Power Law in Popular Media

Michael Tauberg
9 min readJun 29, 2018

“No one man should have all that power”

— Kanye West

We’ve all heard that the media business is cutthroat. In books, or movies or music, a few dominant artists tower over the rest. These superstar directors and writers and musicians sell millions of units while their peers languish in obscurity.

I wondered, are all forms of media equally competitive?

To find out, I scraped the internet for as much media data as I could find¹. To my delight and surprise, whenever I ordered things by the biggest winners, the same pattern emerged. It’s called power law, and you can see it below.

What is Power Law?

tall trees and scarce sunlight

Have you heard of the long tail? the 80–20 rule (Pareto distribution)? Winner-take-all markets? Those are all examples of power law at work.

In technical terms, power law is just a mathematical relationship. Here’s what it looks like.

from https://en.wikipedia.org/wiki/Power_law

The part in green dominates, hoarding most of the distribution. This section is followed by a long tail in yellow. Together, these two parts form the power law pattern.

Basically, power law is like a forest². There are tall trees which soak up the sun and grow to be enormous. Then there are all the shrubs on the forest floor.

Media Data and Plots

Books

The New York Times web API³ provides a list of fiction best sellers from the last 7 years. If we measure success by weeks on the list, we can compare the most and least successful books.

Below are plots organized by novel, author, and publishers. I also show the top-20 results in each category, both for fun and to prove that the data is correct.

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Michael Tauberg

Engineer in San Francisco. Interested in words, networks, and human abstractions. Opinions expressed are solely my own.