Layla Parast has learned a hard lesson:

Summer is my favorite time of year. To me, summer means watermelon, pools, and the smell of sunscreen and mosquito repellent. My favorite, well-known example explaining how correlation is not causation involves summer: the numbers show that ice cream sales and shark attacks are correlated, so do more ice cream sales increase shark attacks? Should we cease selling ice cream? Of course not. Summer is the answer. In the summer, it’s hot, more people buy ice cream, and more people go to the beach and go in the water.

I am very fearful of a shark attack. I used to do triathlons, but then in graduate school in Boston, I got hit by a car while riding my bike, and fractured my back. I moved on to races that were swim–run only, leaving out the bike portion. However, over time, I became too scared of the swim portion because in Southern California, they tended to be in the ocean. Often, when I mentioned that I am scared of a shark attack, people would laugh and say the phrase that gets me every time: “Don’t you know you’re more likely to be struck by lightning than be attacked by a shark?” Especially as a statistician, they would say, how can you be afraid of a shark attack?

We don’t have an accurate estimate of the probability of being attacked by a shark. The best resource I have found is the International Shark Attack Files created by the Florida Museum of Natural History at the University of Florida. They categorize shark attacks into unprovoked vs. provoked attacked, and tabulate attacks by country. The US leads the world in the number of unprovoked shark attacks, which is perhaps unsurprising given that it is the third largest country by population — but it is ninth in terms of miles of coastline.

The difficulty with estimating the probability of shark attack is the denominator. We don’t have the right denominator. Some sources provide a probability estimate that simply takes the number of shark attacks as the numerator with the country’s population in the denominator. Clearly, that is not what we want. The best estimate I have found has the number of beach users in the denominator. But still, this is not what we want. The denominator needs to be the number of hours at risk of a shark attack. We want a rate that tells us the probability of a shark attack per hour of exposure, not just the relative risk. Laying out at the beach is not exposure. Playing volleyball on the beach is not exposure. Going in the water, even waist-deep, is exposure. Swimming, surfing, snorkeling are all exposures. And that denominator seems nearly impossible to get. We don’t have the estimate that we want.

To be sure, more people are struck by lightning than attacked by sharks. One is more likely to die in a car accident than be attacked by a shark. Many other things I do in life carry higher risk. But my probability of being attacked by a shark if I don’t swim in the ocean is essentially zero. I worked on this fear for a while with my CrossFit mental training coach (yes, I have one). I signed up for a triathlon in Hermosa Beach CA, my first in 10 years and each week I would practice going in the ocean and swimming a little bit further out each time, sometimes even doing an open-water swim. And I absolutely hated it. Leading up to the race, I had nightmares, I couldn’t sleep. My heart-rate would skyrocket just driving to the beach and my smart watch would ask what workout I was in the middle of. A friend bought me an ankle device that emits something to keep sharks away, but I was scared to use it, afraid that it would somehow actually attract sharks to me.

I told my coach, this isn’t working, I don’t know what to do, how do I conquer this fear? And finally, she told me: don’t. Don’t do the race. Stop doing your ocean swims. Your body is telling you that it just can’t handle this right now. Your plate is full, so stop. Quit. Somehow quitting something, and telling people I was quitting, seemed scarier than getting in the ocean. I did quit and I do feel like I failed. But maybe that was the lesson for me. Sometimes quitting is the tougher thing to do.

Happily, now in Texas, most of the triathlons here are in non-ocean bodies of water. But I am still waiting for that accurate estimate of shark attack risk.