Prices, Probabilities, and Parlays: Systematic Bias in Sports Prediction Markets

2026-07-15

AI Summary

Prediction markets often treat prices directly as probabilities, yet systematic biases persist in practice. Drawing on 23 million sports-related trades from the Kalshi platform, this study employs time-stratified calibration models, fits Prelec probability weighting functions, and compares prices across single- and multi-leg parlays to uncover two key findings: first, calibration bias evolves dynamically with time to expiration, exhibiting a step-like convergence near settlement; second, multi-leg parlays display a systematic premium independent of single-leg calibration, with the premium increasing monotonically with the number of legs. These results underscore that accurate probability estimation in prediction markets must jointly account for time to expiration and contract structure, offering new empirical evidence and a refined framework for understanding market pricing mechanisms.

Abstract

Prediction market prices are routinely interpreted as probabilities, both in academic work and in derivative products built atop these markets. We document two systematic ways this interpretation fails on Kalshi, a major U.S. event-contract exchange, using 23 million moneyline trades across major sport leagues. First, calibration, the agreement between quoted prices and realized event frequencies, is not a static property of a contract: fitting calibration models within time-to-expiry buckets, we find that parameters sit at their perfect-calibration reference values in the middle of a contract's life but depart sharply as expiry approaches. In the final ten minutes before settlement the empirical calibration curve becomes step-like, fitting a Prelec form with curvature parameter well above one, the opposite sign of the canonical lottery-choice fit, consistent with insurance-demand behavior by traders holding losing positions. Second, cross-game parlays on Kalshi are systematically overpriced relative to the product of their contemporaneous leg prices, with overpricing growing in leg count. This holds when the parlay legs are drawn from the TTE regime in which leg-level calibration is essentially perfect, indicating a separate, market-level markup at the parlay-pricing stage. Both deviations are systematic and therefore admit computational correction. Practical use of prediction-market prices as probabilities requires conditioning on time to expiry and on product type, not on price alone.

Problem

• prediction markets
• calibration
• parlays
• systematic bias
• time-to-expiry

Innovation

• prediction markets
• calibration
• time-to-expiry
• parlays
• systematic bias