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.

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.