EVERY SUNDAY,
FIFTY THOUSAND
TIMES.
A projection is one guess. A distribution is every guess, weighted. Each streak below is one simulated world falling into place — the histogram isn't drawn, it's earned, one Sunday at a time.
THE MEAN IS EARNED SLOWLY. THE TAIL IS EARNED NEVER.
The law of large numbers is patient: after a few hundred worlds the running mean still swings like a compass near a magnet; after fifty thousand it has settled to within a rounding error of the projection. That's why SimSlate never trusts a small sample — a thousand sims will lie to you about a player's mean, and lie worse about his ceiling.
But watch the p99 line. It never settles the way the mean does — tail estimates converge at a fraction of the rate, because worlds that far out arrive once in a hundred Sundays. The rarer the event, the more worlds you owe it. Fifty thousand is the rent we pay to see the tail clearly.
WORLDS FALL IN PAIRS — THE COPULA TETHER.
A quarterback and his receiver do not live in separate universes. When the passing game erupts, both erupt — one touchdown is two stat lines. SimSlate draws every player's world from a Gaussian copula: correlated normal scores under the hood, each mapped back onto its own fitted marginal so no player ever loses his personal distribution.
Drag the tether. At ρ = 0 the pair rains independently — a great QB world says nothing about the WR. At ρ = 0.62 (a real same-team stack value) the streaks start falling together: ceilings arrive in bundles. That bundle is why stacking wins tournaments — you're not betting on two events, you're betting on one.
THE INSTRUMENT.
Observatory hardware, as flown in production. Nothing on this page is a mockup of the engine — the rain above runs the same inverse-CDF sampling the real simulator uses.