The random sampling of bound ligands gives a numerical method for calculating a density of ligand binding states in energy (or score). This distribution is required in formulating a statistical derivation of expectation values of various quantities such as 1) expected binding free energy, 2) protein-ligand intermolecular energy, 2) entropy of bound ligand, 3) the breakdown of the former into conformational modes, into atoms, and 4) the reduction of a free ligand to a set of energetically different conformational bound modes with fewer degrees of freedom. These calculated quantities, albeit from a molecular model, can be measured in NMR and x-ray experiments or compared energetically against different experiments, as in a screening of compounds.