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The Brier score is the mean squared error between a stated probability and the binary outcome (1 if it happened, 0 if it did not): $B = \frac{1}{N}\sum_{i=1}^{N} (p_i - o_i)^2$. where $p_i$ is the forecaster’s stated probability on question i and $o_i$ $\in$ \{0,1\} is the realized outcome. Lower is better; a perfectly calibrated coin-flip forecaster scores 0.25 on a 50/50 question, and a forecaster who says 100 percent and is wrong scores the maximum possible 1.0.

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