Proposed by Glenn W. Brier in 1950, the Brier score is a proper score function that measures the accuracy of probability forecasts. It applies to tasks in which predictions must assign probabilities to a set of mutually exclusive discrete outcomes, which can be either binary or categorical in nature. Probabilities assigned to a set of outcomes using the Brier score must sum to one, and each individual probability falls in the range of zero to one, says Eumetcal.
At times, the Brier score can be interpreted as either a measure of the calibration of a set of probability forecasts or as a cost function. Across all items in a set of predictions, the Brier score measures the mean squared difference between predicted probability assigned to the possible outcomes and the actual outcome. As a result, a lower Brier score confirms that its predictions are better calibrated.
Today, the largest possible difference between probable and actual outcomes is one. However, in the original formulation, the range is double, from zero to two. The Brier score is appropriate to use for binary and categorical outcomes that can be structured as true or false. Because it assumes that all possible outcomes are equivalent in distance from each other, the Brier score is inappropriate for ordinal variables that take on three or more values.