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

(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:

#### BL1Y

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

#### Winner

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

#### Scott Templeman

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. http://www.flmnh.ufl.edu/fish/sharks/attacks/relarisk.htm
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).

#### Scott Templeman

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

#### hibob

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.

#### Eric M. Jones.

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

Jus' sayin'....

#### Vince Kellen

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...

#### Nikki

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.

#### AaronS

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."

#### hibob

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

That's where all the stingrays are!

#### frankenduf

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

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 howstuffworks.com 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.

#### Mary

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.

#### Mary

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.

#### Mike B

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.

#### BL1Y

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).

#### BL1Y

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.

#### Jeremy Miles

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.