Proteins need to selectively interact with speci c targets among a multitude of similar molecules in the cell. Despite a rm physical understanding of binding interactions, we lack a general theory of how proteins evolve high speci city. Here, we present a model that combines chemistry, mechanics and genetics, and explains how their interplay governs the evolution of speci c protein-ligand interactions. The model shows that there are many routes to achieving discrimination -by varying degrees of exibility and shape/chemistry complementarity -but the key ingredient is precision. Harder discrimination tasks require more collective and precise coaction of structure, forces and movements. Proteins can achieve this through correlated mutations extending far from a binding site, which ne tune the localized interaction with the ligand. Thus, the solution of more complicated tasks is aided by increasing the protein, and proteins become more evolvable and robust when they are larger than the bare minimum required for discrimination. Our model makes testable, speci c predictions about the role of exibility in discrimination, and how to independently tune a nity and speci city. Thus, the proposed theory of molecular discrimination addresses the natural question "why are proteins so big?" A possible answer is that molecular discrimination is often a hard task best performed by adding more layers to the protein.Significance statement. Proteins excel at discriminating between molecules. Otherwise, cells would not be able to accurately translate mRNA into protein sequences, chemical signals would get mixed up, and enzymes would catalyze unwanted interactions. To understand how proteins can achieve this, we develop a model of protein binding to study evolution of molecular discrimination through the interplay of shape, exibility, chemical binding and entropy. The model reveals that mutations far from the binding site can ne-tune binding interactions, and larger proteins are better discriminators. Proteins thus solve the discrimination problem by being large so that they have many ways of ne-tuning binding.