Brier score
A measure of the quality of a forecast expressed as a probability, which makes it possible to grade an underwriter or a model afterward on what it had announced.
The Brier score measures the gap between an announced probability and what happened: for each forecast, one takes the square of the difference between the probability given and the outcome, scored one if the event occurred and zero otherwise, then averages. A score of zero is perfect; always announcing fifty percent earns a quarter. Glenn Brier proposed it in 1950 to verify weather forecasts, and it has spread to every activity that commits itself in probabilities. For underwriting, it offers what is most lacking: a way to judge decisions on their probabilistic accuracy rather than on the luck of a single year, provided the probabilities were written down before the event. It breaks down into a calibration part, which says whether the seventy percent announced come true seven times in ten, and a resolution part, which says whether the forecaster tells cases apart.
Hypothetical case: an underwriter announces an 80 percent chance that an account will suffer no major loss during the year. If it suffers none, the forecast costs 0.2 squared, or 0.04; if it suffers one, it costs 0.8 squared, or 0.64. Over a hundred forecasts graded this way, the average says what the underwriter's judgment was worth, independently of the luck of the year.
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