Boldness-Recalibration for Binary Event Predictions

TL;DR

This paper introduces a Bayesian approach to recalibrate binary event predictions, balancing the trade-off between calibration and boldness to produce more informative probability forecasts.

Contribution

It develops a Bayesian model selection method for assessing calibration and a strategy for boldness-recalibration under specified calibration constraints.

Findings

Slight relaxation of calibration constraints can significantly increase prediction boldness.

The method effectively emboldens predictions while maintaining desired calibration levels.

Case study on hockey data demonstrates practical utility and improved prediction ranges.

Abstract

Probability predictions are essential to inform decision making across many fields. Ideally, probability predictions are (i) well calibrated, (ii) accurate, and (iii) bold, i.e., spread out enough to be informative for decision making. However, there is a fundamental tension between calibration and boldness, since calibration metrics can be high when predictions are overly cautious, i.e., non-bold. The purpose of this work is to develop a Bayesian model selection-based approach to assess calibration, and a strategy for boldness-recalibration that enables practitioners to responsibly embolden predictions subject to their required level of calibration. Specifically, we allow the user to pre-specify their desired posterior probability of calibration, then maximally embolden predictions subject to this constraint. We demonstrate the method with a case study on hockey home team win probabilities and then verify the performance of our procedures via simulation. We find that very slight relaxation of calibration probability (e.g., from 0.99 to 0.95) can often substantially embolden predictions when they are well calibrated and accurate (e.g., widening hockey predictions range from .26-.78 to .10-.91).