A new decomposition of the Brier score: formulation and interpretation

Abstract A new decomposition of the Brier score is described. This decomposition is based on conditional distributions of forecast probabilities given observed events, and, as a result, it differs in a fundamental way from most previous partitions of quadratic verification measures. The new decomposition consists of 1) a term involving the variances of the conditional distributions and 2) a term related to the mean errors in the forecasts, which involves the squared differences between the means of the conditional distributions and the respective mean observations (the latter are necessarily either zero or one). Decrease in these variances and/or mean errors generally lead to improvements in the Brier score. The decomposition may be useful in verification studies, since it appears to provide additional insight into the quality of probabilistic forecasts.