Week 9: Distributions

Repeat supplied interruption and weather draws to produce two complete finishing-position distributions and a fair paired comparison

3 May 2027

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Last week we evaluated a finite set of forecast paths exactly. This week we sample repeated interruption and weather scenarios, then preserve where each strategy finishes across the resulting trials.

A trial is one sampled interruption-and-weather scenario passed through the supplied deterministic outcome map. Monte Carlo repeats that operation and summarises the resulting sample. Our output is a finishing-position distribution: a probability for every valid place from P1 to P8, including places with zero finishes. A count total must equal the number of trials, and the probabilities must sum to one.

The comparison has another constraint. On each trial we draw one interruption value and one weather value, then pass that same pair to both strategies. This is common random numbers: one generated scenario, two counterfactual strategies. If A receives easier scenarios than B, their difference includes different luck. Shared draws remove that within-pair mismatch. They do not make a finite sample noiseless, and they do not guarantee a less variable comparison in every model.

We validate the strategy records, the synthetic thresholds and the physical-set ledger before the first draw. Then a supplied seeded wrapper makes the pseudo-random sequence reproducible. The wrapper is test machinery; we do not build a generator or claim its sequence represents real Formula 1 uncertainty.

The paired result answers one narrow question: how often did A beat B on the shared trials? It does not replace A’s distribution or B’s distribution. Lower finishing position wins inside each pair; adjusted finish breaks only a same-position tie. Every threshold, outcome and probability in this week’s fixture is synthetic and uncalibrated.

The final instrument must publish the full distributions and the assumptions beneath them. The live race uses one cohort-wide draw so that every alternative faces the same sampled race. This week makes that shared luck readable. Later weeks decide whose objective ranks the alternatives, what reaches the wall and whether stated probabilities deserve belief.