Science of Fear (Dan Gardener) to better understand why their mind irrationally focuses on low risk threats (sharks are among the best example of this) over very large risk ones (which currently kill people in the US at a rate about 10,000x more annually).

    Well-loved. Like or Dislike: Thumb up 29 Thumb down 3
    • Scott Templeman says:

      I meant to cite Auto Accident death in relation to sharks :o)

      Thumb up 3 Thumb down 2
      • hibob says:

        I’ve always guessed that each time I go surfing the greatest risks to my life come from: 1, getting hit in the head by my board, 2, getting hit in the head by someeone else’s board, 3, driving on a highway in California. Plenty of juvenile Great Whites swimming around near shore, but they aren’t interested in us.

        Well-loved. Like or Dislike: Thumb up 16 Thumb down 2
  3. Eric M. Jones. says:

    In the local classified ads, someone is selling a “bait vending machine”. Is this somehow relevant?

    Jus’ sayin’….

    Well-loved. Like or Dislike: Thumb up 14 Thumb down 4
  4. Vince Kellen says:

    What is the risk of having a shark attack while swimming in an ocean? What is the risk of having a vending machine injure you when you are near one?

    This is the relevant risk that is not at all teased out in the highly reported statistics. It might me impossible to calculate this risk because we don’t know how many people are outside when lightening is likely to be present and we probably don’t have data on how many people are in the ocean throughout the year. I would be curious to know if anyone has done a thought experiment on this…

    Well-loved. Like or Dislike: Thumb up 18 Thumb down 1
  5. Nikki says:

    In Freakonomics, the risk of flying is compared to the risk of riding a car in terms of deaths per hour of travel. Obviously in other comparisons of danger, exposure to the risk should be taken into account as well.

    Well-loved. Like or Dislike: Thumb up 12 Thumb down 2
  6. AaronS says:

    As someone who never gets more than knee-deep in the waves (since every shark within a 200-mile radius is now aware that I’m in the water via top-secret shark telepathy) I always get a chuckle out of what’s missing in the statistics you mentioned.

    Yes, the chances of DYING from a shark attack may be less than dying from a murderous vending machine. Ah, but the chances of HAVING YOUR ARM VICIOUSLY RIPPED FROM YOUR BODY, YOUR SURFBOARD EATEN, HAVING YOUR LEG AMPUTATED BY SHARP TEETH, BEING OTHERWISE MAIMED, AND CRAPPING YOUR SWIM SHORTS OUT OF SHEER FEAR? The sharks win ever time.

    The point is that most of us aren’t just interested in whether we DIE by shark bite. We’re interested in whether we will encounter a shark at all, whether our hand will get bitten off, etc.

    Put THAT in the statistics and I’m betting sharks move ahead.

    This whole statistical matter is obviously created by humans who are in league with the shark kingdom. It’s about like saying, “You have more chances of winning the lottery than being bit by a grizzly on the toe in Key West.”

    Well-loved. Like or Dislike: Thumb up 25 Thumb down 20
    • hibob says:

      >As someone who never gets more than knee-deep in the waves

      That’s where all the stingrays are!

      Well-loved. Like or Dislike: Thumb up 23 Thumb down 2
    • James says:

      Ah, but how about the chance of becoming obese, developing diabetes, and having a leg amputated as a result of eating the stuff you get from vending machines?

      Well-loved. Like or Dislike: Thumb up 35 Thumb down 3
    • Ben says:

      You completely make up that sharks are more likely to cause injury, and pass it off as fact.

      Incident for incident, if you are being killed more often by something, by an order of 2, you are going to be getting injured by it on a greater order as well.

      So if you are afraid of being bit by fish, you should still fear losing an arm or leg to that vending machine.

      Or even the most probable, losing your face to a car hitting you, ripping your face clean off your head, and you then live to be a hideous faceless man with gaping holes where your nose, mouth, and eyes would have been. Car accidents that will maim you for life are very likely to happen to you, since you can’t control the hundreds of people passing you daily.

      Thumb up 3 Thumb down 3
    • WillBS says:

      You’ve obviously never encountered one of those Christine-like vending machines that try to make you amputate your own arm 127 Hours-style after you stick your entire arm inside to get a stuck candy bar. Or those “Old Sparky” loving vending machines that try to electrocute you every chance they get. Those sick bastards are certainly murderous and the people need to be made aware of their true, sadistic nature

      Thumb up 5 Thumb down 1
  7. frankenduf says:

    i would guess that most VM deaths are from people trying to steal, not ‘bust it loose’

    Well-loved. Like or Dislike: Thumb up 9 Thumb down 1
  8. Imad Qureshi says:

    Although you mentioned this a little bit in your post but I am still a little confused. I still think that comparison is not fair because we “encounter” (use) vending machines way more often than we encounter sharks. So I think vending machines are safer on one on one comparison basis. But I think using a vending machine is more riskier than swimming on a beach where you “might” be attacked by a shark. So, does that make vending machines more dangerous than a shark? I don’t think so. To compare which is more dangerous you need to compare number of encounters on one on one basis.

    I read a similar statistic on few years ago comparing driving with sky diving. They arrived at the conclusion that sky diving is safer than driving because you’re more likely to die if you drive 10000 miles (or something around that) a year than you sky dive 6 times a year. The thing is, if you sky dive as often as driving, then sky diving is way more risky. six sky dives a year are probably safer than daily driving but daily sky diving is definitely not safer than daily driving.

    Well-loved. Like or Dislike: Thumb up 17 Thumb down 0