Murphy’s Decomposition#
A breakdown of a probabilistic score into calibration and refinement parts.
Important
✨ AI-generated content. This page was written with the assistance of an AI language model and is provided as a learning aid. Despite careful review, it may still contain mistakes, omissions, or out-of-date information. Whether you are new to the topic, a team lead, or a senior practitioner, treat it as a starting point rather than an authoritative reference: read it critically and independently verify anything you act on (code, commands, figures, and factual claims) against official documentation and primary sources before relying on it.
What it is#
Murphy’s decomposition (1973) splits a proper scoring rule — classically the Brier score — into three interpretable pieces:
It reveals why a probabilistic forecast scores as it does.
The three terms#
Reliability is the calibration error (how far forecast probabilities sit from observed frequencies — lower is better); resolution is how much the forecasts vary from the base rate to separate outcomes (higher is better); uncertainty is the irreducible variance of the event itself, independent of the model.
Why it matters#
It shows a good score needs both good calibration and good resolution — a perfectly calibrated model that always predicts the base rate has zero reliability error but zero resolution, and is useless. It is the theoretical reason calibration metrics like ECE tell only half the story.
Theme: Probability Calibration · All terminology
Hint
Mind map — connected ideas
Adaptive ECE (Expected Calibration Error with Adaptive Binning) · Maximum Calibration Error (MCE) · Strictly Proper Scoring Rules · Confidence Level · Probabilistic Forecasts · Temperature Scaling
Hint
More in Probability Calibration
Adaptive ECE (Expected Calibration Error with Adaptive Binning) · Brier Score · Calibration quality (Model Calibration) · Expected Calibration Error (ECE) · Isotonic Regression · Maximum Calibration Error (MCE) · Overconfident · Platt Scaling · Reliability Curves (also called Calibration Curves) · Temperature Scaling · Underconfident
See also
Source article Adapted (context, re-expressed) in our own words from: Murphy’s Decomposition (insightful-data-lab.com).