Developing a predictive understanding of protein folding requires quantitative measures of sequence-structure compatibility. A folding criterion is presented whose optimization over a training set of structures yields the commonly used statistical and optimized potentials as two limiting cases, whereas these potentials are more often inferred from databases using two very different approaches. A statistical potential is shown to be a form of optimized potential within the context of an independent pair approximation. (C) 2003 American Institute of Physics.