We present an analysis of the assumptions behind some of the most commonly used methods for evaluating the goodness of the fit between a sequence and a structure. Our studies on a lattice model show that methods based on statistical considerations are easy to use and can capture some of the features of protein-like sequences and their corresponding native states, but unfortunately are incapable of recognizing, with certainty, the native-like conformation of a sequence among a set of decoys. Meanwhile, an optimization method, entailing the determination of the parameters of an effective free energy of interaction, is much more reliable in recognizing the native state of a sequence. However, the statistical method is shown to perform quite well in tests of protein design.