The Dice co‐efficient: a neglected verification performance measure for deterministic forecasts of binary events

Abstract

ABSTRACTWhen deterministic forecasts of binary events are made, there are circumstances in which the number of ‘correct rejections’, d, is difficult to define or is so large that it will dominate in calculations of most performance measures. For this reason it is sometimes desirable to use a measure that is independent of d. The usual measure of choice in meteorology is a/(a + b + c), variously known as the threat score, or the critical success index (CSI), where a, b, c are the numbers of hits, false alarms and misses respectively. An alternative measure that is in common use in ecology is the Dice co‐efficient 2a/(2a + b + c), but it does not appear to have been used in meteorology. The aim of this note is to introduce the Dice co‐efficient to a meteorological audience with a brief history, and compare its properties with those of the CSI. The two measures share many properties, both good and bad, but the Dice co‐efficient has some appealing interpretations not shared by the CSI. In particular, it can be calculated by dividing the number of hits by the average of ‘total number of events observed’ and ‘total number of events forecasted’. It is also obtained as the harmonic mean of the hit rate a/(a + c) and the frequency of hits a/(a + b).