Power Laws: The Hidden Force Shaping Success, Risk, and Life’s Surprises

When we think about the world, we often expect things to be “normal.” Most people are of average height, most apples are about the same size, and most days at work are, well, pretty typical. This expectation comes from what mathematicians call the “normal distribution”: the classic bell curve where most outcomes cluster around the average, and extreme events are rare.

But here’s the thing: much of life doesn’t play by these rules. Instead, it’s governed by something far stranger (and far more powerful) called a power law.

Photo by Max Bender on Unsplash

What is a power law?

Imagine you’re looking at the distribution of wealth, the size of earthquakes, or even the popularity of YouTube videos.

You’ll notice a pattern: a few outliers dominate, while the vast majority are small players. Incomes, for example, don’t cluster tightly around an average. Instead, a handful of people earn vastly more than everyone else: sometimes 10, 100, or even 1,000 times more. This isn’t just about money.

It’s true for city populations, book sales, and even the number of links to websites.

Mathematically speaking, a power law means that as you double the size of something (like income), the number of people or events at that size drops off by a consistent factor. On a graph, this creates a straight line when plotted on a log-log scale. This is a signature of the power law world.

Why power laws matter for leaders and achievers

Power laws make the world unpredictable. In a normal world, you can plan for the average. In a power law world, a single outlier can change everything.

• Extreme events are more common than you think: In business, a handful of products or clients may generate most of your revenue. In content creation, a few viral posts can dwarf the rest. In nature, rare disasters like massive earthquakes or wildfires can reshape entire landscapes.
• The average is misleading: If Bill Gates walks into a coffee shop, the “average” wealth in the room skyrockets. But that average tells you nothing about what most people actually have.
• Persistence beats consistency: In power law domains, it’s not about steady, incremental progress. It’s about making repeated, intelligent bets, knowing that most will fail, but one wild success can pay for all the rest. This is how venture capital works.

Real-world examples

• Venture capital: Most investments lose money, but a few outliers (think: the next Google or Airbnb) generate the majority of returns.
• Publishing and streaming: Most books and shows flop, but a tiny fraction become runaway hits like Harry Potter, Game of Thrones, or Squid Game.
• Online content: On YouTube, less than 4% of videos ever reach 10,000 views, but those account for over 93% of all views.

A lesson for leadership: know what game you’re playing

If you’re in a world governed by normal distributions (running a restaurant or an airline) consistency is key. You need steady performance, and outliers don’t help much.

But if you’re in a power law world (like startups, creative work, or investing) you should adjust your strategy. Here, it pays to:

• Take smart risks: Don’t be afraid of failure. Most attempts won’t work, but you only need one big win.
• Be persistent: Keep showing up, keep creating, keep experimenting. The next try could be the one that changes everything.
• Prepare for surprises: Don’t be lulled into a false sense of security by a string of small, uneventful outcomes. The big one (good or bad) can come out of nowhere.

Why predictability is hard and why embracing uncertainty matters

Power law systems are “scale-free” and “critical.”

In plain terms, there’s no typical size or outcome: small actions can trigger massive effects. A single spark can ignite a forest fire and a tiny shift underground can unleash a devastating earthquake. In these systems, unpredictability isn’t a bug.

It’s a feature. Past performance offers no guarantees about what comes next.

This reality may feel unsettling, but it’s essential if you’re aiming high.

Extraordinary results rarely come from playing it safe in a predictable world. If you want average outcomes, stick to the familiar. But if you’re chasing impact, recognize when you’re in a power law environment. Here, bold moves and a willingness to accept uncertainty aren’t just recommended. They’re required.

Because in a world shaped by power laws, one idea, one connection, or one action truly can transform your entire life.

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If you found this article insightful and want to discuss more about leadership, productivity, or the surprising ways math shapes our world, feel free to connect with me on LinkedIn.

Source: This post is inspired by the brilliant Veritasium video on power law.