Protein-protein recognition plays a central role in most biological processes. Although the structures of many protein-protein complexes have been solved in molecular detail, general rules describing affinity and selectivity of protein-protein interactions do not accurately account for the extremely diverse nature of the interfaces. We investigate the extent to which a simple physical model can account for the wide range of experimentally measured free energy changes brought about by alanine mutation at protein-protein interfaces. The model successfully predicts the results of alanine scanning experiments on globular proteins (743 mutations) and 19 protein-protein interfaces (233 mutations) with average unsigned errors of 0.81 kcal/mol and 1.06 kcal/mol, respectively. The results test our understanding of the dominant contributions to the free energy of protein-protein interactions, can guide experiments aimed at the design of protein interaction inhibitors, and provide a stepping-stone to important applications such as interface redesign.