What is a Brier score? A plain-English guide for probability forecasts
A Brier score is the average squared gap between a forecast probability and what happened (1 if the event occurred, 0 if not). It runs from 0 (perfect) to 1 (worst). Always guessing 50% scores 0.25, so a useful model needs to score clearly below that.
A worked example
Suppose a forecaster says there is a 70% chance a level holds, and it holds. The error is 1 − 0.7 = 0.3, squared is 0.09. If it breaks instead, the error is 0 − 0.7 = −0.7, squared is 0.49. The Brier score is the average of these squared errors over every forecast. Confident wrong calls are punished far more than hedged ones.
How to read it
Compare against a baseline, not against zero. A model that says 50% every time scores exactly 0.25. A model that only repeats the base rate scores a little better. A lower number than those baselines means the probabilities carry real information. Brier score rewards both getting the direction right and being honest about confidence.
How ApolloAlpha uses it
ApolloAlpha publishes the Brier score next to its accuracy. For the Apollo Axiom 2 model, tested out-of-sample across 163 markets, the Brier score is 0.183. It is a historical test, not live trading, and past results do not guarantee future results.
Frequently asked questions
Is a lower Brier score better?
Yes. 0 is perfect and 1 is the worst possible. Always forecasting 50% scores 0.25.
Why not just use accuracy?
Accuracy ignores confidence. A model that is right 70% of the time but says 99% each time is badly calibrated. The Brier score penalises that, so it checks the probabilities themselves.
Published 2026-11-07. See the track record and audit for the full method. Statistical model output, not financial advice. Past results do not guarantee future results.