Brier Score & Binary Cross-Entropy (Log Loss) Probability Calibration Calculator

Compute Brier Score, Brier Skill Score (BSS), and Binary Cross-Entropy Log Loss (nats & bits).

Brier Quadratic Calibration Score
0.032 Brier (0 = ideal)
Binary Cross-Entropy Log Loss (nats) 0.199 nats
Surprisal / Log Loss in Bits 0.286 bits
Brier Skill Score vs. Base Rate 0.942 BSS
Inputs
⚡ Scenarios:
p
Model predicted probability p of positive class (0.001 to 0.999).
0 or 1
Observed ground-truth binary outcome y (1 = event occurred, 0 = did not occur).
base rate
Baseline prevalence / climatology rate for Brier Skill Score.
Results & Graph
Brier Quadratic Calibration Score
0.032 Brier (0 = ideal)
Binary Cross-Entropy Log Loss (nats)
0.199 nats
Surprisal / Log Loss in Bits
0.286 bits
Brier Skill Score vs. Base Rate
0.942 BSS

Brier Quadratic Calibration Score

Graph 1 • Brier Score & Log Loss • Domain Architecture & Live Telemetry Maps Predicted Probability P, Actual Outcome0or1, Historical Base Rate Climo through Brier Score & Log Loss Formula.
Brier Score & Binary Cross-Entropy (Log Loss) Probability Calibration Calculator • Custom Domain Schematic (Machine Learning & Classification Metrics) predicteactualOuBrier Score & Log Loss Predicted Probability P: 0.820 p • Actual Outcome0or1: 1 0 or 1 BRIER QUADRATIC CALIBRATIO 0.032 Brier (0 = ide • Binary Cross-Entropy L: 0.199 nats • Surprisal / Log Loss i: 0.286 bits Eq: Brier = (p − y)²; LogLoss = −[
Graph 2 • Brier Quadratic Calibration Score Across Predicted Probability P Sweep (40% → 160%) Evaluates Brier = (p − y)²; LogLoss = −[ y·ln(p) + (1 − y)·ln(1 − p) ]; BSS = across 7 operating points (current input highlighted).
0 Brier 0.550 Brier 1.10 Brier 0.452 0.328p 0.258 0.492p 0.118 0.656p 0.0320 0.820p 0 0.984p 0 1.15p 0 1.31p
Graph 3 • Joint Sensitivity: Predicted Probability P × Actual Outcome0or1 Compares Brier Quadratic Calibration Score when Actual Outcome0or1 is shifted +25% (solid) vs. −25% (dashed).
0 Brier 0.550 Brier 1.10 Brier --- Actual Outcome0or1 @ 75% 0.181 -30% 0.0920 -15% 0.0320 +0% 0.00300 +15% 0 +30%
Summary: Predicting p=0.82 for outcome y=1 yields a Brier Score of 0.0324 (Brier Skill Score 0.942) and Cross-Entropy Log Loss of 0.1985 nats (0.2863 bits).
Summary: Predicting p=0.82 for outcome y=1 yields a Brier Score of 0.0324 (Brier Skill Score 0.942) and Cross-Entropy Log Loss of 0.1985 nats (0.2863 bits).
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Formula & Mathematical Methodology: Brier Score & Log Loss Formula

Brier = (p − y)²
LogLoss = −[ y·ln(p) + (1 − y)·ln(1 − p) ]
BSS = 1 − (Brier / Brierclimo)
Brier = (p − y)²; LogLoss = −[ y·ln(p) + (1 − y)·ln(1 − p) ]; BSS = 1 − (Brier / Brier_climo)
  • predictedProbabilityP: Predicted Probability P (p)
  • actualOutcome0or1: Actual Outcome0or1 (0 or 1)
  • historicalBaseRateClimo: Historical Base Rate Climo (base rate)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: Brier Score & Log Loss

Compute Brier Score, Brier Skill Score (BSS), and Binary Cross-Entropy Log Loss (nats & bits).

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: Brier = (p − y)²; LogLoss = −[ y·ln(p) + (1 − y)·ln(1 − p) ]; BSS = 1 − (Brier / Brier_climo).
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes Brier Score & Log Loss via Brier = (p − y)²; LogLoss = −[ y·ln(p) + (1 − y)·ln(1 − p) ]; BSS = 1 − (Brier / Brier_climo).

Frequently Asked Questions

How does the Brier Score & Binary Cross-Entropy (Log Loss) Probability Calibration Calculator compute the solution?

It evaluates Brier = (p − y)²; LogLoss = −[ y·ln(p) + (1 − y)·ln(1 − p) ]; BSS = 1 − (Brier / Brier_climo) directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Machine Learning & Classification Metrics

Brier Score & Binary Cross-Entropy (Log Loss) Probability Calibration Calculator: inputs, method, and how to read the result

Compute Brier Score, Brier Skill Score (BSS), and Binary Cross-Entropy Log Loss (nats & bits).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Predicted Probability P: Model predicted probability p of positive class (0.001 to 0.999).
  • Actual Outcome0or1: Observed ground-truth binary outcome y (1 = event occurred, 0 = did not occur).
  • Historical Base Rate Climo: Baseline prevalence / climatology rate for Brier Skill Score.

What the calculation includes

With the default values shown, Brier Quadratic Calibration Score is 0.032 Brier (0 = ideal). The calculation follows Brier Score & Log Loss Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Predicted Probability P from 0.82 p to 0.9 p changes Brier Quadratic Calibration Score from 0.032 Brier (0 = ideal) to 0.01 Brier (0 = ideal). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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