The Response of Performance Metrics for Binary Forecasts to Hedging that Approaches Random Change

Abstract

Critical performance ratio (CPR) expressions for the eight conditional probabilities associated with the 2 ? 2 contingency table of outcomes for binary (dichotomous ?yes? or ?no?) forecasts are derived. Two are shown to be useful in evaluating the effects of hedging as it approaches random change. The CPR quantifies how the probability of detection (POD) must change as frequency bias changes, so that a performance measure (or conditional probability) indicates an improved forecast for a given value of frequency bias. If yes forecasts were to be increased randomly, the probability of additional correct forecasts (hits) is given by the detection failure ratio (DFR). If the DFR for a performance measure is greater than the CPR, the forecast is likely to be improved by the random increase in yes forecasts. Thus, the DFR provides a benchmark for the CPR in the case of frequency bias inflation. If yes forecasts are decreased randomly, the probability of removing a hit is given by the frequency of hits (FOH). If the FOH for a performance measure is less than the CPR, the forecast is likely to be improved by the random decrease in yes forecasts. Therefore, the FOH serves as a benchmark for the CPR if the frequency bias is decreased. The closer the FOH (DFR) is to being less (greater) than or equal to the CPR, the more likely it may be to enhance the performance measure by decreasing (increasing) the frequency bias. It is shown that randomly increasing yes forecasts for a forecast that is itself better than a randomly generated forecast can improve the threat score but is not likely to improve the equitable threat score. The equitable threat score is recommended instead of the threat score whenever possible.