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, *c _{t}* is the proportion correct in category

- Brier, G. W. (1950), “Verification of forecasts
expressed in terms of probability,”
*Monthly Weather Review*, 75, 1-3. - Lichtenstein, S., B. Fischhoff & L. Phillips (1982),
“Calibration of probabilities: The state of the art to 1980,” in Kahneman, D.,
P. Slovic & A. Tversky (eds),
*Judgment Under Uncertainty: Heuristics and Biases.*New York: Cambridge University Press. - Murphy, A. H. (1972), “Scalar and vector partitions of the
probability score (Part I), Two state situation,”
*Journal of Applied Meteorology*, 11, 273-282.