# Explainer: Fat Tails

Let’s talk about tails. In everyday use, I’m sure we’re all familiar with the idea of a tail. For example, in this picture — courtesy of Mr. de Saint-Exupéry — there are two tails:

Because, of course, this is not a picture of a hat, but rather a boa constrictor digesting an elephant.

And, just like a boa constrictor digesting an elephant, a normal distribution (or if you prefer, a bell curve, or a Gaussian) also has two tails:

In both cases, the tails are thin — and that’s exactly what they’re called in the business; thin tails. In a thin-tailed distribution, common occurrences rule and the impact of extreme events is negligible. Coin tossing, Galton Boards and people’s heights are just some examples of things that are normally distributed. Google tells me that the average human height is 170 cm. Most people are pretty close to that height, and the average is largely representative of reality — maybe some people are a little bit shorter, others taller, but no one is, say, 40 meters high.

Now let’s talk about fat tails. One of the most well-known fat-tailed distributions is the Pareto distribution (a.k.a. a power law, 80/20 rule, etc):

As you can see, that left tail is *very* fat! The interesting thing about fat tails is that the tools you’d normally use to analyse thin tails don’t work anymore. Take the example of people’s wealth. If you took Bob off the street, and looked at the net worth of him and a few of his closest friends, maybe you’d get an average of something like $250,000. Okay, now what would be the average net worth of Bob, his friends and Jeff Bezos? Something in the billions. Oops. Clearly, that doesn’t give you any useful information.

Other examples of fat tails include Pandemic casualties, cash generated by startups, land ownership, drivers involved in car accidents, work done by employees, and so on.

Don’t mistake thin tails for fat tails — many things in this world aren’t normally distributed!

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