Aberrant expression and activation of EGF receptor (EGFR) has been implicated in the development and progression of many human cancers. As such, targeted therapeutic inhibition of EGFR, for example by antibodies, is a promising anticancer strategy. The overall efficacy of antibody therapies results from the complex interplay between affinity, valence, tumor penetration and retention, and signaling inhibition. To gain better insight into this relationship, we studied a panel of EGFR single-chain Fv (scFv) antibodies that recognize an identical epitope on EGFR but bind with intrinsic monovalent affinities varying by 280-fold. The scFv were converted to Fab and IgG formats, and investigated for their ability to bind EGFR, compete with EGF binding, and inhibit EGF-mediated downstream signaling and proliferation. We observed that the apparent EGFR-binding affinity for bivalent IgG plateaus at intermediate values of intrinsic affinity of the cognate Fab, leading to a biphasic curve describing the ratio of IgG to Fab affinity. Mathematical modeling of antibody-receptor binding indicated that the biphasic effect results from nonequilibrium assay limitations. This was confirmed by further observation that the potency of EGF competition for antibody binding to EGFR improved with both intrinsic affinity and antibody valence. Similarly, both higher intrinsic affinity and bivalent binding improved the potency of antibodies in blocking cellular signaling and proliferation. Overall, our work indicates that higher intrinsic affinity combined with bivalent binding can achieve avidity that leads to greater in vitro potency of antibodies, which may translate into greater therapeutic efficacy.