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Hurricane Sandy and the gambler's fallacy

There are presently no shortage of articles being written about Hurricane (now Post-Tropical Cyclone) Sandy and what role climate change has played in the formation of the "Frankenstorm" that has left over 7.5 million people without power. I came across one article, however, that should be addressed: Hurricane Sandy: The Worst-Case Scenario For New York City Is Unimaginable (by Mike Tidwell, at ThinkProgress.org).

Much of the article is a traditional "worst-case scenario" description found commonly in the media for seemingly all combinations of disasters and major cities. Of note, however, is the following paragraph (emphasis added):

Another major storm struck in 1892, then another in 1938 when the borderline Category 4 “Long Island Express” passed through the outskirts of greater New York, inflicting widespread death and destruction across New York state, New Jersey and much of New England. But that storm, 68 years ago, was the last major hurricane (Category 3 or above) to strike the New York Metropolitan region. It’s now a matter of when, not if, a big hurricane will strike again, according to meteorologists. And history says “when” is very soon.

The bolded statement is a classic example of the gambler's fallacy. It seems as if hurricanes can be reasonably modeled by a Poisson process, a useful probability model (e.g. this website, this paper (pdf), and this paper (pdf)), and this assumption will be used throughout this post.

One of the important properties associated with this model is called memorylessness. Essentially, what this means is that at any given time period, the probability of an event occurring does not depend on the history up to that point. That is, it doesn't matter how long a system has been running, a 'success' is just as likely to occur at this time period if this is the first time period, if this is the 10th time period, or if this is the 76th time period.

For example, when playing roulette, the probability of spinning a 'black' are the same on every spin, irrespective of how many times you have previously spun the wheel. Even if there have been 999 'red' in a row, we are not 'due' for a black spin (assuming the wheel is fair, etc.).

Just because New York City hasn't had a major hurricane for a while does not mean that it is due or overdue for one. Each hurricane season is a new cycle and does not remember the previous years' hurricanes.

I am not an expert in the fields of research associated with most disasters, but this makes sense in terms of hurricanes (both from various sources and my life as a Floridian). For other disasters (e.g. volcanoes and earthquakes), my understanding is that pressure builds over time and therefore reasonable models for those systems should not have the memorylessness property, so perhaps talking about 'overdue' for a major disaster is warranted. Maybe not, but I do want to emphasize that this is specific to hurricanes.

(It might also be worth checking out these comics related to the gambler's fallacy.)

Satellite image of Hurricane Sandy (25 October 2012)
Satellite image of Hurricane Sandy (25 October 2012)

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