Exact formula
How is a three-outcome Brier score calculated?
Subtract the observed outcome—1 for what happened, 0 for what did not—from each probability, square all three errors, add them, then divide by three.
Brier3-class average((pH − yH)² + (pD − yD)² + (pA − yA)²) ÷ 3
54 / 26 / 20 + home result = (0.46² + 0.26² + 0.20²) ÷ 3 = 0.1064
Reference points
What does the number mean?
- 0.0000
- A perfect probability of 100% assigned to the result that occurred.
- 0.2222
- An equal 33.33% / 33.33% / 33.33% forecast, regardless of which result occurs.
- 0.6667
- The maximum: 100% assigned to one outcome while a different outcome occurs.
One match can reward or punish a probability split, but it cannot establish model quality. Judge a model across a complete sample alongside calibration, sample size and publication proof.
Continue the audit
Calculate here. Verify on the public ledger.
Football Proof AI uses the same class-averaged definition for its settled 1X2 record. The glossary fixes the terminology; the accuracy page shows how the metric behaves across real samples.