Longshot Bias in Prediction Markets: Why Cheap Tails Are Usually Overpriced

Longshot bias is the tendency of very low-probability outcomes to trade above their true probability. In a prediction market it looks like a 2-cent contract that should be 1 cent, or a 97-cent favourite that should be 98. The pattern is one of the best documented in betting markets. It is also one of the easiest to trade badly, because the payoff is deliberately skewed and the variance can hide a losing strategy for a long time.

The bias is not a signal by itself. It tells you that cheap tails are often overpriced on average. It does not tell you that any particular 2-cent contract is overpriced, and it does not tell you that selling it is safe.

What the evidence actually shows

Thaler and Ziemba documented the favourite-longshot bias in parimutuel racetrack betting and state lotteries: longshots were overbet relative to their chance of winning, while favourites were underbet. The pattern implies that a bettor who consistently backed favourites earned a better return than one who backed longshots, before considering the track's take.

Snowberg and Wolfers tested two explanations for the same pattern using a large dataset of win, exacta, quinella and trifecta bets. They asked whether the behaviour was consistent with risk-loving gamblers or with misperception of probabilities. Their evidence favoured misperception, in the direction predicted by prospect theory: people overweight small probabilities.

That matters for prediction markets because the same psychology applies to a contract that pays $1. A 1-cent contract offers a 99-to-1 payout, and a 99-to-1 payout is exactly the shape that makes a small probability feel larger than it is.

The caveat is important. The evidence comes mostly from horse racing and lotteries, not from Polymarket. A parimutuel pool aggregates bets into odds; a central limit order book lets professional market makers quote both sides. The bias may be smaller in liquid prediction markets, and it may be arbitraged away in the most watched ones. Treat the research as a reason to check tail pricing, not as a promise that the check will pay.

Why cheap tails attract buyers

Four forces push the price of a longshot above its probability.

Probability weighting. People do not treat a 1% chance as one in a hundred. They round it up, especially when the outcome is vivid. Prospect theory describes the overweighting of small probabilities, and the longshot bias is one of its cleanest market expressions.

The lottery multiple. A 1-cent contract that pays $1 is a 99x return. The absolute downside is one cent, which feels trivial. Buyers compare the small stake with the large multiple, not the stake with the probability.

Affordability and attention. A cheap contract lets a trader take a position in a market they find interesting without committing capital.

The seller's balance sheet. Someone has to take the other side. Market makers who sell tails accumulate a portfolio with many small gains and rare large losses. They need to be compensated for that risk, and the compensation shows up as a price above the true probability.

None of this guarantees a mispricing. It explains why the mispricing, when it exists, tends to be in one direction.

The arithmetic of a cheap tail

Expected value per share for buying Yes at price c with true probability p is:

p × $1 minus c minus the taker fee.

The fee is share count × category rate × c × (1 − c). At 2 cents with the politics rate, the fee is 0.04 × 0.02 × 0.98, or 0.0784 cents per share. That is small in absolute terms and almost 4% of the 2-cent stake.

If the true probability is 1% and you pay 2 cents, expected value is 0.01 minus 0.02 minus 0.000784, or about −1.08 cents per share. You lose roughly 54% of your stake per bet on average.

If the true probability is 3% and you pay 2 cents, expected value is +0.92 cents per share, about +46% of the stake. The entire trade is the difference between your probability estimate and the market's. The bias only helps if your estimate is independently grounded.

Now take the other side. Buying No at 0.98 to sell the longshot pays $1 if the event does not happen. With a true event probability of 1%, expected value is 0.99 minus 0.98 minus 0.000784, or about +0.92 cents per share, roughly 0.94% of the 98-cent stake.

That looks attractive until you look at the risk. You are risking 98 cents to make about 0.9 cents. One loss erases more than 100 wins. The break-even probability is not 2%; it is about 1.92% after the fee. If your estimate is off by one percentage point in the wrong direction, the trade is negative. A strategy with a 100-to-1 loss-to-gain ratio and a one-point margin for error is not a safe way to collect a small edge.

Payout skew and sample size

The buyer of a longshot has positive skew: many small losses and a rare large win. That is psychologically attractive and statistically deceptive. A buyer can lose 50 bets in a row and still be running a positive-expected-value strategy, or win one 99-to-1 payout and conclude he has skill.

The seller has negative skew: many small wins and a rare large loss. The equity curve looks smooth for months, then gives back everything in one resolution. This is the "picking up pennies in front of a steamroller" pattern, and in binary markets the steamroller is a single ambiguous rule or a single upset.

Sample size makes both problems worse. At a 1% probability, you expect one win per hundred independent bets. The standard deviation around that expectation is large, so a hundred bets tell you very little about whether your probability estimate is calibrated. Judging a tail strategy by its win rate is close to judging a coin by one flip.

Sizing a skewed bet

The Kelly fraction for buying a binary contract at price c with probability p is (p − c) divided by (1 − c). At p = 0.03 and c = 0.02, the fraction is 0.01 divided by 0.98, or about 1% of bankroll. That is already small, and it assumes your estimate is exact.

For the seller at 0.98 with p = 0.01, the same formula gives 0.01 divided by 0.02, or 50% of bankroll. That answer is a warning, not a recommendation. It assumes the probability is known, that the bet is independent of everything else, and that a 50% drawdown is tolerable. None of those assumptions survives contact with a real market. Use a fraction of Kelly, cap the position, and treat the cap as the binding constraint.

A practical rule set for tails:

1. Write your probability estimate and the evidence behind it before looking at the price.
2. Require an edge of at least twice the round-trip fee and spread.
3. Risk no more than 1% of bankroll on any single tail.
4. Cap total exposure to one event, because tails in the same event are correlated.
5. Check the resolution rule. A 1% contract that can resolve 50/50 is not a 1% risk.
6. Track calibration by price bucket, not just profit and loss.

What the research does not say

The studies do not establish that every longshot is overpriced, and they do not give a universal magnitude. The bias varies with the pool, the market, the participants and the period. It is not a constant of nature. Prediction markets add features the racetrack did not have: prices quoted directly as probabilities, professional market makers, and fees that are small in absolute terms near the tails.

That last point cuts both ways. Low fees make tail trading cheaper than it looks, but they also make it easier for others to arbitrage the same bias. The edge, if it exists, is likely to be small and to live in markets that are too obscure for professional capital.

The defensible conclusion is modest. Cheap tails are often priced above their probability, especially where retail attention is high. The trade is a bet on your calibration, sized for a payoff that is deliberately unpleasant. If you cannot state why your probability is better than the market's, the bias is not an edge; it is a story that makes the losing ticket feel clever.