# Brier score

Also written quadratic score.

*https://predictionmarkets.tools/glossary/brier-score · next to Forecasting Platforms*

**Definition:** The squared distance between a stated probability and what happened, averaged over forecasts, where lower is better. Brier's 1950 original sums that distance over every answer option, so a yes/no forecast scores between 0 and 2. The common shortcut scores one option and runs from 0 to 1. The same forecast is twice as large on the first scale, and platforms rarely say which one they print.

This catalogue uses the Brier score as a unit more than as a subject. Eleven cards carry the
calibration-scoring flag, and most of them either print a Brier figure, compute one, or explain
why they do not. The trap everyone runs into first is the one where two conventions differ by a
factor of two, and it has [its own treatment](https://predictionmarkets.tools/guides/what-a-forecasting-score-measures), including
the one-question test that tells you which convention a platform uses. This page covers the parts
that guide does not: where the two conventions come from, why only one of them handles a question
with more than two answers, and why the same forecaster gets a different average on a different
set of questions.

## How it works

Glenn Brier defined it in the *Monthly Weather Review* in January 1950 for rain forecasts. On each
of n occasions the event falls into one of r mutually exclusive classes. The forecaster states a
probability for every class, and the score is the squared difference between each stated
probability and 1 or 0 (whether that class happened), **summed over the classes and averaged over
the occasions**. Brier states the range himself: zero for perfect forecasting and a maximum value
of 2 for the worst possible forecasting.

So the 0-to-2 scale is not a variant. It is the original. The 0-to-1 form, which the WMO
verification reference gives as the mean of (forecast − observation)², is what you get when a
yes/no question is written as one probability instead of two. Both are the same rule. Gneiting and
Raftery list it as the quadratic score, proposed by Brier (1950), and it is proper under either
scaling.

### Only the original handles more than two answers

Good Judgment Open publishes a three-option worked example: 60% on A, 10% on B and 30% on C, and A
happens.

```text
(1 - 0.6)^2 + (0 - 0.1)^2 + (0 - 0.3)^2 = 0.16 + 0.01 + 0.09 = 0.26
```

The single-probability form has nothing equivalent to offer here. If you score only the option
that happened, you get 0.16, which is not half of 0.26. The two conventions stop being related by
a factor of two as soon as a question has a third answer. This is why a tool that keeps the
single-probability form has to do something else with multiple-choice questions. Brier.fyi, for
example, splits them into yes/no pieces or tracks only the winning option, depending on the
platform.

### The score has a floor, and the questions set it

Brier's paper makes a second point that a leaderboard never repeats. If a forecaster issues the
same forecast on every occasion, the best score available to them comes from forecasting the
observed frequencies, and it equals 1 minus the sum of the squared frequencies. His own example
has ten forecasts, three of which saw rain. A forecaster who said 30% every time would score 0.42,
a forecaster who used a climatological 20% would score 0.44, and the actual forecaster scored 0.19.

On a set of yes/no questions where a fraction p resolves yes, that no-skill figure is:

| share resolving yes | 0-to-2 convention | 0-to-1 convention |
|---|---|---|
| 50% | 0.50 | 0.25 |
| 20% | 0.32 | 0.16 |
| 10% | 0.18 | 0.09 |
| 5% | 0.095 | 0.0475 |

The last column is p(1 − p), the "uncertainty" term in the decomposition that the WMO reference
credits to Murphy (1973). It depends on the questions and not on the forecaster. Gneiting and
Raftery draw the consequence: scores are directly comparable only when they refer to exactly the
same set of forecast situations. Otherwise, how predictable the questions were gets mixed up with
how well they were predicted.

## What the catalogue records

For the cards that touch a Brier score, this is the convention each one uses, and how the corpus
knows:

| card | convention | where it comes from |
|---|---|---|
| [Fatebook](https://predictionmarkets.tools/tools/fatebook) | 0 to 2 | the card, read from the source code |
| [Good Judgment Open](https://predictionmarkets.tools/tools/good-judgment-open) | 0 to 2 | its FAQ states a worst score of 2 |
| [Brier.fyi](https://predictionmarkets.tools/tools/brier-fyi) | 0 to 1 | its about page gives (p − r)², worse towards one |
| [Confido](https://predictionmarkets.tools/tools/confido) | rescaled, −3 to 1, higher is better | the card, read from the source code |
| [Manifold](https://predictionmarkets.tools/tools/manifold) | not stated | its calibration page prints 0.17375 with no unit |

Brier.fyi also cuts its letter grades on the 0-to-1 scale, with an F running from 0.36 to 1.
A 0-to-2 figure has to be halved before it is read against that table.

Confido's formula, `(0.25 − (outcome − p)²) × 4`, is 1 minus the one-option Brier score divided by
0.25, the score of a 50% forecast. In other words, it is a skill score against a fixed coin flip.
On yes/no questions all three scales convert exactly. The 0-to-2 figure is twice the 0-to-1
figure, and Confido's score is 1 minus four times the 0-to-1 figure. Nothing converts across a
multiple-choice question. [Metaculus](https://predictionmarkets.tools/tools/metaculus) is absent from the table on purpose,
because its scores are built on the log score and its scores page does not publish a Brier figure.

## Why it matters here

**Two numbers from two platforms are two different measurements until you have named both
conventions.** Fatebook and Good Judgment Open agree with each other and with Brier's paper.
Brier.fyi uses the other scale, and Confido uses a third one pointing the opposite way. If you are
choosing where to keep a track record, you are choosing which of these your history will be
written in. Moving it later means a conversion that works for yes/no questions only.

**A platform-wide Brier score is partly a statement about the question mix.** Manifold's 0.17375
is exactly what a forecaster with no skill would score if about 22% of the sample resolved yes and
the scale is 0 to 1, or if about 10% did and the scale is 0 to 2. It is well clear of the no-skill
figure on either scale if the sample was split evenly. Neither the yes-share nor the convention is
printed beside it, so there is no way to tell which of those it is. For any aggregate, the missing figure
is the share of questions that resolved yes. Without it, a low average may be showing you easy
questions rather than a good forecaster.

**Your own number moves when your questions change.** A private log in Fatebook full of near-certain
personal questions will average far lower than a season of hard geopolitics on Good Judgment Open,
even with identical judgement. The crowd-relative scores on both sites exist to strip that out,
and their limits are covered in [the guide](https://predictionmarkets.tools/guides/what-a-forecasting-score-measures).

**Brier is bounded, and that decides what it can tell apart.** It cannot tell a confident miss from
an absurdly confident one, which is the log score's territory. Whether any of these numbers
rewards an honest forecast at all is a property of the rule, and that is the subject of
[proper scoring rule](https://predictionmarkets.tools/glossary/proper-scoring-rule).

## Where you will meet this

- [Brier.fyi](https://predictionmarkets.tools/tools/brier-fyi.md)
- [Confido](https://predictionmarkets.tools/tools/confido.md)
- [Fatebook](https://predictionmarkets.tools/tools/fatebook.md)
- [Futuur](https://predictionmarkets.tools/tools/futuur.md)
- [Good Judgment Open](https://predictionmarkets.tools/tools/good-judgment-open.md)
- [Hypermind](https://predictionmarkets.tools/tools/hypermind.md)
- [Manifold](https://predictionmarkets.tools/tools/manifold.md)
- [Prediki](https://predictionmarkets.tools/tools/prediki.md)
- [Quantified Intuitions](https://predictionmarkets.tools/tools/quantified-intuitions.md)
- [Social Science Prediction Platform](https://predictionmarkets.tools/tools/social-science-prediction-platform.md)

## FAQ

### Can I halve a Good Judgment Open Brier score to compare it with a Brier.fyi one?

On a yes/no question, yes. Good Judgment Open sums the squared error over both options and Brier.fyi scores one, so the first is exactly twice the second. On a question with three or more options it does not work. Good Judgment Open's own three-option example scores 0.26, and scoring only the winning option of the same forecast gives 0.16, not 0.13.

### Is a Brier score of 0.1 good?

That depends on the questions more than on the forecaster. Saying the base rate to every question scores p(1 − p) on the 0-to-1 scale. If one question in ten resolves yes, that is 0.09, with no skill involved at all. Ask for the share of questions that resolved yes before you read any average, and ask which convention the number uses.

### How do I turn a Confido score into an ordinary Brier score?

For a yes/no question, subtract the Confido score from 1 and divide by 4 for the 0-to-1 convention, or by 2 for the 0-to-2 one. A Confido score of 0.64 is a Brier score of 0.09 or 0.18. Confido's rescaling points upwards and every other Brier figure in this catalogue points down, so convert before comparing.

## Sources

1. [Verification of forecasts expressed in terms of probability](https://journals.ametsoc.org/view/journals/mwre/78/1/1520-0493_1950_078_0001_vofeit_2_0_co_2.xml) — Monthly Weather Review, volume 78, number 1, 1950-01-01. The paper that defines the score. Later conventions changed its scale, not its content, and nothing has replaced it as the original statement.
2. [Strictly Proper Scoring Rules, Prediction, and Estimation](https://sites.stat.washington.edu/raftery/Research/PDF/Gneiting2007jasa.pdf) — Journal of the American Statistical Association, volume 102, number 477, 2007-03-01. A mathematical review rather than a rulebook, and still the standard reference for the Brier score as a proper rule.
3. [Forecast verification - methods, issues and FAQ](https://jwgfvr.github.io/forecastverification) — WMO WWRP Joint Working Group on Forecast Verification Research, read 2026-09-26
4. [FAQ](https://www.gjopen.com/faq) — Good Judgment Open, read 2026-09-26
5. [About](https://brier.fyi/about/) — Brier.fyi, read 2026-09-26

*Last updated 2026-09-26. A reference page, corrected in place — not a dated post.*