The Long Tail Upside Down

On the one hand, long-tail distributions (a fancy name for something like 1/x) are well studied in science when it comes to outliers. They demonstrate that although outliers are very unlikely because their distributions fall off relatively quickly, these distributions are also extremely long. Thus, the probability of extreme outliers is still quite finite, and they occur more often than intuitively expected.

Rare words occur more frequently in texts than we are used to [1], stock market crashes are more likely than financial analysts like to think [2], and floods, for example, can sometimes be so severe that they are even given their own name: Flood of the Century.

So it seems that long-tail distributions are capturing the effect of outliers, occurring rarely, but producing a large impact. On the other hand, long-tail distributions were introduced to the general public when Chris Anderson published his article of the same name in the magazine “Wired” [3] and applied the concept to the realm of business (worth reading!).

He argued that the success of goods sold digitally, let it be immaterial things like music, films, code, or even real-world stuff like books, follows a long tail behavior: usually, the winner takes all. While standard economics usually focuses on the head of the distribution, i.e. things that sell outstandingly well to the average customer, Anderson puts attention to the fact that there is also a lot of business to make from the long tail.

Like Amazon did when it started out selling books online: Adding another book to the online catalog involved only marginal costs, but it enabled Amazon to serve a huge and diverse range of customers, even those with a very peculiar taste for odd books.

So in this picture, the business comes from the long tail of books that only sell fewer and fewer times to more specific customers. Still, as there are also more and more of these odd books, the economic impact, i.e. the overall revenue from selling all of these books, can be substantial.

How do we fit these two views together? Well, it depends from which perspective you are looking at a long-tail distribution. The perspective of Anderson (“Business Perspective”) introduces long-tail distributions as “impact over occurrences,” in other words, “revenue made over the number of items sold.” In contrast, the perspective of natural disaster research (“Science View”) takes a look at the rare number of times events with a tremendous impact occur.

TL;DR If you turn a long tail distribution upside down, it still remains a long tail distribution!

[1] David M. W. Powers. “Applications and explanations of Zipf’s law.” In: Association for Computational Linguistics (1998), S. 151–160.

[2] Nassim Nicholas Taleb. The Black Swan: The Impact of the Highly Improbable. Penguin 2008.

[3] Chris Anderson. The Long Tail. Wired 2004

Chris Anderson. The Long Tail: Why the Future of Business is Selling Less of More. Hachette Books 2008.

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