the paradox of skill<br>the paradox of skill<br>May 21, 2026 • 14 min. read
when i came across this concept of the paradox of skill, it resonated. not sure if this is my imposter syndrome or sense of jealousy talking, but sometimes, i feel like my own professional accomplishments (e.g. like getting accepted into YC) and those of others around me, are increasingly influenced by luck, even though the people surrounding me have gotten more talented. this concept gave me an intuitive framework to explain that. let me start with a hypothetical:
let's say you're hiring for a role, and you have a pool of candidates who have applied. naturally, you want to find the most skilled person amongst the candidates and offer them the job. to find them, you devise a series of assessments and interviews that test for the skills you care about. after administering these tests, you would expect the best person for the job to be the one that measures the highest on the tests. of course, this is not the case if the evaluations are poorly designed, but let's assume for the sake of argument that they are. then, you should be able to identify the best candidate, but — and this is the subtlety — reliably doing so depends on the distribution of skill across that pool.
for example, if the size of your pool was two, and candidate A was much more skilled than candidate B, then your testing scheme should easily identify candidate A as the superior one. but if candidate A only had a slight edge over candidate B, then it would be much harder to isolate that. why? well, it's partly because the tests themselves are not perfect. you can improve your methodology, but you can never eliminate all the error. so it's also because as the skill levels get closer, the outcome becomes more effected by that error, or noise--the randomness that impacts measurement, e.g. the interviewer's mood that day, getting asked an obscure question, etc.
this is the phenonmenon that is known as the paradox of skill:
as the skill level of a group increases, the outcome of any competition among them becomes more dependent on chance, and less a function of skill.
this is because as skill levels get closer, the noise in the measurement becomes more significant relative to the differences in skill. this concept was popularized by Michael Mauboussin (author of The Success Equation, a good read), and even though it's stated in terms of increasing skill, it applies just as well to any situation where the distribution of skill becomes more compressed, e.g. if the skills levels are all very low, then the outcome is also influenced more by chance. but in the real world, this effect is more interesting with rising (not falling) average performance, so that's the context i'll focus on.
demonstration
i'm sure there's a way to ground this idea in statistical theory, but i don't have the chops to do that. instead, i'll explain it with some fun simulations.
let's switch to a simpler example: a freethrow shooting contest. it works like this: each player gets 100 shots, and the one that makes the most shots, wins. easy. let's look at a single participant, player A. we can model their performance as a normal distribution, where the mean (μ) is the average number of shots they make in 100 attempts, and the standard deviation (σ) measures how much their performance varies across games.
Mean (μ)75<br>Standard deviation (σ)5.0
when you have multiple players, each will have their own normal distribution. for our first scenario, let's pick four players with widely varying skill levels (e.g. from a casual shooter to an elite one).
Player A (μ=55, σ=5)Player B (μ=68, σ=5)Player C (μ=80, σ=3)Player D (μ=87, σ=4)
in this case, the distributions are nicely separated, i.e. the skill levels are spread out. if you were to repeat the same contest among these players over and over again, you'd expect player D to win most of the time, player C to win some of the time, players A and B to win rarely. in other words, the outcome would mostly be determined by skill. we can verify this by running a simulation of 1000 games:
Run<br>Player A
Player B
Player C
Player D
you'd be hard pressed to find a scenario where player D doesn't win the majority of games by a large margin.
now let's consider what happens when the player distributions are closer together.
Player A (μ=84, σ=4)Player B (μ=86, σ=4)Player C (μ=88, σ=4)Player D (μ=90, σ=4)
the ranking of players by skill is unchanged (player D still has a higher average than player C, who has a higher average than player B, etc.), but now the curves overlap heavily, with the means bunched between 84 and 90. what happens when we run the same simulation of 1000 games?
Run<br>Player A
Player B
Player C
Player D
players D still wins most of the time, but now player C wins a lot more often, and players A and B also win a non-negligible number of games. this is intuitive but also strange at the same time...why is there more randomness in the outcome, even...