How Unequal is Success on Medium?

As I showed in my last post¹, the distribution of success in media tends to follow a power law pattern. That is, there are outsize gains for those at the very top, then a long tail of people with middling results.

Should we expect Medium to be any different? Is success on Medium more equitably distributed than in classical media? Let’s investigate.

Do Medium Posts Follow Power Law?

Thanks to the hard work of a fellow medium-member², we have a list of the top 500 medium posts of all time. The plot below shows these top 500 posts ordered by the number of claps they received.

This sure looks like a classic power law curve. The top stories tower above the rest in terms of number of claps. As we get further along, we see the beginning of a long tail.

Fitting the Data

If we fit this data to one form of the classic power law relationship (y = a*x^b+c), we get a pretty good fit. The plot below shows the fitted line in green.

Testing for Power Law

Power law relationships are notable for appearing linear when plotted in log-log format. Let’s take a look at the log-log plot of medium posts below

The linear look of the log-log plots confirms that medium posts do indeed follow the power law pattern of success.

The next question we can ask is, how does this compare to classic media?

Inequality of Success on Medium

The fact is, Medium posts follow the same power law pattern as other forms of media. Nevertheless, this does not mean that the probability of success is the same.

In my previous post on power law, I collected data on New York Times bestsellers in fiction as well as U.S. newspapers and their circulation. Both of those follow similar power law distributions of success (In the case of books — weeks on the bestsellers list, in the case of newspapers — circulation)

We can compare the steepness of the books, newspaper, and medium posts power law curves. The steeper the curve, the more unequal the distribution³.

Comparing medium posts to classic forms of media, we see that the steepness of success is much lower. This means that the distribution of success (in this case, claps) is much more equal than it is in books or newspapers.

Testing the Pareto Principle

Another way to compare the equality of success on Medium with that of traditional written media is to test the Pareto principle. The table below shows the percentage of success — claps, weeks on bestsellers list, circulation — that is held by the top 20% of each distribution.

Again, we see that medium posts have the lowest concentration of success at the top. Only about 41% of claps are reserved for those with the top 20% of posts.


Popularity is a network effect and networks follow power law. This means that any form of media will exhibit a large inequality of success. The top posts on Medium will get promoted, shared, and read much more than rest, just as happens in traditional media. Nevertheless, it is a testament to Medium that on this platform, success is more evenly distributed. Your odds of writing something that will be read by millions of people is better than it ever has been.


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3 — Testing using the PoweRlaw R library give similar results :

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