Edge Score Methodology V1

1. “n = 8,656 is a single draw from a fat-tailed population. Findings don't generalize under Hill α = 1.28.”

The paper does not claim universal generalization. Every statistical claim is scoped to the Polymarket profit leaderboard cohort at 2026-04-15 and its out-of-fold structure. V1.5 is planned to replicate the composite on Kalshi and Manifold cohorts once per-position outcome data is available. Until V1.5 ships, the accurate read of V1 is “this is what the leaderboard-filtered Polymarket population looks like,” not “this is what prediction-market skill looks like in general.”

2. “OOF Spearman +0.514 is a point estimate on an infinite-variance target. Confidence intervals are suspect.”

Spearman is a rank statistic. Its sampling distribution is computed over the empirical ranks of the joint distribution, which are bounded by construction. The sampling distribution of Spearman is therefore well-behaved even when the underlying variable (realized PnL) has infinite theoretical variance. Bootstrap confidence bands reported in §5.1 and §5.4 of the paper are on Spearman itself; the paper does not report Pearson correlation, OLS R², or any t-statistic on realized PnL. Parametric moment-based inference would fail under α = 1.28; rank-based inference does not. Spelled out in paper §7.

3. “Survivorship bias. The leaderboard is a positive-profit filter.”

Acknowledged directly in paper §7 as the first limitation. The cohort describes differences among survivors, not expected outcomes for a randomly drawn new trader. Peters (2019) on ergodicity is the relevant reference. V1.5 adds a supplementary cohort of active-but-unranked wallets to measure the selection shift explicitly.

4. “The V3b-over-V1 tiebreaker was tested on the same training cohort. Circular.”

Correct, and acknowledged in paper §5.4 and §7. V3b is the shipped composite because its first feature (baseline-adjusted Brier) is structurally harder to game than V1's raw Brier, not because it has out-beaten V1 in a blinded test. The definitive test is a held-out cohort with deliberately injected market-selection gaming, planned as a V1.5 follow-up experiment. Today, the preference is a principled methodological choice, not a validated empirical one.

5. “The Fama-French bootstrap assumes permutability. Under fat tails, permutations don't preserve the tail structure.”

The bootstrap in §5.6 permutes wallet-PnL labels and recomputes Spearman against the held-out composite. Under the null hypothesis that Edge Score has no association with PnL, wallet-PnL pairings are exchangeable by construction. The permutation distribution preserves the tail structure of the marginal PnL distribution because the operation permutes labels, not values. The tail shape is determined by the PnL marginal and is fixed across every permutation; only the wallet-to-PnL mapping varies. This is the standard Fama-French (2010) protocol applied without modification. Spelled out in paper §7.

6. “Sizing and concentration are endogenous to conviction. You've measured chicken-and-egg.”

Concentration as defined in §3 is the share of realized PnL attributable to the wallet's single largest event. This is a sizing-independent ratio. A wallet that sized uniformly across 100 bets and got lucky on one large winner has high concentration but low sizing; a wallet that sized every bet at $10K uniformly has roughly equal stakes but can have low concentration. The composite does not use total_risked or any capital proxy, precisely to avoid conflating conviction with capital. Endogeneity between concentration and conviction is real but operates through outcome realization, not through model construction.