The trouble with risk

It’s relatively hard, but absolutely important

There’s a primordial fear that we all have whilst swimming in the ocean. A twinge of anxiety that preys on our senses as we paddle through the darkening waters, a faint shiver that has nothing to do with the icy water.

And as you look down into the murky depths, it’s impossible not to think to yourself;

How likely is it that I will get mauled by a shark?

Shark Attacks

Sharks are a great way of showing just how bad we are at interpreting risk. Swimming out into the deeps paves the way to an irrational fear of something that you can’t run away from that wants to eat you.

In fact, you are more likely to die from swimming in the sea than be attacked at all by a shark.

There’s some maths coming up, so if you find that scary, ignore the italics.

Taking the highest estimate, there are ~33 shark attacks in Australia each year. Australia has an estimated 8.2 million yearly ocean swimmers. These range from surfers and daily swimmers who spend hours each week in the sea to once-yearly swimmers who live inland. Let’s assume that the average number of hours spent swimming per year is 1 per person (this is likely higher, but we are just guessing here). That means that your chance of shark attack is about 0.0004% per hour swum.

To put it another way, if your full-time job was swimming, and you worked overtime every week doing 50 hours for a whole year, you’d only have a 1% chance of being attacked by a shark.

That’s really not a lot. In fact, you are more likely to be injured driving to the beach than by a shark swimming in the water. And yet, none of us fear cars. Is it because they lack rows of sharp teeth and only rarely eat people? Perhaps. Or maybe it’s because we live each day with the risk of road accidents. We acclimatize to the danger. We internalize the risk. Even though it’s very high, we brush it off as a factor of living our modern lives.

But sharks are scary. And we fear them. So when we think of how risky they might be, our estimates explode to mammoth heights.

Relative vs. Absolute Risk

Now what is something that happens far more often in the sea?

If you answered “toddlers urinating”, you are both right and a terrible person.

If you answered “drownings”, you are still right, and either a pessimist or a public health expert.

Each year 84 people in Australia drown whilst swimming in the sea. Considering the number of people who swim each year, this is actually staggeringly low — here we should pause to thank the amazing and selfless work of lifesavers around the country.

Say I’m a morbid person (seriously, go ahead and say it, I really am). I want to know how much more likely it is that I will die from drowning than from being torn limb-from-limb by a marine predator. There are two ways of doing this; either by calculating the relative or the absolute risk.

This requires some more maths. Let’s assume that the denominator for both of these equations is 8.2 million hours per year. That makes everything very simple, because the risk of being attacked by a shark becomes 33/8,200,000 and the risk of drowning becomes 84/8,200,000. The relative risk of these two events is simply the probability of one divided by the probability of another, so;

84/8,200,000 ÷ 33/8,200,000 = 84/33 = 2.55

So we can say that the relative risk of drowning is 2.55 times higher than being attacked by a shark. Another way to put this is that you are 2.55 times more likely to drown than to be attacked by a shark.

If this sounds super high, that’s because relative risk is, by itself, a shit way of looking at the world. Drowning might be more than double as likely as having your insides ravaged by a deadly ocean stalker, but it is still a super rare event. Remember, it only happens to 84 out of 8.2 million people.

This leads us to the absolute risk increase. Where the relative risk tells us how much more likely one thing is relative to another, the absolute risk increase tells us how much more likely one thing is overall.

Maths again (it’s simple, don’t worry). To calculate the absolute risk, we just have to subtract the risk of one event from the risk of another, so;

84/8,200,000–33/8,200,000 = 51/8,200,000 = 0.000006

This means that drowning has an absolute risk difference of 0.0006% compared to shark attack.

So you can either say “you are 2.55 times more likely to die by drowning than shark attack” or “you are 0.0006% more likely to die by drowning than shark attack”.

Which one do you think sounds scarier?

Which one do you think people use more often when they report their results?

Analyzing Risk

Congratulations! You now have a better understanding of risk in scientific studies than most journalists. If you read the math-y bits, you’ve actually done about 1/10th of an epidemiology course at uni.

I would charge, but dammit everyone should know this stuff.

So what does it mean in practice?

You might remember the huge furore last year about the contraceptive pill and depression. Journalists worldwide screamed loudly that women on the pill were 23% more likely to have depression, and in some age groups they were 2.2 times worse off!

With your fancy new epidemiological skills, you might recognize this as the arse-music of the poorly informed.

These are all relative risks. The absolute risk increase that the researchers found when taking the contraceptive pill was actually about 0.5%. Women on the pill are 0.5% more likely to be diagnosed with depression than those not on the pill, which equates to one extra diagnosis of depression per 2–300 women taking the pill.

It sounds much less scary, but also much more like the truth.

This happens everywhere you look. A quick Google of “science news” turns up this article that claims that obese people are 60% less likely to conceive than healthy weighted people, this article that links common pain medications with a 2.5 times increase in gastro-intestinal symptoms, and this article claiming that kids born in June were twice as likely to receive medication for ADHD than those born in July.

And this bullshit has real consequences. When the media ran a scare campaign based on misunderstanding of the risks of heart medication, people stopped taking their heart medication.

People literally died because most of us have no clue what risk really means.

After reading this, you might think that relative and absolute risk are pretty easy concepts. You’d be right. So start using them.

When you read an article that mentions risk, have a look and see if they’ve included the actual numbers from the study. Do your own calculations (if you’re having trouble, the British Medical Journal has a really simple online guide because doctors screw this up with wonderful regularity). If you can, go back to the original study and spend 5 minutes crunching the numbers yourself.

If you’re really stuck, send me a message. I’ll be glad to help you out.

You can reach me on