In this paper we analyse two common measures of discriminatory power - the Accuracy Ratio and the Area Under the Receiver Operator Characteristic - in a probabilistic framework. Under the assumption of a random default event, we verify that the measures will be portfolio dependent as discovered by Hamerle et al. (2003) and furthermore stochastic as indicated by Blochwitz et al. (2005). As an extension of these two papers we first study how the structure of a portfolio influences the measures. Furthermore we demonstrate that the measures contain information about a rating system's calibration quality. To this end a testing procedure is developed that also allows for a comparison of the measures across different portfolios. Our analysis leads to the final conclusion that high granularity and good calibration quality are sufficient to maximize attainable discriminatory power and are thus the sole criteria to be considered in any validation exercise.