The Power Law

There’s an underlying rule of the universe that governs much of what we see, do, read, watch, consume… It’s called The Power Law. I summarize it as follows:

Most of the output comes from little of the input. Most of the input contributes little to the output.

You may have heard of the similar Pareto Principle, also known as the 80/20 Rule. Many naturally occurring phenomena follow the pattern, in which 80% of the consequences come from 20% of the causes.

For instance, across businesses, on average, 80% of sales come from the top 20% of clients. In economics, 80% of the world’s GDP is concentrated in 20% of its population. In sports, 80% of the points scored tend to come from the top 20% of performers. In companies, 80% of the time spent is on the last 20% of projects.

The Power Law generalizes this further. Let’s put aside numbers for now and think more broadly. For much of the universe and life within it, we should anecdotally understand that these two things are true: Most of the output comes from little of the input. Most of the input contributes little to the output.

Some examples:

• Most of the content consumed on the internet (the output) comes from a few concentrated sources (the input). Most of the content created on the internet (the input) is rarely consumed (the output).

• Most of the products we buy come from a handful of wildly successful companies. Most of the companies out there make products that we do not buy.

• Most of the articles I write for this newsletter come from bursts of inspiration. Most of the time I sit down to write, it doesn’t lead to anything of value.

Here’s a way to visualize this more general Power Law:

The distribution of inputs and outputs might change, but the concept of concentrated, disproportionate impact is as universal as any other statistical law. There is no way around it.

Why Does the Power Law Happen?

There are mathematical explanations for why we see this phenomenon occur so ubiquitously. Yet I prefer to think about it intuitively.

Let’s take a hypothetical example of companies competing with one another: Imagine ten pizza restaurants opening in the same town. The Power Law dictates that, over time, one or two of them will sell most of the town’s pizza. And the remaining majority of pizza places will sell to a small percentage of the town’s population.

When we start though, we’re looking at an even distribution of pizza sales:

Over time, the distribution begins to resemble The Power Law distribution instead:

Why does this happen? The answer, in part: Positive and negative flywheels (a topic I’ve written about before here). Once a pizza place gets positive reviews online, others are more likely to check it out, leading to more positive reviews, and so on. Once a pizza place appears crowded, people are more incentivized to go there. And, by contrast, once a pizza place begins appearing empty, people are more hesitant to go there. Once it gets a negative review, fewer people try it out, so it can’t get enough good reviews to offset the bad.

It should hardly be surprising that one pizza place therefore eats (some pun intended) into the market share of the others.

This same logic governs why content goes viral on the internet. Content that’s starting to get shared is more likely to get shared again. By a combination of both quality differences and random fluctuations, a snowball starts rolling, and once it starts rolling…

The Opposing Force

Yet, by that logic, shouldn’t the snowball continue to grow and grow? Shouldn’t pizza places that attract more and more customers eventually drive their competition out of business entirely? Is the 80/20 rule just a pit stop on the way to a 90/10 rule and eventually a 100/0 rule?

This sheds light on what I believe is one of the most overlooked aspects of The Power Law. To explain it, let’s look at this principle from one other vantage point:

That curve on the bottom is called a normal distribution (or the “bell curve”), and it’s another statistical phenomenon that appears seemingly everywhere. We find it in probability, in physics, in standardized testing, in polling, in finance, in biology…

And unlike The Power Law, which dictates that the output becomes increasingly concentrated amongst the winners, the normal distribution dictates that no matter how much concentration you get, you’ll always have exceptions.

So there are, in reality, two statistical phenomena at play here that are counterforces of one another.

Not everyone will want pizza from the one popular spot. Some will prefer certain locations, certain decors. Some will have loyalty to their old favorite restaurants. Some will not like how crowded the popular one gets. Some, in other words, will not gravitate toward the center of the distribution (its mean) but away from it.

So let’s qualify each of those bullets I mentioned earlier:

• Most of the content consumed on the internet comes from a few concentrated sources. Most of the content created on the internet is rarely consumed. But there will always be people out there who will find and consume some of that long tail content.

• Most of the products we buy come from a handful of wildly successful companies. Most of the companies out there make products that we do not buy. But there will always be people out there who will find and purchase some of those other products.

• Most of the articles I write for this newsletter come from bursts of inspiration. Most of the time I sit down to write, it doesn’t lead to anything of value. Or rather, it doesn’t lead to anything of apparent value. It still gets used, even to help shape my future writing, and therefore has inherent value.

Some Borrowed Wisdom

I find myself thinking about these two laws (The Power Law and normal distributions) often, and that’s because they’re so omnipresent in our lives. I’m not the only one either. To finish this off, a few great quotes about both phenomena that I find thought-provoking or inspiring:

Know someone who might enjoy this newsletter? Please share it with them! It’s the number one way Z-Axis is able to grow.

First time reader? Consider subscribing to this free weekly newsletter by clicking here.