This paper describes a thermodynamic analysis of multivalent interactions, with the goal of clarifying the influence of the linker on the enhancement in avidity due to multivalency. The use of multivalency represents a promising approach to inhibit undesired biological interactions, promote desired cellular responses, and control recognition events at surfaces. Several groups have synthesized multivalent ligands that are orders of magnitude more potent than the corresponding monovalent ligands. A better understanding of the theoretical basis for the large enhancements in avidity would help guide the design of more potent synthetic multivalent ligands. In particular, there has been significant controversy regarding the extent to which the loss of conformational entropy of the linker influences the enhancement in avidity due to multivalency. To help clarify this issue, we present the thermodynamic analysis of a heterodivalent ligand-receptor interaction. Our analysis helps reconcile seemingly competing theoretical analyses of multivalent binding. Our results indicate that the dependence of the free energy of multivalent binding on linker length can be weak even if there is a signficant decrease in the conformational entropy of the linker on binding. Our results are also consistent with studies demonstrating that the use of flexible linkers represents fin effective strategy to design potent multivalent ligands.