OmensWhat does a market price say about probability?
Learn how to compare prediction market prices with settled outcomes using calibration, sample sizes, confidence intervals and Brier scores.
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Omens · Updated
A 70¢ outcome price is often described as a 70% market-implied probability for a binary contract that pays $1 on a winning outcome. That interpretation is useful, but the price is not proof that the true chance is 70%. It is a market observation to evaluate against later results.
Start with the price definition
Before studying accuracy, decide whether the observation is a midpoint, a last execution or a volume-weighted average. Those can differ, especially in a market with a wide spread or infrequent trades. Mixing them changes the question being measured.
Fix a sampling time before resolution. Comparing a five-minute-before-close price with a five-second-before-close price without accounting for the horizon can hide meaningful differences. The outcome definition and settlement source must also stay consistent.
Calibration compares prices with observed frequencies
A calibration analysis groups probability observations and compares them with their eventual binary outcomes. For a hypothetical group priced at 70%, about 70% would settle Yes if that group were well calibrated over repeated comparable observations. One losing 70% outcome does not, by itself, demonstrate a bad probability.
For a band such as 70–80¢, compare the observed settlement frequency with the average sampled price in that band, not automatically with 70% or the midpoint. Keep the eligible count and the sampling period visible. Wide bands can conceal patterns, while very narrow bands can leave little evidence.
The same percentage can carry very different uncertainty
Consider two illustrative samples: 16 Yes outcomes out of 20 observations, and 160 out of 200. Both show 80%, but the smaller sample is much less precise. Approximate 95% Wilson intervals are shown below. These are worked examples, not Omens market results.
| Illustrative sample | Observed rate | 95% Wilson interval |
|---|---|---|
| 16 / 20 | 80% | 58.4%–91.9% |
| 160 / 200 | 80% | 73.9%–85.0% |
An interval does not remove sampling bias
A binomial interval assumes comparable independent observations with a common underlying rate. Correlated crypto rounds, repeated snapshots from one event, missing source history and choosing only busy markets can break those assumptions. Grouped analysis or resampling by event or day may be more appropriate for a specific research design.
A 95% confidence procedure is designed to cover the underlying rate in 95% of repeated samples under its assumptions. It does not assign a 95% probability that the next event will win, and it does not make an incomplete dataset representative.
Brier score measures probability error
For binary outcomes, set y to 1 when the selected outcome occurs and 0 otherwise, and express p on the 0–1 scale. The binary Brier score is the average squared difference between p and y; lower is better on the same evaluation sample. A 70% observation contributes 0.09 if the outcome occurs and 0.49 if it does not.
A low score alone does not establish good calibration across price bands. Compare against a suitable baseline on the same sample and inspect the distribution of outcomes. These formulas introduce methods for interpreting probability research; they are not a published Omens performance score.
Binary Brier score = (1 / n) × Σ(p − y)²
Make a statistical claim reproducible
Useful research identifies the market population, date range, source, timestamp rule, exclusions, sample counts and calculation method. Any fitted model should be assessed on held-out later data without using the final result to select an earlier observation.
Omens currently connects trade-based charts with historical round statistics and inspectable samples. As additional mathematical studies are published, they should state their method and limitations alongside the result. A historical association, a calibrated forecast and an executable strategy are separate claims.
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