Calibration of Polymarket prices against 6,776 resolved markets

Prediction-market prices are good probability estimates on average, and that held in this sample. The question was whether they bend in a repeatable way. Vultax assembled 6,776 resolved Yes/No Polymarket markets with known outcomes, fit a mapping from market price to resolved frequency, and scored it on held-out markets with the Brier score. The calibrated mapping improved the held-out Brier score from about 0.0352 to 0.0319, a gain of roughly 9.6% over raw prices. The gain sat at the ends of the price range, where long shots resolved less often than their price and near-certainties slightly more often, the favourite-longshot pattern described in the literature. A second check, added in October 2026, read 9,132 markets a day before they closed, July to September 2026, and found the same shape. The study also shows how a volume floor can invent a bend: football contracts at 10 to 30 cents a day before kick-off came true 32.5% of the time when only markets with $50,000 traded by close were kept, and 24.1% when every market of each match was counted, because upsets draw trading during the match. The study says what the model cannot do. The improvement is an average over thousands of markets; it does not say which market is mispriced today, and after spreads and fees the small dislocations are rarely worth trading. Files: the page at https://vultax.com/research/prediction-market-fair-value-calibration as a research note (PDF) and page (HTML, PDF) on 27 October 2026, the study's calculation-proof record, and a CITATION.cff.