Can a calibration metric be both testable and actionable?

Abstract: Forecast probabilities often serve as critical inputs for binary decision making. In such settings, calibration$\unicode{x2014}$ensuring forecasted probabilities match empirical frequencies$\unicode{x2014}$is essential. Although the common notion of Expected Calibration Error (ECE) provides actionable insights for decision making, it is not testable: it cannot be empirically estimated in many practical cases. Conversely, the recently proposed Distance from Calibration (dCE) is testable but is not actionable since it lacks decision-theoretic guarantees needed for high-stakes applications. We introduce Cutoff Calibration Error, a calibration measure that bridges this gap by assessing calibration over intervals of forecasted probabilities. We show that Cutoff Calibration Error is both testable and actionable and examine its implications for popular post-hoc calibration methods, such as isotonic regression and Platt scaling.