The Brier score measures how good a set of probability forecasts is. It was proposed by the meteorologist Glenn Brier in 1950 for weather forecasts and is now standard wherever forecasts are stated as probabilities.
The calculation
For each forecast, take the probability that was given (say 0.70 for "Bitcoin higher in seven days"), subtract the outcome (1 if it happened, 0 if not), and square the difference. The Brier score is the average of those squared errors across all forecasts.
- Forecast 0.70, event happened: (0.70 − 1)² = 0.09
- Forecast 0.70, event did not happen: (0.70 − 0)² = 0.49
Reading the number
- 0 would mean every forecast put 100% on what happened.
- 0.25 is what you get by always saying 50% — the score of a forecaster with no view.
- 1 would mean every forecast put 100% on the wrong outcome.
Because errors are squared, confident misses are punished far more than hesitant ones. That makes the Brier score a proper scoring rule: a forecaster gets the best expected score by reporting what they actually believe, rather than exaggerating confidence.
Why a raw Brier score is not enough
A score of 0.21 sounds good until you learn that a forecaster who simply said "up" at the historical up-rate every time would have scored 0.20. How good a Brier score is depends on how predictable the events were in the first place. That is why forecasts are compared against a reference using the Brier skill score, with the reference usually being the base rate.
In MoonWire analysis
Every daily prognosis publishes the running Brier score of its resolved calls together with the naive baseline's score on the same calls and the sample size — including when the baseline beats us. A bare accuracy number without that comparison is not something we publish.