According to the Washington Post, “Florida had seen just 17 confirmed fatal alligator attacks in the previous 58 years. In less than a week, there appears to have been three.”

How strange is this? 17 attacks in 58 years is about 0.3 attacks per year. But there are a lot more people in Florida now than there were 58 years ago or even 25 years ago, so we might expect the rate of attacks to be increasing with time (though I don’t know if that’s true). Suppose the current “true” rate is 1 attack per year, or 0.02 per week. In that case, given that there is one attack, the odds of having two more within a week would seem to be roughly 0.0004. (We look at the question this way because we are interested in the question “what is the probability of having three attacks in the same week”, not “what is the probability of having three attacks in this particular week.”)

So according to this crude estimate, 3 fatal alligator attacks in a week is indeed an extremely unlikely occurrence, although not spectacularly so. There could be some important modifiers, though. For instance, maybe there is a seasonality to alligator attacks, either because alligators are more aggressive at some times of year or because more people do risky activities during some times of the year.

On a related subject, I’m never exactly sure how to think of these “freakish coincidence” stories. We’d be having this same sort of discussion if instead there had been three fatal bear attacks in a week in Oregon, or three fatal shark attacks in Hawaii, or three fatal mountain lion attacks in California, or whatever, so maybe a “three fatal something attacks in a week” story shouldn’t be all that rare. On the other hand, it does seem worthwhile trying to figure out if anything has changed in Florida that would make gator attacks a lot more common, because 3 in a week sure seems exceptional.