ToolJoltTools

Brier Score Calculator

Mean squared error of probability forecasts — the calibration metric for weather, risk and probabilistic models.

Brier score
Base-rate baseline
Brier skill score

Lower is better; 0 is perfect, 0.25 is the always-0.5 forecast. Unlike log loss, the Brier score is bounded [0,1] and doesn't explode on confident mistakes — gentler, which suits weather and risk forecasting where it originated.

Formula

Brier = (1/N) Σ (pᵢ − oᵢ)² · skill score = 1 − Brier / Brier_baseline (baseline = always forecast the base rate)
References: Brier (1950), Verification of forecasts expressed in terms of probability; Murphy (1973), A new vector partition of the probability score

About Brier Score Calculator

How good are your probability forecasts? The Brier score answers it as a mean squared error between predicted probabilities and binary outcomes — the standard in weather forecasting, clinical risk models and any setting where the probability itself is the product. This calculator computes the Brier score, the base-rate baseline (what you'd score by always forecasting the long-run frequency), and the Brier skill score that tells you whether your model actually beats that trivial baseline. Unlike log loss it's bounded and forgiving of confident errors, which is exactly why forecasters prefer it.

How to use Brier Score Calculator

  1. 1Enter your values into Brier Score Calculator — sensible, domain-typical defaults are pre-filled so you see a real result immediately.
  2. 2The result recomputes live using the formula shown on the page; there is no button to press.
  3. 3Adjust any input to compare scenarios, then read the worked example to see the substituted numbers.

Why use Brier Score Calculator?

  • Computes Brier Score instantly in your browser — no sign-up, no upload, no server round-trip.
  • 100% free and unlimited, with the exact formula shown: Brier = (1/N) Σ (pᵢ − oᵢ)².
  • Runs entirely client-side, so every value you enter stays private on your device.
  • Live recompute as you type, with a worked example and authoritative references for trust.

Frequently asked questions

Brier score vs log loss — when to use which?+

Both measure probability quality. Log loss (cross-entropy) punishes confident mistakes severely and is unbounded — good for training and when overconfidence is dangerous. Brier is bounded [0,1], penalizes errors quadratically (gentler on extremes), and decomposes cleanly into calibration + refinement — preferred for reporting forecast skill.

What is the Brier skill score?+

It rescales the Brier score against a reference forecast (usually always predicting the base rate): 1 − BS/BS_ref. A skill score of 0 means you're no better than that trivial baseline; positive means skill, negative means worse. It makes Brier scores comparable across problems with different base rates.

Can the Brier score be decomposed?+

Yes — Murphy's decomposition splits it into reliability (calibration: do your 70% forecasts happen 70% of the time?), resolution (do your forecasts vary usefully with outcomes?) and uncertainty (inherent base-rate variance). This is why it's beloved in forecast verification: it diagnoses WHY a model scores as it does.

What Brier score is good?+

Context-dependent — compare to the base-rate baseline (this tool's skill score does that automatically). For balanced problems, 0.25 is the no-skill (always-0.5) point; for rare events the baseline is much lower (p(1−p)), so a small Brier score isn't impressive unless the skill score is clearly positive.

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