In parameter estimation, we take advantage of the Cramer±Rao lower bound (CRLB) to evaluate the performance of estimation algorithms since the CRLB provides a theoretical upper bound on estimation accuracy. In pattern recognition, the same concept can be quite useful in terms of knowing the point of diminishing return. In this paper, we develop an innovative approach to quantifying the classi®cation CRLB by combining the concepts of sucient statistics and data compression with a metric that measures class separability. This approach allows us to assess the degree of performance optimality attained by each classi®er. Instead of ranking performance of each classi®er based on a confusion matrix, the proposed approach assigns a quantity called the optimality score that indicates the extent to which a classi®er approximates the Bayes classi®er. We illustrate the power of this approach with two interesting examplesÐtwo-class prediction problems with known and unknown class-conditional probability density functions. The latter case deals with prediction of S&P 500 price-movement direction based on raw price data and technical indicators.