<p>A major aim of weather and other types of environmental forecasting is to provide early warning of extreme hazards that can then be used to take preventative actions to reduce loss. This study investigates what determines the loss distribution in the simplest context of repeatedly predicting/diagnosing the occurrence or not of a severe event/condition. Mathematical expressions for the expected total loss and variance of the total loss are derived in terms of the probability of event occurrence (the base rate), the cost-loss ratio and the hit rate (H) and false alarm rate (F) of the forecasting system. Expected loss and variance behave very differently as functions of hit and false alarm rate: expected loss is a linear function of <span></span><math>