---
title: "What Is a Brier Score?"
term: "Brier score"
type: glossary_term
canonical: https://www.moonwire.org/insights/glossary/brier-score.html
---

# What Is a Brier Score?

> A score for probability forecasts: the average squared gap between the probability given and what happened (1 or 0). Lower is better; 0 is perfect, and always saying 50% scores 0.25.

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](https://www.moonwire.org/insights/glossary/brier-skill-score.md), with the reference usually being the [base rate](https://www.moonwire.org/insights/glossary/base-rate.md).

## In MoonWire analysis

Every [daily prognosis](/insights/prognosis-daily-2026-09-09.html) 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.

## Further reading

- [Wikipedia: Brier score](https://en.wikipedia.org/wiki/Brier_score)
- [Wikipedia: Probabilistic forecasting](https://en.wikipedia.org/wiki/Probabilistic_forecasting)

## Where this appears in MoonWire analysis

- [Prognosis daily - 29 Aug: one fresh Solana lean, the rest of the book left running](https://www.moonwire.org/insights/prognosis-daily-2026-08-29.md) — Sep 11, 2026

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