Decomposition
Brier score decomposition breaks overall error into components that reflect calibration (reliability), discrimination (resolution), and the inherent uncertainty of the task.
Definition
Brier decomposition is a way to understand Brier score by splitting it into interpretable parts. It helps you see whether your score is bad because you are miscalibrated, because your forecasts do not separate cases well, or because the problem itself is inherently uncertain.
Standard components
The common decomposition is expressed as:
BS = Reliability - Resolution + Uncertainty
Reliability is the penalty for miscalibration (worse calibration increases BS).
Resolution rewards separating cases where outcomes differ (better resolution decreases BS).
Uncertainty depends on the base rate of outcomes and is not under the forecaster’s control for a fixed question set.
Why it matters
Two forecasters can have the same Brier score for very different reasons. One might be well calibrated but low information (low sharpness and low resolution). Another might have high resolution but be overconfident and miscalibrated. Decomposition tells you which knob to turn.
Practical use
When you generate a scorecard, track calibration and resolution separately. If reliability is the problem, move probabilities toward the center. If resolution is the problem, you may need better signals or better modeling of context.