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.