The Uneven Shape of Change
How power laws, not averages, reveal the real drivers of risk, growth, and influence
Most of us are taught to think in averages. Average cost. Average returns. Average customers. Average outcomes. We’re told that being above average is “good enough.” And when we think about things such as economic development, business, or progress, we often frame it through that same lens.
But averages can be misleading. Imagine an aid worker in a food-insecure region telling a child, “On average, children here are not hungry.” That average hides the very real suffering of individuals.
The problem is that in politics, economics, and business, many of the most important dynamics don’t follow neat averages. They follow power laws.
And if you’re involved in economic development, leading a company, or navigating a complex career path, understanding this pattern can transform how you perceive risk, success, and influence. It’s the first step toward becoming more effective.
What Exactly Is a Power Law?
In statistics, the shape of how outcomes are spread is called a distribution. Some shapes (like the bell curve) suggest most people cluster around the average, while others, like a power law, suggest a few dominate and most will barely register.
A power law distribution describes those situations where a small number of things account for a very large share of the results. It underlies the famous 80/20 rule, where 20% of inputs drive 80% of outcomes.
But power laws run deeper than productivity insights: they explain why a handful of companies dominate markets, why in geopolitics a few nations can reshape the international system, and why a single decision can alter the trajectory of an entire career.
Formally, the probability of an event scales with its size raised to a power of a negative exponent. To put that in plain English: big outcomes are rare, but not as rare as a simple average would suggest. That’s why blockbuster movies, billionaires, or viral posts on social media appear more often than intuition based on averages would predict. It also explains why the same few business books appear on the airport bookshelves, no matter where you are in the world — a power law of publishing in action.
Where Did the Power Law Come From?
The idea goes back to Vilfredo Pareto, the Italian economist and sociologist, who in 1896 noticed that 80% of Italy’s land was owned by 20% of the population. This observation became known as the Pareto Principle.
Mathematicians and statisticians subsequently formalised this into power law distributions. Unlike the bell curve (normal distribution), where things cluster around the middle, power laws describe systems where the “tails” — the extremes of the distribution — dominate.
Power laws appear across disciplines:
Physics and statistics: Benoît Mandelbrot (the father of fractal geometry) used power laws to explain complex patterns in finance and nature.
Computer science: They describe the size of networks (Why a few websites get most of the clicks).
Economics and business: They reveal why most startups fail — but a few flourish and become unicorns.
The “power” in power law reflects mathematical scaling, not just influence.
Why Power Laws Matter
Once you know how to look, it will become more apparent that power laws are everywhere:
Business: A handful of products or people generate most of the profits. This means we should focus our energy on these vital few.
Markets: Just a few firms dominate the major indices. Understanding their scale and network effects is key.
Politics: A small number of regions, donors, or voter blocks can swing outcomes. We should find the leverage points.
Media: A few voices or stories capture most of the attention. So we should build our presence where it counts.
Wealth: A tiny group holds outsized capital. We should expect feedback loops that reinforce inequality.
Example: The Hollywood Film Industry
Hundreds of thousands of actors exist; everybody believes they are going to make it big if they move to Hollywood, but only a tiny handful consistently land blockbuster roles. The most famous directors attract disproportionate funding and attention. Producers with the right track records get to greenlight the biggest projects. But the rest are most often left to fight over the scraps in the long tail of B movies and direct-to-video.
Yes, it's not “fair,” there is lots of talent out there yet to be discovered. But it’s not random either. What's happening here is the power law in action. Power laws emerge from feedback loops: success attracts more success, attention begets attention, and wealth creates more wealth. Systems tend to reinforce themselves. It’s not that some are predestined to make it. Rather, small and sometimes random breaks get amplified through reinforcing loops, so the system magnifies differences over time.
Power laws often dominate outcomes: a small number of products, firms, voters, stories, and wallets drive a disproportionate share of results. So we should prioritise the vital few.
What It Means for Your Career
Careers are not distributed like school grades; they rarely follow a neat bell curve.
In a bell curve world, steady effort ensures steady returns.
In a power law world, positioning, leverage, and visibility tend to matter more than raw effort.
Opportunities, recognition, and resources tend to compound: success attracts further success, and small advantages can scale into outsized rewards.
While some industries (e.g., civil service, mid-level corporate roles) may have more bell-curve-like distributions, a lot of the time this is not the case. In many fields, a handful of projects, relationships, or opportunities can drive the majority of career growth.
That means it makes sense to:
Focus where the leverage is—don’t spread effort evenly.
Build a unique edge to avoid being interchangeable.
Recognise tipping points: moments when one opportunity can shift us into the head of the curve.
Being better than the average colleague may mean you keep your job, but the few who learn to play at the head of the curve capture the majority of rewards.
In a power law world, effort is necessary but not sufficient. What really shifts careers is being in the right place, on the right project, at the right time — where small wins can scale into outsized rewards.
Change Under the Power Law: Rare but Radical
Change in power law systems does not happen gradually. It comes in spikes. Most meetings, projects, or hires may matter little. But a single high-leverage hire, breakout product, or bold strategic move can redefine the game. This is the realm Nassim Taleb calls the Black Swan—rare, unpredictable events that carry massive impact. Recognising that most change comes from these outliers is essential for navigating uncertainty.
Politics tends to work the same way: there are long periods of quiet, punctuated by revolutions, reforms, or shocks. As Lenin (often cited) observed:
“There are decades where nothing happens; and there are weeks where decades happen.”
That is not to say that what we do every day is not important; rather, the insight is knowing that most activity is noise, but a few moments can be significant.
Insight for Leaders
In a power law world, effective leadership requires:
Prioritise leverage – allocate energy where outsized returns are likely.
Watch the long tail – outliers often matter more than averages.
Guard against fragility – reliance on a few dominant elements increases systemic risk.
Reframe failure – most bets won’t pay off; one success can offset many setbacks.
Design for tipping points – create conditions that allow success to compound until breakthroughs occur.
Power, Systems, and Distribution
Power laws intersect with political economy, inequality, and legitimacy. When wealth or influence gets too concentrated, backlash tends to follow. But redistribution and regulation aren’t just ethical; they are also mechanisms to keep systems from breaking. What the power law world gives, it can also take away.
Implications for leaders:
Understand your position in larger systems.
Anticipate political and public responses to concentration.
Think systemically, not in silos.
Final Thought
The “average case” is comforting, but it is also misleading. In reality, most things don’t matter much, and a few things matter a lot. Intuitively, if we open a newspaper with this in mind, this makes a lot of sense.
By spotting the vital few, while ignoring the trivial many, and preparing for disproportionate change, leaders gain an edge.
In a world defined by outsized events and asymmetric returns, power belongs to those who understand the shape of the system and then act accordingly.