Random mutagenesis of genes followed by positive genetic selection in bacteria requires that the variant molecules confer biological activity, and is thus the most demanding approach for generating new functionally active molecules. Furthermore, one can learn much about the protein in question by comparing the population of selected molecules to the library from which they were selected. Described here is a mathematical method designed to guide such comparisons. We use as examples the results of randomization-selection studies of four different proteins. There exists, in general, a positive correlation between the number of amino acid substitutions in a critical region of a protein and the likelihood of inactivation of that protein; a correlation long suspected, but developed here in detail. At this time, we are comparing regions in different proteins and our conclusions must be limited. However, the method presented can serve as a guideline for anticipating the yield of new active mutants in genetic complementation assays based on the extent of randomization.