Brier score for Bitcoin forecasts
How the Brier score evaluates probability forecasts and why confidence is punished when the outcome goes the other way.
The basic calculation
For a yes-or-no event, the Brier score is the squared difference between the forecast probability and the outcome. The outcome is recorded as 1 when the event occurs and 0 when it does not. A forecast of 70% that occurs scores (0.70 − 1)² = 0.09. If it does not occur, the score is (0.70 − 0)² = 0.49.
Lower scores are better. A perfect probability forecast for an individual outcome scores 0, while a confidently wrong forecast approaches 1.
Why the score is useful
Direction accuracy treats 51% and 99% forecasts as identical guesses even though they express very different confidence. The Brier score preserves that distinction. Being confidently wrong costs much more than being cautiously wrong.
The score should normally be interpreted across many comparable forecasts. A single event cannot establish whether a 70% forecast was well calibrated: events assigned around 70% should occur around seven times in ten over a suitable sample.
A score needs a competitor
An isolated Brier score has limited meaning. It should be compared with simple reference forecasts evaluated on the same outcomes. Depending on the question, useful controls can include a constant historical frequency, a neutral probability, or a frozen price-based model.
How BTC Horizon uses it
BTC Horizon records Brier score alongside sample size, direction accuracy, log loss, price error, and interval coverage. No single metric is allowed to turn a small forward sample into proof. The current public site explains the research while the qualifying model continues to accumulate private forward outcomes.