Brier Score

Commonly used calibration evaluation metrics include Expected Calibration Error (ECE) and Reliability Diagrams.

The Brier score assesses calibration quality by calculating the square of the difference between the predicted probability and the actual outcome, with a lower score indicating more accurate predictions

The benchmark uses a deterministic checker for scoring—answers are either correct or incorrect—and does not use a large model as a judge.

Model calibration refers to the degree to which a model's output probabilities match its actual accuracy rate; for a well-calibrated model, if the probability it gives for a certain type of question is 0.8, then about 80% of such questions are indeed answered correctly.

The Brier skill score is calculated as 1 - BS_model/BS_ref, where a value greater than 0 indicates the model is better than the reference, equal to 0 indicates no improvement, and less than 0 indicates worse than the reference.

The Brier score can be decomposed into three parts—reliability (calibration), resolution (discrimination), and uncertainty—which helps locate the source of problems.

The Brier score is the mean squared error between predicted probabilities and actual outcomes; lower is better, and it penalizes both wrong direction and overconfidence.

The core mechanism of Calibration Court is to write each AI prediction into a hash-chain ledger before the outcome is revealed, and to score it using the Brier score, log loss, and calibration curves.

The calibration toolchain provided by the system includes three methods: expected calibration error (ECE), Brier score and temperature scaling.

In prediction markets, confidence usually denotes the subjective probability a model assigns to a binary or multinomial outcome and can be calibrated after the fact using metrics such as the Brier score; in LLM-driven systems it is often obtained from model self-assessment or by averaging the logits of multiple samples, with reliability far lower than that of statistical models.

It is recommended to request all options or the full CDF in a single call for multiple-choice and numerical questions and then renormalize, and for other cases to project answers post-hoc onto a self-consistent probability set, as this projection does not worsen the Brier score.

In the held-out prediction task, IRT achieved the best Brier score among the five methods evaluated.

The Brier score formula is BS = (1/N)Σ(f_i - o_i)^2, measuring the mean squared error between predicted probabilities and actual outcomes, where a lower score indicates greater accuracy and a perfect prediction scores 0.

Rolling adaptive rules continuously refit thresholds from historical batches with previously revealed answers, achieving the best average Brier score among all deterministic systems in tests spanning 16 subsequent LLM versions.

A strictly proper scoring rule refers to a class of scoring functions that can be expected to yield the highest score if and only if the forecaster reports their true subjective probability; common examples include the logarithmic scoring rule and the Brier Score.

The core property of a strictly proper scoring rule is that the expected score is maximized if and only if the forecaster reports the probability they truly believe, with common examples including log-likelihood loss and the Brier score.