[ChadyWady]

From what I understand of the article, the "1 in 500 years" measure is based on the estimated probability of a flood on a given year in a local area. So the probability of a "1 in 500 year" flood in Houston is independent of the probability of a "1 in 500 year" flood for another city.

[twinkletwinkle]

Right what the parent comment is saying is that look at a map of the US, how many major cities are there. The odds of two "1 in 500 year" floods happening consecutively are low for any individual city. But if you have enough cities it will happen somewhere. And then you write the article about it.

It's kind of analogous to hitting a golf ball into an open field and then exclaiming "Of all the blades of grass, the ball landed on this one!" It's only interesting if it goes in the hole with the flag, otherwise you have a sort of selection bias going.

[ChadyWady]

That makes sense, I was confused since the Birthday problem is more about the pigeonhole principle rather than larger samples being more likely to have individually unlikely outcomes.

But for this case, it would still be very unlikely. For any arbitrary 3-year span, the probability of consecutively getting a "1 in 500 year" flood for 3 years is (1/500)^3. If we have N cities, then the probability of none of these cities having 3 consecutive floods is (1-(1/500)^3)^N. For even a vast overestimate such as N=20000, it is still a significantly improbable event. Of course, this doesn't account for "3 consecutive years or more within some year range" and it is a gross simplification, but I think there are probably better explanations than selection bias, such as the inaccuracy of the model or the fact that these events might be temporally dependent on each other.

[analog31]

My understanding is that by definition, a 500 year flood has a probability of 1/500 per year. But I live at the top of a hill in the Midwest, so a 500 year flood in my locale has a much different severity than a 500 year flood in Houston.