Brier score
Updated November 10, 2026
The Brier score measures forecast accuracy: average squared error between your stated probability and the 0/1 outcome. For binary forecasts, lower is better (0 = perfect, 1 = worst on the standard [0,1] scale).
You forecast 70% on three events; outcomes are yes, no, yes (1, 0, 1). Squared errors:
(0.7−1)² 0.09
(0.7−0)² 0.49
(0.7−1)² 0.09
Brier score = (0.09 + 0.49 + 0.09) / 3 ≈ 0.22. A 50% guess on every toss scores 0.25, so you beat chance this round.
- Brier score, 70% on three events
- 0.22
- Outcomes yes, no, yes
- A 50% guess on every toss
- 0.25
The formula, and why it squares the error
For binary forecasts the Brier score is BS = (1/N) Σ (f − o)², where f is the forecast as a decimal between 0 and 1, o is the outcome (1 if it happened, 0 if it didn’t) and N is the number of forecasts. The worked example is that formula with N = 3.
Squaring makes a confident miss cost far more than a cautious one. A 95% forecast on something that doesn’t happen adds 0.9025; a 60% forecast on the same miss adds 0.36. A hit at 95% adds only 0.0025. So the score rewards stating a high number when the evidence supports it and punishes stating one when it doesn’t.
Reading the number
The useful comparison is against 0.25, the score for saying 50% on everything, more than against zero. A score of 0 needs every forecast to be 0% or 100% and every one right. Scores above 0.25 typically come from confident calls in the wrong direction, and 1 is the maximum: 100% certain every time and wrong every time.
Scores are only comparable across the same set of questions. Near-certain questions are easier to score well on than genuinely uncertain ones, so a lower number on an easier set doesn’t show more skill. Small samples are noisy too: with three forecasts, one surprising outcome moves the score more than any real difference in skill would.
Scoring a market price
The same arithmetic works on contract prices. Take a market’s implied probability at a fixed time before resolution, such as a week out, and use it as f. A contract at 72¢ that resolves yes scores (0.72 − 1)² ≈ 0.08; if it resolves no, it scores (0.72 − 0)² ≈ 0.52. Choose the timestamp before you start and score every market in the set, since a price a day before resolution will usually score better than one a month out, and picking only the memorable markets flatters the result.
FAQ
What is a good Brier score?
Below 0.25 is better than saying 50% on everything, and the further below, the better on that question set. Scores aren’t comparable across different sets of questions.
How do you calculate a Brier score?
Square the gap between each forecast and its 0/1 outcome, then average the squares. Three forecasts at 70% with outcomes yes, no, yes score about 0.22.
What is the difference between a Brier score and calibration?
The Brier score is one number for overall error. Calibration checks whether each stated probability level matches how often those events happened, so it shows where the error sits.