aggregate metric

Brier score

Σ (p_i − y_i)² / n

The Brier score measures probability quality: the mean squared difference between a predicted probability and what actually happened (1 or 0). It rewards being confident when right and punishes being confident when wrong, so it is the natural metric for Jev's p(yes) outputs.

how it is computed

From results to a number

For each boolean case, take the evaluator's probability of “yes” and the gold answer as 1 or 0; square the difference; average. 0 is perfect, 0.25 is a coin flip, 1 is confidently wrong every time.

inputs

Per-item probabilities and binary gold outcomes.

live · same 40 judgments · change how confident the judge is
observed positive ratestated probability, 5 bins
brier score
0.097
0 perfect · 0.25 coin flip · 1 confidently wrong
ECE
0.178
bars on the dashed diagonal = calibrated

Hedging toward 0.5 lowers ECE but caps Brier at 0.25 with no information. Pushing to extremes helps Brier only when the judge is right.

when to use it

Reach for it when

  • Any Noul evaluator: security, possible, coherence, agent_goal, chunk_relevance verdicts.
  • Comparing a probabilistic judge with one that only emits yes/no (the latter is scored at p = 1 or 0 and is punished for every miss).
  • Deciding whether probabilities are trustworthy enough to act on without a threshold.

Not the right number when

  • Multi-level rubrics (use MAE or the multi-class Brier over the level distribution).
  • You only ever threshold and never use the probability.

Watch out for

  • Brier mixes calibration and sharpness; a judge that always says 0.5 gets 0.25 with perfect calibration and no information.
  • Small sets are noisy; report n.
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Evaluators that produce this

related metrics
questions people ask
What is a good Brier score?
Below 0.1 is strong for a hard judgment task. 0.25 is what you get from always answering 0.5. Above 0.25 means the probabilities are worse than useless.
Why does jeval emphasise Brier over accuracy?
Because Jev returns probabilities. Two judges can both be 90% accurate while one says 0.51 on every case and the other says 0.95 on the ones it gets right; Brier separates them.