What is the Brier score?

Explained, with an example

Introduced by Glenn Brier in 1950 for weather forecasts ^[1]. Example: forecasting 0.8 for an event that happens scores (0.8 − 1)² = 0.04; forecasting 0.8 for one that does not scores 0.64. Brier's original form sums over every outcome category, which doubles the common binary value — check which version a leaderboard uses. Forecasting benchmarks such as ForecastBench report Brier-based comparisons of AI models and human forecasters ^[2].

Formula

BS = (1/N) · Σ (forecastₜ − outcomeₜ)²
outcome ∈ {0, 1}; 0 is perfect, lower is better

Related terms

• Calibration — A forecaster (or market) is well calibrated when events given an X% probability happen about X% of the time over many forecasts.
• Prediction market — A prediction market is an exchange where people trade contracts whose payout depends on whether a future event happens, so the trading price can be read as the crowd's probability estimate.
• Kelly criterion — The Kelly criterion is a formula for the fraction of a bankroll to stake that maximises long-run growth, given your probability estimate and the odds; it comes from J.

Try it: tools and tutorials

• Prediction-market prices vs bookmaker odds

Frequently asked questions