The favourite–longshot bias in event contracts

The regularity#

The favourite–longshot bias (FLB) is one of the oldest empirical results in the economics of betting: in horse-race pari-mutuel markets, horses with long odds win less often than their odds imply and heavy favourites win slightly more often. Snowberg and Wolfers (2010), using a large data set of US races, show that the bias is large at the extreme tail. Bets on the longest shots lose a far larger fraction of their stake on average than bets on favourites.

Prediction markets share the payoff structure and much of the participant psychology, and studies of exchange-traded event contracts report related patterns: compression of prices toward the middle in some categories, overpricing of cheap contracts in others. A 2026 study of Kalshi and Polymarket contracts (arXiv:2602.19520) decomposes calibration by domain, horizon and trade size and reports that prices in politics are often compressed toward 50%. The lesson for a practitioner is not "the tails are always mispriced", but that a raw price is a biased probability estimate whose bias depends on context.

Two families of explanation#

Risk-love. If bettors are risk-seeking, they accept a lower expected return on high-variance bets, so longshots (the highest-variance bets) are overbet. This is a preference story: prices are "wrong" as probabilities but right as utilities.

Misperception. If bettors overweight small probabilities, as in prospect theory, they overvalue longshots because they think a 2% chance is closer to 5%. Snowberg and Wolfers distinguish the two using exotic bets (exactas, trifectas), whose prices the two theories predict differently, and find the evidence favours misperception.

Two further mechanisms are specific to exchange-traded event contracts:

• Capital asymmetry. Correcting an overpriced 4¢ longshot requires selling it, which on most venues means buying No at 96¢. That ties up 96¢ of capital per contract to earn 4¢ minus the true probability, a poor return on capital for anyone with alternatives. Arbitrage capital is scarce exactly where the bias is largest.
• Fees and carry at the tails. Covered in the last section; both widen the band inside which mispricings are not worth correcting.

A probability-weighting model#

Suppose the marginal participant setting the price values a Yes contract by the Prelec (1998) weighting of its probability,

and values No symmetrically. Normalising so that Yes and No prices sum to one gives

With $\alpha =1$ the market is calibrated ($P=p$). Smaller $\alpha$ means stronger overweighting of small probabilities. The expected return per dollar for a Yes buyer is $p/P-1$.

Reading the table#

A mild distortion is enough to produce large percentage losses on longshots. The price error at 2% is only about 2 points (4.1¢ against 2%), but it is a 100% overpricing in relative terms, and a buyer loses half their stake on average. On the favourite side the error is a few points of underpricing on a large stake: buying the 95% side at 92¢ returns about 3% per dollar before costs.

That asymmetry explains why the bias persists. The profitable side is the one that needs the most capital per unit of expected profit, and the 3% must be earned over the time to resolution. For a contract three months out, 3% is roughly 12% annualised before fees, which is attractive. For a contract a year out, it barely beats a money-market fund once fees are paid. The bias should therefore be strongest in long-dated contracts, which is consistent with what practitioners report.

Implications for pricing#

• Never use raw tail prices as probabilities. A 3¢ quote on a low-attention contract is evidence for a true probability nearer 1–2%, unless your own calibration history says otherwise.
• Calibrate per category and horizon. The bias is not one number. Fit a recalibration map (isotonic regression or a two-parameter weighting like equation (1)) on your own resolved history, separately by domain and time to resolution. Our calibration note covers the scoring side.
• Account for the capital cost of the correcting side. Expected return per dollar is the wrong ranking metric when one side ties up 25 times the capital of the other. Use return on capital per unit time.

Estimating the bias on your own data#

The model above is for intuition. In practice the correction is estimated from resolved contracts. The simplest robust approach is a logistic recalibration of market prices:

fitted by maximum likelihood on (price, outcome) pairs taken at a fixed horizon before resolution. A slope $b>1$ means prices are too compressed toward 50% (the market is underconfident); $b<1$ means prices are too extreme at both tails, the signature of a favourite–longshot bias. The intercept $a$ captures any overall tilt toward Yes, which matters in markets where participants systematically prefer to buy Yes.

import numpy as np
from scipy.optimize import minimize
def fit_recalibration(P, y):
    x = np.log(P / (1 - P))
    def nll(t):
        q = 1 / (1 + np.exp(-(t[0] + t[1] * x)))
        return -np.sum(y * np.log(q) + (1 - y) * np.log(1 - q))
    return minimize(nll, [0.0, 1.0]).x   # (a, b)

Three practical cautions. Fit separately by category and horizon, because the bias is not one number. Use one observation per contract per horizon, or account for repeated observations, as with clustered questions. And never fit on the last trade before resolution: by then most contracts are near 0 or 1 and the fit is dominated by trivially easy cases. Equation (3) is also equivalent to the Prelec model of equation (1) in the tails when $b\approx \alpha$, so a fitted slope of about 0.85 corresponds to the mild distortion tabulated above.

Limitations#

The model is a one-parameter caricature: a single representative price-setter and symmetric weighting of Yes and No. Real prices are set by a mix of participants, including market makers who are not subject to probability weighting at all, and the observed bias is the outcome of that mix plus the capital and fee frictions above. We use the model to size the effect and to show how small distortions in probability become large distortions in return, not to estimate $\alpha$ for any venue.

Questions#

References#

1. Snowberg, E. and Wolfers, J. (2010). Explaining the favorite–long shot bias: is it risk-love or misperceptions? Journal of Political Economy, 118(4), 723–746.
2. Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527.
3. Wolfers, J. and Zitzewitz, E. (2004). Prediction markets. Journal of Economic Perspectives, 18(2), 107–126.
4. Decomposing crowd wisdom: domain-specific calibration dynamics in prediction markets (2026). arXiv:2602.19520.

DisclosureThis note is research and education. It is not investment advice or an offer to trade, and nothing in it describes the firm's own results. Code and outputs: research/flb.py in our research repository, reproducible with a fixed seed.