Swimming with Ben Franklin

I headed to the pool yesterday, in mostly sunny weather, but just when I got there, distant thunder could be heard. The lifeguard followed the standard procedure and ordered all the people out of the pool before I could get my toes wet. I didn't have time to stay and wait for half an hour or more, so I turned around and walked home, not getting the 20-30 minute swim I had hoped for.

I wonder whether this risk-averse policy of preventing lightning strikes in the pool makes sense. To answer that question, we need some quantitative measures of risk, not just an explanation why it is risky to be in water in or near a thunderstorm. Of course, being in water increases risk, but by how much? There are indications that expert advice tends to be more risk-averse than most people would be willing to follow. For example, the National Lightning Safety Institute says that cars are safe (because of their metal shell), but only if you

close the windows, lean away from the door, put your hands in your lap, don't touch the steering wheel, ignition, gear shifter, or radio.

That means you shouldn't drive in a storm. But how realistic is that? Imagine the traffic coming to a standstill every time a thunderstorm is near. Similarly, if you are at home, you shouldn't take a shower or wash your hands during a storm, because plumbing is part of the house's conductive shield, and touching it - directly or through water - puts you at risk. But seriously, how many people have died or been injured by lightning while washing hands at home?


Numbers matter because foregoing unsafe actions is usually costly. If traffic stopped in storms, there would be significant economic losses, and moreover (if you think money is not worth the risk), parents would be late picking up children from day care and patients would not get to hospitals on time. Not washing hands may increase your risk of getting ill, which may - depending on the numbers - outweigh the risk of getting shocked by lightning. Similarly, in my case, I am not sure if foregoing swimming to reduce the risk of lightning was a net benefit to me.

Exercise is healthy; it improves life expectancy as well as the quality of life. I estimate that half an hour of swimming would have increased my life expectancy by a few minutes. My reasoning for that estimate uses the analogy with smoking. It is often reported that smoking one cigarette shortens your life expectancy by about 10 minutes. (That's consistent with the assumptions that an average smoker smokes 20 cigarettes per day for 40 years and lives about 6 years less than a non-smoker with the same characteristics.) While I have no data supporting this, it seems intuitively plausible that a good aerobic exercise session would improve one's health by about the same order of magnitude as one cigarette would damage it.

Now, my life expectancy is about 20,000,000 minutes, so I should be willing to risk a one-in-a-few-million chance of being struck by lightning to obtain the life-prolonging benefits of exercise. And so far, this calculation doesn't take into account the pleasure derived from swimming. We pursue pleasures involving risk of death every day. Driving 7-8 miles to the mall or theater implies about 1 in 10 million chance of dying in a car accident (and a much higher chance of being injured). 5,000 food poisoning deaths per year in the US amount to about 5 per meal (1 in 60 million), with serious illness requiring hospitalization being 60 times as likely. And I am not even talking about activities that are normally perceived as risky.

What about lightning? It is hard to find relevant statistics. About 1 in 6 million Americans is killed by lightning every year, and about 8% of those deaths are water-related (but 40% are "unknown"). However, a lot of the water-related lightning accidents occur on small open boats, so it is unclear how many are swimming-related. And, of course, most people take safety measures, so it is hard to know the exposure underlying those accident statistics. They don't help with the specific question I had:

What is the probability of being struck by lightning during a single 30-minute swim in an outdoor swimming pool when a thunderstorm is nearby?

If this risk is of the order of one in several million, it is better to swim anyway. If it is, say, one in a hundred thousand or less, the standard safety procedures make a lot of sense.

I could make it more precise by listing several other factors. Lightning was not visible and by the rolling sound of thunder, I am pretty sure the storm was more than 5 miles away. The pool is lower than most surrounding areas, including the pool house. A train station is just about 200 yards away, with various structures likely to attract lightning. There are plenty of houses, trees, and electric lines in the vicinity - it is a densely populated area. It seems to me that all those factors reduce the risk of a direct strike to the pool (and thus of a deadly strike to the swimmer), although some of them might increase the risk of a strike close enough that some charge might find its path through the pool (but this would seem to be more relevant to the risk of lighter injuries).

Does anyone have some relevant quantitative data?