{
  "status": "shipping",
  "advantages": [],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-17",
  "slug": "brier-score",
  "term": "Brier score",
  "aliases": [
    "Brier loss",
    "binary Brier score"
  ],
  "definition": "For a binary event, the Brier score is the mean squared difference between each forecast probability and its observed zero-or-one outcome.",
  "note": "The convention here is BS = sum((p_i-y_i)^2)/N for N observed outcomes, y_i in {0,1} and event probabilities p_i in [0,1]; lower is better and the range is [0,1]. State normalization: the unhalved sum over class-probability components instead ranges up to 2. [sklearn-brier]\n\nBrier loss reflects both reliability and the separation of different event risks, so a lower value does not by itself establish better calibration. Compare forecasts on the same outcomes and include a declared constant-probability reference. [sklearn-calibration]",
  "limitations": [
    {
      "text": "Editorial implication: An unobserved prediction horizon is not a zero outcome; a score cannot replace documentation of follow-up, event labels, population and any weighting.",
      "citationIds": [
        "sklearn-brier"
      ]
    }
  ],
  "related": [
    "probability-calibration",
    "class-prevalence",
    "prediction-horizon",
    "average-precision"
  ],
  "citations": [
    {
      "id": "sklearn-brier",
      "title": "scikit-learn: brier_score_loss, binary normalization and range.",
      "url": "https://scikit-learn.org/stable/modules/generated/sklearn.metrics.brier_score_loss.html",
      "accessed": "2026-10-17"
    },
    {
      "id": "sklearn-calibration",
      "title": "scikit-learn: probability calibration, reliability diagrams and limits of Brier loss.",
      "url": "https://scikit-learn.org/stable/modules/calibration.html",
      "accessed": "2026-10-17"
    },
    {
      "id": "hesela-calibration",
      "title": "Hesela: synthetic ranking, decision and calibration example; not measured drive results.",
      "url": "https://hesela.com/analyses/ml-disk-failure-prediction/#probability-calibration",
      "accessed": "2026-10-17"
    }
  ]
}