(iStockphoto)
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)
and 
. You can also watch it on 
We came up with this exact same stat one slow day at the office in the summer of 2001. The news was slow that summer… 9/11 was yet to come…and shark attacks were the big cable news scare along with Chandra Levy. We looked up the shark data and decided that not only was a shark attack remarkably unlikely, but that the summer of 2001 had actually been below normal despite the news hype.
We also noted that vending machines have round, softer plastic around them and blocks to prevent reaching in. These new vending machines changes are clearly the result of lawsuits. Now, vending machines are less scary when they attack. However, I still keep my 9-iron handy when I get a coke at the golf course just in case I have to fend one off.
I wonder how dangerous a shark would be if you treated it like vending machine?
Imagine screaming and kicking a shark and reaching into it’s mouth.
Considering their treatment, I think vending machines are remarkably docile and retrained. I’m surprised they don’t attack more often.
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Part of the problem is that simple death rate statistics are misleading. Yes vending machines kill more people, but that is almost expected because there are so many more vending machine-human interactions than human-shark interactions. The proper point of comparison is to tally the number of times any human anywhere interacts with (ie gets near) a vending machine, then do the same for sharks then calculate the rate of death per interaction.
This has come up before in terms of airline vs passenger car safety. Most stats compare deaths per miles traveled, which planes win hands down because they travel so many more miles than cars to. However if you compare deaths per HOURS traveled the rates become much more competitive. Human intuition is an amazing tool, but it is often wrong or incomplete. However just because it isn’t perfect doesn’t mean that it should be discounted. There is often a nugget of truth to these seemingly irrational misconceptions and only be discovering why we feel the way we do can the full answer be determined.
Deaths per mile traveled is the correct figure to use. We generally plan trips based on distances (I want to go from Atlanta to DC) not based on time (I think I’ll just head towards DC, and see how far I can get in 2 hours).
Now, what would be interesting in comparing plane and car safety is how many more miles people tend to travel because of airplanes. I flew from New York City to Huntsville, AL (and back) 5 times in 5 years; I doubt I would have made the trip that many times if I had to drive. Though air travel is very safe, not having air travel would have been even safer, because I wouldn’t have traveled at all.
Applying the same idea to vending machines, in gauging how dangerous they are we should think about the alternative. Would you instead of walked down two flights of stairs and across the street to the news stand to buy your candy bar? That has some risk to it, probably greater than the risk of being crushed by a vending machine (though your improved health from the exercise may offset the risk of falling or being hit by a car).
I should add that there are some instances where hours traveled is the relevant number.
As I said, you may go more miles because air travel is an option. So, if you’re planning something such as a vacation, you may be only willing to spend a certain amount of time traveling. For instance, on a three-day weekend, you might want to get away, but spend no more than 4 hours traveling one-way. In this case, your risk does come down to hours traveled, rather than miles.
Yes, but when you are deciding between two different journeys, the distance becomes relavant. It is unfair on plane journeys to compare long-haul flights with a short car run to the shops also.
In the big scheme of things, you can either say, fly from New York to LA, or you can drive – the deaths per interaction isnt as relevant, in this scenario, as death per miles here, in my opinion.
You want to take on a journey with as little risk of death as possible, so a drive from NY to LA is the equivolvent of maybe 500 trips to the shops (or interactions as you put it).
You need to apply the same reasoning to vending machines. I read some research on this, quite some time ago, and I can’t find the details. But the gist of it is that the vending machines that are likely to kill you are (or were) soda machines, that sells cans of soda, and do it by dropping them into a slot. These machines are heavy – they hold a lot of cans of soda, and they’re top heavy – the soda is loaded into the top, so gravity can do the dispensing work.
You get angry with the machine for not giving you the soda, so you push it and it falls on top of you.
This is not likely to happen to just anyone – you need to be fairly strong, and fairly angry. To help with both of these, you need to be young and male. And in the article, it said that this was a particular risk for members of the armed forces. So I’d suspect that the risk of being killed by a vending machine for a slightly older than young economist approaches zero.
I think that one of the reasons that people are more concerned about sharks is that the vending machine is not willful. The shark is attacking THEM, on purpose. The vending machine is just falling over on some (other) idiot that pushed them. We feel that we have control over what happens with a vending machine. Not so much with the shark.
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Jimfive
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Perhaps even more than that. According to the back cover of Eduardo Porto’s (highly recommended) The Price of Everything, “a life saved from a terrorist attack [is] felt to be worth two saved from a natural disaster.” Apparently it may be the case that intentional killing is perceived as the worst kind of death overall, not only in comparison with scenarios where the victim is at fault.
Just a quick note; it seems to be Edward Porter’s “The Price of Everything:The Cost of Birth, the Price of Death, and the Value of Everything in between “
“…the vending machine is not willful.”
I bet you haven’t known many vending machines
But seriously, are sharks willful, in the sense that they decide to eat humans? Or are they just reacting to stimulii in the same (though more elaborate) way that the vending machine reacts to having money stuffed in its slot?
“…are sharks willful…?”
Without getting into a debate about the existence of free will in the universe, the easy answer is: It doesn’t matter. As long as people *perceive* the shark to be acting under its own volition while they perceive the vending machine to be falling due to gravity then they will fear the shark more, even if it is less dangerous.
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JimFive
But a lot of us do perceive the vending machine (or other bits of machinery) as having malign intent. After all, machinery should function as designed. If it doesn’t, there must be a reason, and intent seems as good as any.
Harvard Psych prof Daniel Gilbert discusses the fact that people feel greater risk from (perceived) threats from willful agents than from simple inanimate risks; see If Only Gas Sex Caused Global Warming.
In mortality there is a concept called ‘exposed to risk’. As the article says, the answer is not to compare the deaths with the whole population but those who have some exposure. For mortality this is usually straightforward as you have some sort of population. In other cases defining the exposure is not always easy, as the comments show – measure air travel by miles travelled or time spent travelling? And then measuring it can be even harder. The real danger is resorting to what can be measured, in this case the whole population, rather than measuring the true exposure. In one sense the statistic is right – pick a random person in the USA and they are more likely to die from a vending machine than a shark. But measure those who use vending machines v those who swim in the sea and you would probably get a different answer.
Despite that this does not remove the basic point – the risk from sharks is truly limited. One death per annum per 250 million is not very much.
It’s definitely the perceived threat and the nature of the death. I dive with sharks every week and take people to see them. Often they are apprehensive of the shark before the dive but afterwards they find themselves enjoying the experience. The thing is we are in an environment that is unnatural to us and we don’t feel in control. Put into that mix a slight possibility that a large animal with lots of teeth may attack us and we get scared. Don’t get me wrong sharks are not harmless but the amount of human / shark interactions that don’t end in attack are staggeringly huge. They just don’t make for good TV. I know that where I dive millions of people over a year go into the water and I’ve seen how many sharks are close by. (Great whites are spotted every other week) and there has been one attack in 20 years.
Actually your undersatanding of the stats of shark attacks and vending machines is off. People putting their arm in a vending machine and it falling on them is causing the accident to take place and is counted. If you put your arm near a shark and it bites it is provoking a shark to bite and is not counted. You do have a risk of being in a unprovoked shark attack, but there is no chance of being involved in a un provoked vending machine accident. Keep beleiving those US folks and be a fool when it comes to sharks.