The steady emergence of SARS-CoV-2 variants gives us a real-time view of the interplay between viral evolution and the host immune defense. The spike protein of SARS-CoV-2 is the primary target of antibodies. Here, we show that steric accessibility to antibodies provides a strong predictor of mutation activity in the spike protein of SARS-CoV-2 variants, including Omicron. We introduce an antibody accessibility score (AAS) that accounts for the steric shielding effect of glycans at the surface of spike. We find that high values of the AAS correlate strongly with the sites of mutations in the spike proteins of newly emerging SARS-CoV-2 variants. We use the AAS to assess the escapability of variant spike proteins, i.e., their ability to escape antibody-based immune responses. The high calculated escapability of the Omicron variant BA.5 with respect to both wild-type (WT) vaccination and BA.1 infection is consistent with its rapid spread despite high rates of vaccination and prior infection with earlier variants. We calculated the AAS from structural and molecular dynamics simulation data that were available early in the pandemic, in the spring of 2020. The AAS thus allows us to prospectively assess the ability of variant spike proteins to escape antibody-based immune responses and to pinpoint regions of expected mutation activity in future variants.