Hill's plots of oxygen binding isotherms reveal the presence of a transition between two different oxygen affinities at the beginning and end of the isotherm. They correspond to the two conformations anticipated by the MWC model, namely, the T and R conformations at the beginning and end of oxygen binding, when the lower affinity of the T form develops into the higher affinity of the R form. The difference between the binding Gibbs free energy changes of the two affinities (Δ G(L)) is the free energy of binding cooperativity. Notably, Δ G(L) is positive in favor of the T form, which moves to a higher energy level upon oxygen release. Osmotic stress reveals a higher volume/surface ratio of deoxyhemoglobin, with a positive Δ G(W) also in favor of the T form. An increasing protein concentration shifts the isotherms to the right, indicating the formation of intermediate polymeric forms. The enthalpy of the intermediates shows a strong absorption of heat at the third oxygenation step because of polymer formation with quinary, and higher-order, structures. The disassembly of intermediate polymers releases energy with a negative Δ G that compensates and allows the positive values of Δ G(L). High-energy polymers are the barrier preventing the relaxation of the T and R conformations into one another. The MWC allosteric model is the best justification of oxygen binding cooperativity.