Power Law Is More Common Than We Think

What is a power law?

A power law describes an exponential distribution — where a few individual points account for a majority of the value in the population.

Image Credit

Basically, Power Law is like a forest¹. There are tall trees, which soak up the sun and grow to be enormous. Then there are all the shrubs on the forest floor.


Power law in software companies

I used to think power law only applied to select few industries like Venture Capital, but lately, I observed it in action in more industries. For instance, companies that have tens of thousands of customers, only a handful of them drive most of the revenue.

According to Slack’s S2 filing, Slack has more than 88,000 paying customers, including 65 Fortune 100 companies. Of those, only 575 customers paying over $100,000 of ARR accounted for approximately 40% of the revenue in the fiscal year 2019.⁵

Pagerduty has more than 10,000 paying customers with 203 customers paying> $100,000 of ARR. Over time, larger customers have constituted a greater share of their revenue.⁶


Power law in blogging

You have to keep pumping out high-quality blog posts, knowing that 90% of them will fail. 

 Ryan Robinson

Aside from Ryan’s 16 top-performing posts, his average blog post only scrambles a few hundred views per month. 


Power law in podcasts

The median podcast only has 124 downloads per episode — but the top 1% has 35K downloads per episode.


Power law in books

In the US book business, 97% of sales are made by 20% of authors. US literary nonfiction sales are even more imbalanced, with 0.25% of books representing 50% of sales. 

The distribution of success looks like this:

Image Credit²

Power law in movies

Image Credit⁴

Power law in venture capital

VCs invest in 1000s of companies and only a handful of them drive the returns. 

Among all the companies that are funded in a year, only 15–20 companies reach over a billion-dollar valuation. If you want a successful VC career, you need to get in those deals at whatever valuation. If you don’t get in those deals, you will be a mediocre VC.

https://twitter.com/BenedictEvans/status/1008038770396942336

To a first approximation, a VC portfolio will only make money if your best company investment ends up being worth more than your whole fund. 

 Peter Thiel

Power law in revenue sources

Power law distribution on revenues³ says that one source of revenue will dominate everything else. For example, if you’re an entrepreneur who opens a coffee shop, you’ll have a lot of ways you can make money. You can sell coffee, cakes, merchandise, and more. But each of those things will not contribute to your success in an equal way. Once you’ve found the variable that matters most, you should place more time on that one and less on the others.


Conclusion

Understanding power law distributions isn’t just about understanding venture capital. There are important personal applications too. Many things, such as key life decisions or starting businesses, also result in similar distributions.

What other industries have you seen power law in action? Let me know in comments.


Notes

  1. This paper shows that African tree canopies form a power law distribution https://www.nature.com/articles/nature06060
  2. https://25iq.com/2017/09/22/a-half-dozen-lessons-about-writing-and-getting-a-book-published/
  3. https://blakemasters.com/post/21869934240/peter-thiels-cs183-startup-class-7-notes-essay
  4. https://medium.com/@michaeltauberg/power-law-in-popular-media-7d7efef3fb7c
  5. https://www.sec.gov/Archives/edgar/data/1764925/000162828019004786/slacks-1.htm#s5328ABFAF1B639BFCB3C567D8E918E08
  6. https://www.sec.gov/Archives/edgar/data/1568100/000162828019003003/pagerdutys-1.htm

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