A measure of the accuracy of a set of probability assessments. Proposed by Brier (1950), it is the average deviation between predicted probabilities for a set of events and their outcomes, so a lower score represents higher accuracy. In practice, the Brier score is often calculated according to Murphy’s (1972) partition into three additive components. Murphy’s partition is applied to a set of probability assessments for independent-event forecasts when a single probability is assigned to each event:

where c is the overall proportion correct, ct is the proportion correct in category t, pt is the probability assessed for category t, nt is the number of assessments in category t, and N is the total number of assessments. The first term reflects the base rate of the phenomenon for which probabilities are assessed (e.g., overall proportion of correct forecasts), the second is a measure of the calibration of the probability assessments, and the third is a measure of the resolution.  Lichtenstein, Fischhoff and Phillips (1982) provide a more complete discussion of the Brier score for the evaluation of probability assessments.