We address the K+ ion selectivity of the KcsA potassium channel by molecular simulations and a physically transparent, statistical mechanical theory. The binding energy distribution of the channel with either K+ or Na+ in the selectivity filter is analyzed using the potential distribution theorem. The difference in the mean binding energy of Na+ relative to K+ is comparable to the corresponding difference in hydration free energies in the bulk. Thus mean binding energies alone do not predict selectivity; the higher fluctuation in binding energy of Na+ relative to K+ is shown to be responsible for selectivity towards K+. Using the number, n, of carbonyl oxygen atoms within a distance λ of the ion as an order-parameter, we decompose the binding energy distribution into a sum of n-dependent distributions. For chemically meaningful values of λ, this multi-state decomposition predicts that the coordination state n= 5, 6 for Na+ and for K+ most influences the thermodynamics, although the binding site allows a maximum coordination by eight carbonyl ligands. We develop these arguments and show the inter-relation of ion-size, coordination number, and energy fluctuations in channel selectivity.