Docking functions are believed to be the essential component of docking algorithms. Both physically and statistically based functions have been proposed, but there is no consensus about their relative performances. Here, we propose an evaluation approach based on exhaustive enumeration of all possible docking solutions obtained with a discretized description of a rigid docking process. We apply the approach to study both molecular mechanics and statistical potentials. It is found that the statistical potential evaluated is less effective than the AMBER molecular mechanics function to provide an accurate description of the docking process when the exact experimental coordinates are used. However, when coordinates of crystal structures obtained with analogous ligands are used, similar performances are obtained in both cases. Possible reasons for the successes and failures of both docking schemes have been uncovered using linear discriminant analysis, on the basis of a set of physicochemical descriptors capturing the main physical effects at play during protein-ligand docking. In both types of potentials steric effects appear critical to obtain a successful docking. Our results also indicate that neglecting desolvation effects and the explicit treatment of hydrogen bonds are the main source of the failures observed with the molecular mechanics potential. On the other hand, detailed consideration of steric interactions, with a careful treatment of dispersive forces, seems to be needed when using statistical potentials derived from a structural database. The possibility of filtering combinatorial libraries in order to maximize the probability of correct docking is discussed.