The Heidke Skill Score as modified by the NWS Climate Prediction Center and commonly used by other practitioners of climate forecasts has virtually all of the undesirable attributes usually associated with a skill score for ordinal categorical forecasts. These include the ability of forecasters to artificially manipulate the score in several ways to their advantage, inconsistency of the score with other related scores, and no dependence of the degree of forecast error or difficulty on forecaster rewards and penalties. There is an alternative called the Gerrity score that for practical purposes has none of these shortcomings and is easy to compute. The Gerrity score is a particular subset of the Gandin and Murphy family of equitable skill scores for ordinal multi-categorical forecasts. Both the Heidke and Gerrity scores will be described, placed in context with the Gandin and Murphy and other scores available in the literature, and their attributes contrasted. CPC and others have argued that the Heidke Score should be retained because it has been used for a long time and because partners and customers are familiar with it. Because digital monthly and seasonal forecast histories exist the Gerrity score can easily be computed for the entire record of these forecasts. Generally CPC partners are knowledgable professionals who can easily comprehend the Gerrity score, while CPC customers generally don't understand the Heidke score anyway. Thus, a recommendation is that CPC adopt the Gerrity score as the official measure of skill for categorical forecasts, thereby encouraging others to do so as well.