The mean squared difference between predicted probabilities and actual outcomes coded as 0 or 1: (1/N) Σ (pᵢ − yᵢ)². Lower is better: 0 is perfect, and always predicting 0.5 scores 0.25.
Card 1 of 259. Answer: The mean squared difference between predicted probabilities and actual outcomes coded as 0 or 1: (1/N) Σ (pᵢ − yᵢ)². Lower is better: 0 is perfect, and always predicting 0.5 scores 0.25.
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The Brier score measures the accuracy of probabilistic predictions. Glenn Brier proposed it in 1950 for weather forecasts. It is a proper scoring rule: you get the best expected score by reporting your true belief, so it rewards honest probabilities. It reflects both calibration and how well the model separates the classes.
Example: three forecasts of rain, 0.9, 0.6 and 0.2, and it rains only on the first day. Brier = ((0.9 − 1)² + (0.6 − 0)² + (0.2 − 0)²) / 3 = (0.01 + 0.36 + 0.04) / 3 ≈ 0.137. The 0.6 forecast on a dry day costs the most.
Two follow-ups. Compared with log loss, it is bounded at 1 and punishes a confident miss far less, so one bad prediction can't dominate. And on rare events it looks deceptively small: always predicting a 1% base rate scores 0.0099 while knowing nothing about individual cases. So compare against a reference forecast with the Brier skill score, 1 − BS / BS_reference.
