Archive / Prediction markets / E013
Prediction-market longshots are priced right, not too high
In resolved binary prediction markets, longshots at 10c or less were off by only -1.1 to -1.6c at 1 to 14 days out; a +3 to +9c underpricing in a volume-selected sample vanished in an unbiased one.
The favourite-longshot bias says bettors overpay for unlikely outcomes and underpay for likely ones. If so, selling a 5c longshot should pay on average. We checked 1,063 resolved on-chain prediction markets, then repeated the test on 1,072 markets sampled without regard to volume. The first sample showed longshots underpriced by 3 to 9c, the reverse of the bias. In the second, that was gone: longshots at 10c or less were priced about right (-1.1 to -1.6c). Selling longshots lost 2 to 8c per share in the holdout, after gaining at most 3c in the two earlier windows.
Unlikely outcomes are overpriced in betting markets, so systematically selling longshots (or buying favourites) earns money.
Why people believe it
People believe that bettors overpay for small chances (a 5c contract that wins less than 5% of the time) and underpay for near-certainties, and that the same behavioural bias would show up in prediction markets.
Why it would persist The argument, as stated before testing
The usual belief is that selling a longshot earns only a few cents per share against a rare large loss, so the bias would not be competed away.
For each resolved yes/no market we read the Yes price 1, 3, 7 and 14 days before the market closed, while it was still open. We grouped prices into bins and compared each bin's price with how often Yes actually happened. Then we simulated two simple rules to resolution: buy No when Yes is at 10c or less, buy Yes when it is 90c or more. The first sample (the 3,000 most-traded markets) gave a surprising answer, so we repeated everything on markets chosen only by closing month.
Reconstructed after the fact, not pre-specified: realised Yes frequency below price for longshots by more than the 1-2c half-spread and fee, with a sell-longshot rule positive after costs in selection, validation and holdout.
Reconstructed after the fact, not pre-specified: no rule positive after costs in all three windows, or the mispricing smaller than the cost.
Half-spread 1c primary, 2c stress; fee 0.07 x price x (1 - price) only in markets with fees enabled.
The calibration table is its own control: a calibrated price gives realised minus price of zero. The outcome-independent second sample is the control for the volume-selected first sample.
In the outcome-independent sample, longshots are priced about right (-1.1 to -1.6c), about the size of the 1c half-spread, and no rule is positive in all three windows.
- In the volume-selected sample (1,063 markets, 745 events), realised Yes frequency exceeded price by +3 to +9c for p between 0.02 and 0.35, with event-clustered standard errors of 2.5 to 3.5c (t about 2 to 2.5), strongest at 7 days.
- Selling longshots in that sample mostly lost in selection and validation, -3.13c to -8.48c per share at 1, 3 and 7 days (1c half-spread); the one exception was +4.47c at 14 days in validation.
- The favourite rule in that sample was +4c in selection but had only 3 to 19 trades per window, so it says nothing.
- In the outcome-independent sample (1,072 markets, 454 events), longshots at p <= 0.10 were off by -1.1 to -1.6c at every horizon; bins 0.02 to 0.10 gave -1.7c (SE 0.8) and -0.7c (SE 1.5). Favourites were off by -0.1 to -3.4c with SE about 3c.
- In that sample, with a 1c half-spread, selling longshots netted -0.08c to +3.73c in selection and validation but -1.77c to -6.67c in the holdout (SE 2.6 to 7.1c); across the 1c and 2c half-spreads the holdout range is -2 to -8c. The holdout 7-day cell was -3.64c on 75 trades in 40 events; its 95% interval (-11.74 to 4.47) is the mean plus or minus 1.96 event-clustered SE, computed by us for one chosen cell, not a pre-specified test.
- The buy-favourite rule changed sign across windows; with a 1c half-spread it lost 13.20c, 9.38c, 6.77c and 5.86c per share in the holdout at 1, 3, 7 and 14 days.
The sample choice flipped the sign
Top-volume markets (first sample)Outcome-independent sample (second sample)
Selection-window net result of selling longshots (buy No at p <= 0.10, 1c half-spread). The volume-selected sample loses at every horizon; the outcome-independent sample is near zero or positive up to 7 days and about zero at 14.
Chart data (cents per share)
| Top-volume markets (first sample) | Outcome-independent sample (second sample) | |
|---|---|---|
| 1 day | -4.2 | 1.48 |
| 3 days | -6.6 | 2.81 |
| 7 days | -8.48 | 2.77 |
| 14 days | -8 | -0.08 |
Selling longshots fails in the holdout
SelectionValidationHoldout
Outcome-independent sample, 1c half-spread. Selection and validation are mostly small gains; the holdout is negative at every horizon, with standard errors of 3 to 7c.
Chart data (cents per share)
| Selection | Validation | Holdout | |
|---|---|---|---|
| 1 day | 1.48 | 3.73 | -6.67 |
| 3 days | 2.81 | 1.21 | -4.26 |
| 7 days | 2.77 | 1.09 | -3.64 |
| 14 days | -0.08 | 2.34 | -1.77 |
Buying favourites changes sign by window
SelectionValidationHoldout
Outcome-independent sample, 1c half-spread. Positive and negative cells alternate in selection and validation, and the holdout is negative at every horizon (-5.86c to -13.20c).
Chart data (cents per share)
| Selection | Validation | Holdout | |
|---|---|---|---|
| 1 day | -1.12 | 3.83 | -13.2 |
| 3 days | 0.52 | -2.68 | -9.38 |
| 7 days | 1.34 | 4.28 | -6.77 |
| 14 days | -1.83 | -1.47 | -5.86 |
Why it failed Interpretation · not established
The first sample picked the markets with the most trading volume. A likely explanation, not tested here, is that volume partly grows because the event happens: a longshot that starts to win attracts late money, so winning longshots would be over-represented and look underpriced without any mispricing. Once markets were chosen by closing month and a low volume floor, longshots were priced at or slightly above their realised frequency, and the gap was about the size of the cost of trading it.
Lesson
When testing resolved markets for calibration, any sampling variable that accumulates with the outcome (volume, for example) builds the answer into the sample. A bias that appears only in the most-traded subset is a property of the selection, so check it on a sample drawn before the outcome is known.
Scope of this result
Covers resolved binary markets on one on-chain prediction market, prices 1 to 14 days before the end date, with end dates 2025-01 to 2026-09 in the second sample. It does not cover multi-outcome markets, prices closer than one day to resolution, or other venues.
A rejected experiment applies to the tested conditions and does not prove an idea can never work. bp = basis point, 0.01%.
1. Test design
Pre-registeredDataUniverseSignalExecutionCostsControlsSample splitPass criterionKill criterionPower2. Result
ObservationsInstrumentsNet mean95% intervalMedianWorstFinding 1Finding 2Finding 3Finding 4Finding 5Finding 63. Interpretation
Why it failedLessonScope4. Reproducibility
StepsGrade