A quantitative model is proposed for the analysis of the thermodynamic parameters of multivalent interactions in dilute solutions or with immobilized multimeric receptor. The model takes into account all bound species and describes multivalent binding via two microscopic binding energies corresponding to inter- and intramolecular interactions (Delta G(o)inter and Delta G(o)intra), the relative contributions of which depend on the distribution of complexes with different numbers of occupied binding sites. The third component of the overall free energy, which we call the "avidity entropy" term, is a function of the degeneracy of bound states, Omega(i), which is calculated on the basis of the topology of interaction and the distribution of all bound species. This term grows rapidly with the number of receptor sites and ligand multivalency, it always favors binding, and explains why multivalency can overcome the loss of conformational entropy when ligands displayed at the ends of long tethers are bound. The microscopic parameters and may be determined from the observed binding energies for a set of oligovalent ligands by nonlinear fitting with the theoretical model. Here binding data obtained from two series of oligovalent carbohydrate inhibitors for Shiga-like toxins were used to verify the theory. The decavalent and octavalent inhibitors exhibit subnanomolar activity and are the most active soluble inhibitors yet seen that block Shiga-like toxin binding to its native receptor. The theory developed here in conjunction with our protocol for the optimization of tether length provides a predictive approach to design and maximize the avidity of multivalent ligands.