A Brier score measures how accurate a set of probability forecasts was, by averaging the squared difference between each forecast and what actually happened.
Last reviewed 29 August 2025 · Educational, not advice
A Brier score is a way to grade probabilistic forecasts after the outcomes are known. For each forecast you take the probability you assigned, subtract the actual result coded as one if the event happened and zero if it did not, square that difference, and then average across all your forecasts. The score runs from zero to one, where zero is perfect and one is as wrong as possible, so a lower score is better. It was introduced by Glenn Brier in 1950 to assess weather forecasts.
The squaring is what makes the score useful. It punishes confident mistakes far more than cautious ones. Saying ninety percent for something that does not happen costs you much more than saying sixty percent for the same miss. That property rewards forecasters who are both accurate and honest about their uncertainty, which is why the Brier score is called a proper scoring rule.
Brier scores connect naturally to prediction markets, where a price can be read as an implied probability. If you treat the price of a contract as a forecast, you can score the market or your own views against what eventually happened. Across many resolved markets a lower average Brier score means the forecasts were closer to reality, which is a more meaningful test than counting how often a side was simply right.
The score blends two things, calibration and resolution. Calibration is whether your stated probabilities match real frequencies, so that things you call seventy percent happen about seventy percent of the time. Resolution is whether you push probabilities away from the base rate when you have genuine information. A good Brier score reflects both, which is why it is a fuller measure than accuracy alone.
A single Brier score means little without context. You need many forecasts to judge skill, and you should compare against a sensible benchmark such as always predicting the base rate. The score also says nothing about money, since being well calibrated does not guarantee a profit once fees and prices are taken into account.
You forecast a 0.8 probability for an event that happens, so the squared error is 0.8 minus 1, squared, which is 0.04. You forecast 0.3 for another event that does not happen, giving 0.3 minus 0, squared, which is 0.09. Across these two the Brier score is the average, about 0.065. A lower number across many forecasts signals better accuracy.
Illustrative only. Numbers are examples, not a quote or a prediction.
A good Brier score shows your forecasts were accurate on average, but accuracy is not the same as profit, and trading still carries a real risk of loss. Stake only what you can afford to lose, never to chase a loss, and never on borrowed money. If it stops feeling like a free choice, step back. In the United States you can call or text the helpline on 1-800-GAMBLER or visit ncpgambling.org.
The mean squared difference between forecast probabilities and actual outcomes, scored from zero for perfect to one for worst, so a lower score is better.
It depends on how predictable the events are, so compare it to a benchmark such as always forecasting the base rate rather than to a fixed target.
A contract price can be read as an implied probability, so you can score the market or your own forecasts against what happened to see how accurate they were.
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