What is a Brier score?

The Brier score grades a numeric probability against what actually happened, on a fixed scale with a perfect score of 0. For a forecast given with probability p and a resolution written as 1 when it happened and 0 when it did not:

Brier (one forecast) = (p − outcome)²

Saying 100% and being right scores 0; saying 100% and being wrong scores 1. Saying 50% scores 0.25 whether yes or no: certainty about nothing. The mean over a whole record of n forecasts is the number people compare. Always answering 50% on every binary question stays at 0.25 forever, so a forecaster who wants to beat 0.25 must actually move their probabilities.

A worked example

Three forecasts: 0.70 on an outcome that happened (0.70 − 1)² = 0.09; 0.60 on one that did not, (0.60 − 0)² = 0.36; 0.30 on one that did not, (0.30 − 0)² = 0.09. Mean = (0.09 + 0.36 + 0.09) / 3 = 0.18. Lower is better than the 0.25 steady state, but the 0.36 row is where the record says this forecaster overpaid confidence.

Skill: better than the lazy baseline?

A raw Brier number hides the base rate. If outcomes come out yes 80% of the time, answering 80% every time scores 0.8·(0.8 − 1)² + 0.2·(0.8 − 0)² = 0.16 on that mix — the least clever record that never moves. That benchmark is the climatology reference, and the Brier skill score (BSS = 1 − Brier ÷ reference Brier) compares a record against it: above zero means you beat it; below zero means the static baseline did better. When every outcome in a sample is identical, the reference is perfect by construction and the skill score has no defined value — an honest record reports that, it does not manufacture a number.

Grading requires order

A probability computed after the outcome is a memory test, not a forecast. Any record worth scoring records p first, writes it down immutably, and only then lets the market decide. That ordering is the product rule here: Tollbridge records the probability, settles on the process's own clock, and grades every call — including refusals — on the public track record. Sample sizes and publication floors travel with every claim.

Keep going

Score your own pasted sample in the browser with the Brier score calculator — the reliability buckets show where the record is honest and where it leaks. Calibration mechanics live on the calibration explorer. Market research begins at the live perp list.

Educational research, not financial advice. Scores describe past records; nothing here predicts future outcomes.