*Basic

Brier score is an evaluation metric that is used to check the goodness of a predicated probability score.[1]

**Intermediate

Brier score is similar to the mean squared error, but only applied for prediction probability scores, whose values range between 0 and 1.[2] The Brier score is applicable to tasks in which predictions must assign probabilties to a set of mutually exclusive discrete outcomes or classes.[3] The lower the Brier score is for a set of predictions, the better the predictions are calibrated.[4] A Brier score takes on a value between 0 and 1, since this is the square of the largest possible difference between a predicted probability and the actual outcome.[5]

***Advanced

For binary forecasts, the original formulation of Brier's “probability score” has twice the value of the score currently known as the Brier score.[6]

Sources

[1] Editors (2021). A brief on Brier Scores. Data.library.virginia.edu
[2] Editors (2016). Brier score. Statisticshowto.com
[3] Editors (2020). What is a Brier Score? Statology.org
[4] Editors (2022). Brier Score: Understanding Model Calibration. Neptune.ai
[5] Editors. What is a Brier score and how is it calcuated? Cultivatelabs.com
[6] Roulston, M. S (2007). Performance Targets and the Brier Score. Rmets.onlinelibrary.wiley.com