False genius simulator

A leaderboard selects the records most favored by both skill and luck. When many equally capable forecasters are ranked after a finite sample, some must appear exceptional. A fresh out-of-sample period reveals how much of that apparent excellence persists.

No bankroll or staking system is being compared. Every forecaster makes the same number of one-unit predictions at the same odd. The experiment isolates selection, multiple comparisons, and regression to the mean.

Practical analysis: Odds.school.

Population and evidence

Forecasters Predictions per period Select the top Decimal odd Ordinary true EV (%) Genuinely skilled (%) Skilled true EV (%) Random seed

True win probability is derived from EV and the common odd: p = (1 + EV) / odd. A selected record is never used to alter the forecaster's true ability in period 2.

In-sample brilliance versus fresh evidence

Reveal genuine skill

ordinary forecaster selected period-1 star genuine skill, when revealed selected and genuinely skilled

Each dot is the same forecaster in both periods. Horizontal position is the result used to select the stars; vertical position is independent evidence that selection did not see. A stable skill signal forms a diagonal relationship. Pure luck forms a cloud.

The selected stars

Period-1 rank	Period 1 ROI	Period 2 ROI	Period-2 rank	True EV

The final column is information available to the simulator, not to a real observer. It is shown so that a strong-looking record can be compared with the ability that actually generated it.

Interpretation: regression to the mean does not prove that skill is absent. It proves that selecting extreme past results also selects favorable noise. A track record becomes stronger evidence when it persists out of sample, over a sufficiently large number of independent observations, under a credible model of the population.