Testing "always pick the favorite" — and why a Monte Carlo can't do it

2026-08-12. calibration_test.py, 6,937 REG games, 1999–2025.

The question that was actually asked

"Can we test always-favorite with a 30-person Monte Carlo?" Yes for one claim, no for the other, and they are constantly conflated:

Why Monte Carlo cannot test the first claim

Expected points is Σ cᵢ·pᵢ where c is the confidence permutationpermutation testRandomly shuffling the labels thousands of times to see what results pure chance produces, then checking whether the real result stands out from that. 1..N and p is P(your pick wins). Maximizing it is closed-form:

1. Per game, pᵢ is maximized by taking the side with p > 0.5 — the favorite.
2. Across games, Σ cᵢ·pᵢ over permutations of c is maximized by pairing the largest c with the largest p — the rearrangement inequality.

So a simulation that draws outcomes from devigged market prices will find that always-favorite wins by construction. It recovers a theorem and says nothing about the NFL. Any Monte Carlo that "confirms" always-favorite here is re-reporting its own generator.

That leaves exactly two ways the strategy can be wrong, both empirical:

• A. Miscalibration — a bucket where favorites win less than the price implies, and specifically less than 50%. The only way the picks are wrong.
• B. Non-monotonicity — win rate not increasing in spread magnitude, so the ordering is wrong even when every pick is right.

Result: both hold. The strategy survives.

B — the ranking is right (no inversions)

Strictly monotonemonotoneConsistently moving one direction as the input increases. A real dose-response effect should be monotone; if more of the cause does not mean more of the effect, the pattern is suspect., zero inversions. SpearmanSpearman correlationA measure of whether two rankings agree, from -1 (opposite) through 0 (unrelated) to +1 (identical). Cares about order, not exact values.(spread_mag, fav_won) = +0.2179 (p = 2.4e-75). Season-clustered bootstrapbootstrapRe-running a calculation on thousands of resampled versions of the data to see how much the answer wobbles. The spread of those answers becomes the confidence interval.; BH-FDR across buckets.

Era split (1999–2012 vs 2013–2025): overall favorite win rate 66.58% vs 66.44%, one trivial inversion early (53.4 → 53.1) and none in the modern era. The ordering is not an artifact of a bygone market.

A — the price is calibrated

Devigged closing moneyline, 5,061 games (2006–2025):

• Multiplicative: implied 66.78% vs actual 66.33%, err −0.45pp, CI [−1.91, +0.99]. No bucket miscalibrated.
• Shin: implied 67.65% vs actual 66.33%, err −1.32pp, CI [−2.77, +0.10].

Buckets where flipping gains points: NONE. No CI upper bound falls below 50%.

Two honest caveats

The one "miscalibrated" bucket is probably noise. Shin's 0.6–0.7 bucket shows −3.28pp, CI [−6.09, −0.30] — an upper bound grazing zero, in 1 of 10 bucket×method tests, with no FDRfalse discovery rateA method for handling many simultaneous tests, controlling what share of your "discoveries" are expected to be flukes. correction applied to the calibrationcalibrationA deliberate sanity check on the method itself: run it on something already known to be true. If it fails to detect the known thing, the method is broken and its other results mean nothing. buckets. The same bucket under multiplicative devigdevigRemoving the bookmaker's cut from odds to recover the market's actual implied probability. is −1.86pp, CI [−4.76, +1.23], i.e. not significant. A result that appears under one devig and vanishes under another is a property of the devig, not the market. Do not trade it.

For NFL sides, Shin over-corrects. Shin implies 67.65% where the market delivers 66.33%; multiplicative implies 66.78%. This is narrower than [[osint_market_signal_2026_08]]'s general warning that multiplicative manufactures fake longshot edges — true for deep longshots, but NFL moneylines are not deep longshots, and here Shin's favorite-longshot correction pushes past calibration. Prefer multiplicative for NFL sides specifically.

The one result that changes something

The bottom game is a coin flip, so the pool flip is nearly free. The 0–1.5 bucket wins 51.5% [46.9, 56.0] — the only bucket that does not beat a coin flip, and 49.4% in 2013–2025 alone. Flipping it to the dog at confidence 1 costs

(0.515 − 0.485) × 1 point = 0.03 points per week ≈ 0.5 points per season

against a ~1,580-point baseline. That is a rounding error, and it independently justifies the flip-candidate highlight added in 62fd95f: the deviation the pool sim recommends is the one the market says is cheapest to make. Two separate analyses landing on the same game is a real convergence, not a coincidence — both are keying on the same thing, that the market has no opinion there.

What is still untested

The pool Monte Carlo's rival model is assumed, not measured. K (rival skill) is swept 0→50 rather than estimated, because nobody has the field's actual picks. The unresolved anomaly from FINDINGS_POOL_2026.md stands: a reported ~1,100 winning score is below the 1,263 floor produced by 29 literal coin-flippers, and matches the coin-flip field mean (1,111) instead. Until the real leaderboard is checked, every pool-level P(win) number is conditional on a rival model that one data point contradicts.

That is the highest-value remaining measurement here, and it costs one screenshot of the standings rather than any compute.