Favorite-Longshot Bias and Expected Value: Why a 5-Cent Contract Can Be a Bad Bet

The favorite-longshot bias is the empirical tendency for low-probability outcomes to trade above their true probability, while high-probability outcomes trade below theirs. In a prediction market it means a 5-cent contract can be negative expected value even when the story is plausible, and a 95-cent favorite can be positive expected value even when it looks boring. The bias is a starting point, not a trade. The price already contains it, and fees, spreads and your own probability error decide whether any edge is left.

"Longshots are overpriced" is a statement about an average. It does not tell you that the next 5-cent contract is overpriced, and it does not tell you that selling every tail is safe. The useful version is a calculation, not a slogan.

What the bias is

Thaler and Ziemba documented the pattern in parimutuel racetracks and state lotteries in 1988: longshots were overbet relative to their chance of winning, while favorites were underbet. Snowberg and Wolfers later tested two explanations on a large dataset of horse-race bets. Their evidence favored misperception of small probabilities over pure risk-love, the mechanism prospect theory predicts.

The prediction-market version is more recent and more directly relevant. A 2026 working paper by Marcos Cardozo and José Ignacio Rivero-Wildemauwe studied 588 million trades by 2.48 million accounts on Polymarket. They estimate that purchases below 10 cents lost 19.3 cents per dollar, while purchases at or above 90 cents earned 0.83 cents per dollar. That is a two-sided pattern: cheap tails underperform, favorites outperform.

The result is not a universal constant. When each contract is weighted equally, longshots lose 6.3 cents per dollar. When related contracts are first grouped by parent event, they gain 4.1 cents. The pattern is robust in crypto and politics but absent in sports. The weighting choice changes both the magnitude and, in one case, the sign. That is a reason for caution.

The EV arithmetic

Let p be the price you pay, q your probability that the contract resolves Yes, and f the fee per share. Expected value per share is q − p − f. For a taker buy, f = r × p × (1 − p), where r is the category rate.

Take a politics contract at 5 cents. The fee is 0.04 × 0.05 × 0.95 = 0.0019, or 0.19 cents per share. If you believe the true probability is 3%, EV is 0.03 − 0.05 − 0.0019 = −0.0219 per share. On a 5-cent stake, that is a loss of about 44% of capital per bet on average. The break-even probability is 5.19%, not 5%. The fee is only 0.19 cents, but it is 3.8% of the stake.

Now take a 95-cent favorite. The fee is 0.04 × 0.95 × 0.05 = 0.0019, the same 0.19 cents. If the true probability is 97%, EV is 0.97 − 0.95 − 0.0019 = +0.0181 per share, or about 1.9% of the 95-cent stake. The same fee is 0.2% of the stake. The asymmetry is the point: a fixed cent cost is trivial on a large stake and enormous on a small one.

Break-even q is p + f. At 5 cents it is 5.19%. At 95 cents it is 95.19%. If your probability estimate is not better than the market's by more than the fee and the spread, the trade is a donation.

These are hold-to-resolution numbers. If you plan to sell before resolution, the exit price and exit fee matter more than the terminal payoff. If you post as a maker, f is zero, but you bear adverse selection: your bid is more likely to fill when the market is about to move against you.

Why cheap longshots can be negative EV

Three forces keep the bias alive. Probability weighting makes a 1% chance feel larger than one in a hundred, especially when the outcome is vivid. The lottery payoff makes the stake feel small: one cent to make a dollar is a 99-to-1 multiple. And the seller's balance sheet demands compensation. Someone has to hold the other side, which produces many small gains and rare large losses. That negative skew is unpleasant, so the seller charges for it.

The corrective trade is also capital-intensive. To short a 2-cent longshot, you buy No at around 98 cents. You risk 98 cents to make 2 cents, and one loss erases 49 wins. The trade can be positive EV and still be a bad business for anyone with a capital constraint or a risk limit. That is why the bias persists: the people who see it cannot always afford to take it at scale.

The same logic explains why the bias is not a license to buy every favorite. A 95-cent contract with a 96% true probability is negative EV after fees. The claim is relative: favorites tend to be underpriced, not every favorite is underpriced.

Sizing the trade

The Kelly fraction for buying a binary contract at price p with probability q is (q − p) ÷ (1 − p). At p = 0.05 and q = 0.07, the fraction is 0.02 ÷ 0.95, or about 2.1% of bankroll. At q = 0.03, the fraction is negative. The formula says do not bet.

Two qualifications matter more than the formula. First, q is an estimate, not a fact. If your true probability is 4% rather than 7%, the 5-cent trade is negative. Size to the low end of your range, not the point estimate. Second, Kelly assumes independent bets. Longshots in the same event are correlated: a slate of 20 candidates in one election is closer to one bet than 20. Cap event-level exposure separately from contract-level exposure.

A practical rule is fractional Kelly with a hard cap. If full Kelly says 2.1%, use a quarter of that, or about 0.5% of bankroll, and cap the total event exposure at 1–2%. The cap is not a comment on the edge. It is protection against the possibility that the edge is an artifact of your own model.

What the evidence does and does not show

The 2026 Polymarket paper is a working paper, not a peer-reviewed final. Its headline numbers are large and its sample is enormous, but its own robustness checks show that the result depends on how contracts are grouped. The sports exception is important: a trader who applies a horse-racing prior to NFL moneylines is using the wrong prior. The weather study by Shouchen Qiu and Huaijun Qiu, a short 2026 symposium paper, adds another caution. In daily maximum-temperature markets, longshot overpricing is concentrated at distant horizons, while favorite overpricing becomes much stronger in the final hours before settlement. The bias is time-varying, not a fixed tax.

None of this tells you the true probability of a specific contract. The market price is the aggregation of everyone else's estimates, including professional market makers who can see the same research. The bias is a reason to check the tail of the book, not a reason to assume every tail is wrong.

Finally, resolution risk sits on top of probability risk. A contract priced at 1% that can resolve 50/50 under an ambiguous rule is not a 1% risk. A contract that can be voided is not a binary bet at all. The expected-value formula assumes the payoff is $1 or $0. Read the rule before you trust the arithmetic.

The defensible conclusion is narrow. The favorite-longshot bias is one of the better-documented patterns in betting markets, and the 2026 Polymarket evidence suggests it has not disappeared. But the tradable version requires a probability estimate that is better than the market's by more than the fee, a price that is actually executable, a resolution rule that pays $1 or $0, and a position size that survives being wrong. Without those four things, the bias is an explanation of why the ticket looked cheap, not a strategy.