Meritocracy’s Standard Deviation: Why Small Variance Swings Create Giant Outcome Gaps
We have a strange, unspoken consensus that the world of human talent operates like the world of human height. In any given room, most people are of roughly average height, with a few outliers on either end. The distribution follows a satisfying, symmetrical bell curve—a Gaussian distribution. We intuitively feel that ability, intelligence, and effort should follow a similar pattern. If you’re 10% taller than someone, you’re about a foot taller. If you’re 10% “smarter” or “more talented,” what should the outcome gap be? Our brain defaults to a linear scale: perhaps a 10% higher salary, a slightly nicer car.
This intuition is profoundly, mathematically wrong. And in that error lies the key to understanding the brutal inequality of outcomes we see in markets, creative fields, and corporate hierarchies.
What if the world isn’t Gaussian? What if it’s log-normal?
This isn't just an academic distinction. It's the difference between a world where a little more talent gets you a little more reward, and a world where a little more talent gets you all the reward. It’s the hidden engine behind meritocracy’s staggering Gini coefficient.
The Tall-and-Talented Paradox
Think about it this way. The difference in height between an average man (5'10") and a very tall one (6'6") is about 12%. The difference between an average NBA player (6'6") and the league’s tallest player (say, 7'4") is also about 12%. The physical variance is constrained.
Now, consider talent. Let’s say CEO A is 10% more effective at capital allocation and strategy than CEO B. Does she earn 10% more? No. She might earn 10,000% more. A startup founder who executes 5% better than a competitor doesn’t capture 5% more of the market. They capture all of it. The winner-take-all dynamic isn't an anomaly; it's the natural result of compounding advantages.
This is where the log-normal distribution comes in. A variable is log-normally distributed if its logarithm is normally distributed. Forget the jargon; the concept is simple. It describes processes of proportionate growth. Think of a bacterial colony. Each bacterium splits, and the growth is proportional to the current size of the colony. The same is true for investment returns; your gains compound based on your current principal.
Human talent, in a competitive system, behaves much the same way. A slight edge in ability or insight allows you to seize an opportunity. That success gives you more resources (capital, reputation, network), which allows you to seize bigger opportunities. The effect isn't additive; it's multiplicative.
Kahneman's Luck and the Multiplier Effect
Nobel laureate Daniel Kahneman has spent a career dismantling the myth of unerring expert judgment, often highlighting the enormous role of luck in outcomes. In his book Thinking, Fast and Slow, he notes that "the illusion that we understand the past fosters overconfidence in our ability to predict the future."
We look at a billionaire CEO and construct a narrative of pure genius because the outcome is so extreme. But Kahneman’s work suggests a different story. Success is a combination of skill and luck. Crucially, a lucky break early in a career—getting funded, landing a key client, joining the right company—isn't a one-off payment. It’s an injection of fuel into a compounding engine. It places you on a slightly higher growth trajectory, and over decades, that tiny initial divergence creates a chasm.
A 5% advantage in skill, combined with a lucky break, doesn’t equal a 10% better outcome. It multiplies, and the result is an order of magnitude larger.
From Theory to Tax Receipts: The IRS Data
If this theory is correct, we should see it in the data. And we do. The income distribution in every developed country on earth is not a bell curve. It’s a grotesquely skewed log-normal (or more accurately, a Pareto) distribution.
According to the IRS’s most recent detailed data, the top 1% of earners in the United States capture over 20% of the adjusted gross income. The top 0.1%? They take home nearly 10%. Go even further, to the top 0.001%, and you’ll find a few thousand families with an average income in the hundreds of millions.
This is not a Gaussian outcome. In a bell-curve world, the highest earner might make ten or twenty times the median. In our world, they make tens of thousands of times the median. This isn’t a moral failing; it’s the mathematical signature of a multiplicative, compounding system. Classic economic models of wages, like those developed by Robert Gibrat in the 1930s, recognized this, proposing that worker income grows proportionally year over year, naturally leading to a log-normal distribution.
Redefining Meritocracy
This brings us to a stark conclusion. Our modern concept of meritocracy is built on a statistical illusion. We search for god-like talents to justify god-like incomes, assuming a linear relationship between input and output.
But the system isn’t linear. It’s a multiplier machine. A small standard deviation swing in initial talent or luck produces a gigantic, almost incomprehensible gap in final outcomes. The person who is 5% better is not the person who gets 5% more. They are the person who gets almost everything.
This doesn't mean merit is irrelevant. That initial 5% edge is very real and very important. But we are psychologically unprepared for its consequences. We see a 1,000x outcome and look for a 1,000x cause. There isn't one. There is only a small cause, relentlessly compounded. The real standard deviation is in the process, not the person.
