Luck contribution
Avg. teams
Seasons analyzed
Observed variance
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A Statistical Analysis of Sports Performances

Luck vs Skill

From the NBA to eSports — using Classical Test Theory and Monte Carlo simulation to quantify how much of winning is skill, and how much is just chance.

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Sports
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Seasons
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Simulations
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When a team wins a championship, how much of that victory was earned through superior skill — and how much was simply the roll of the dice?

The Continuum

Where Each League Falls

14 sports across traditional leagues, motorsport, and eSports — each positioned by their luck contribution. Hover to explore.

Pure Skill Pure Luck
0% 25% 50% 75% 100%
Methodology

Classical Test Theory

We decompose every observed outcome into its constituent parts — the skill that teams bring and the luck that fate deals. Extended to eSports with Monte Carlo simulation.

The fundamental equation
Observed = Skill + Luck
σ²obs
8.69
=
σ²skill
4.70
+
σ²luck
3.99
NFL 2010 season example
1

Measure the real world

Calculate the variance of actual point distributions across all teams in each league season.

2

Simulate pure luck

Run 100 simulations per season where every game is a coin flip — no skill differences exist.

3

Compare the variances

The ratio of simulated (luck) variance to observed variance reveals luck's contribution.

4

Average across seasons

Aggregate results over 9–23 seasons per sport to get robust, reliable estimates.

The Evidence

Real Season vs. Pure Luck Simulation

When skill matters, real seasons show clear hierarchies. In a luck-only world, points cluster near the average.

Observed Results
NFL 2010 — Variance: 8.69
Simulated (Luck Only)
NFL 2010 — Variance: 3.99
League Profiles

Deep Dive Into Each League

Explore the statistical fingerprint of every league analyzed.

Pattern

Does Season Length Reduce Luck?

Intuitively, more games should let skill shine through. The data largely supports this — with some notable exceptions.

Luck Contribution (%)
Games / Matches / Races per Season
Insights

Why These Differences Exist

The Selection Filter

Basketball rewards extreme height, shrinking the talent pool. With fewer viable candidates, the skill gap between teams narrows — making the NBA the most skill-driven league.

Sample Size Matters

The NBA plays 82 games per season while the NFL plays only 17. Fewer games mean less opportunity for skill to separate from noise — raising the NFL's luck contribution.

Money Talks

Leagues without strict salary caps (like European football) let wealthy clubs hoard talent. This amplifies skill differences — lowering apparent luck in leagues like the Premier League.

eSports: Digital Meritocracy

LoL (23% luck) is more skill-driven than MLB or La Liga. Structured league formats and best-of series help the best teams rise. Dota 2's higher variance (34%) reflects its comeback mechanics.

The Bigger Picture

The Complete Luck–Skill Continuum

Sports exist on a vast spectrum. Here's how our leagues compare to activities at the extremes.