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There’s something about swimming in the ocean that awakens a fear deep inside us. As we paddle through the darkening depths, it’s impossible not to glance down into the deep blue and wonder, “Is a shark going to eat me?”
It’s an understandable fear. Sharks are some of the most terrifying apex predators around. I live in Sydney, Australia, a city known for its amazing opera house, beautiful bridge, and, occasionally, for being invaded by great whites.
They are bloody scary.
So it might surprise you to hear that there is something that, as a scientist, I find far more frightening than a shark. It has fewer teeth, no tiny inhuman eyes, and is rarely found stalking prey through the massive expanse of the Pacific Ocean.
I am talking, of course, about bathtubs.
Shark Attacks: A Risky Proposition
Shark attacks are one of my favorite examples of just how bad we are at calculating risk, because it’s very hard to be rational when something wants to make you into a tasty snack. But putting aside for a moment the stark terror brought about by the thought of row upon row of sharp teeth sinking into your side, let’s ask the question:
“What is the risk of me being attacked by a shark?”
If we take the highest estimate of shark attacks in Australia, there are about 33 per year. We love swimming Down Under, with approximately 8.2 million people taking a dip in the ocean each year. The amount of time they spend in the water varies hugely, with some people surfing daily while some travel for hours to spend a day getting sunburned in the hot Bondi sun.
Now, we don’t really know what the average number of hours each of these people swim each year, but let’s assume it’s at least one. The real number is likely higher — some surfers spend more than an hour in the ocean each day — but that still gives us a reasonable estimate for the number of hours people spend in the habitat of the great white each year.
With these numbers, your chance of being attacked by a shark is 0.0004 percent per hour swum.
In other words, if you decided to give up your day job, jump into the sea, and become a professional ocean swimmer who spends seven hours per day getting your fingers wrinkly, you’d still have a less than 1 percent chance of being attacked by a shark in any given year.
To put it into context, you’re more likely to be hit by a car driving to the beach than attacked by a shark. Far more likely. But no one is paralyzed by the fear of driving, because it’s internalized. Part of our everyday lives. Driving is a boring, tedious risk that is just part of living in a modern world.
But sharks? Sharks are goddamn scary. And so, when we compare the risk of sharks to the risk of cars, we overestimate the risk of the scary sharks and underestimate the risk of the actually much scarier cars.
And almost every media story on science that you’ve ever read has exploited this fear to sell you a terrifying story pretty far from the truth.
Death by Bathtub
So we know that being attacked by a shark isn’t all that likely.
What if we compare shark attacks to something much, much scarier?
The Evil Bathtub
It’s a bit tough to directly compare these two stats because they have very different denominators (total deaths and total number of hours swum), but let’s say I wanted to find out how much more likely I was to die in a bathtub than in the jaws of a marine predator.
Well, your chance of dying due to a porcelain murderer is 340/3000000=0.01%. Taking your chance of being attacked by a shark each year (0.0004 percent), we calculate the relative risk, which is just the probability of one event divided by the other:
This means that you are 25 times more likely to die in a bathtub than you are to be chowed on by a saw-toothed fish.
Relative Risk Is Absolutely Important
Before you run screaming in terror from your bathrooms, I should tell you: Relative risk is often bloody useless. It’s true that you are 25 times more likely to die from bathtub than shark, but neither of these things happen all that often. Out of the 3 million people who die in the United States every year, only a tiny fraction die in bathtubs, and of the 8.2 million people who swim in the ocean, virtually none get attacked by sharks.
Whenever you read a news story, you’ll see risk represented in one of two ways. It will either be a relative risk, like I’ve calculated for you above, or an absolute risk, which is often much more accurate.
The relative risk tells you how much more likely one scenario is in relation to another scenario. The absolute risk tells you how much more likely it is overall.
To calculate the absolute risk, we just take the probability of the first event happening and subtract the probability of the second, so:
What this means is that, in absolute terms, there is only a 0.0096 percent difference between these two events.
So we could either say “You are 25 times more likely to die in a bathtub than get bitten by a shark” or “You are 0.0096 percent more likely to die by bathtub than be bitten by a shark.”
Which would terrify you more?
Which do you think gets reported in the media more often?
If this all sounds absurdly simple to you, it might be surprising to learn that you’ve just done a big chunk of a university-level epidemiology course.
Turns out, this stuff isn’t actually all that hard.
Unless, of course, you’re a journalist reporting on the latest Big Scary Study.
You might remember the most recent uproar a few months ago about the scary medicine ibuprofen. Barely researched articles from around the world were blaring that ibuprofen increased your risk of heart attack by up to 30 percent!
With your newfound epidemiology skills, I’m sure you’ve realized that this is basically complete bollocks.
Ignorant people were reporting the relative risk increase from taking ibuprofen. When you look at the absolute risk increase, it was more like 0.1 percent. That’s infinitely less terrifying, but it sounds quite a bit more like the truth. If ibuprofen were super risky, we’d all be dead by now.
And reporters with limited time, understanding, or interest do this every day. A quick foray into the jungle of the world wide web unearths articles saying that scented candles increase pollution in the home by 30 percent, that living near plants results in 34 percent fewer respiratory deaths, and that women who are on hormone-replacement therapy are 15 percent more likely to experience hearing loss. These are all relative risks, and they are all making you much more afraid than you should be.
So the next time someone tries to sell you the story of their new, terrifying discovery, take a second to ask if the risk is relative or absolute. If they’re only telling you the relative risk, smack them over the head with a rolled-up newspaper for being a bad journalist, and go have a look at the numbers yourself.
Chances are, they aren’t as scary as you’ve been told.