Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. Although control of these viruses is becoming increasingly effective through improvements in vaccine strain selection, predicting the antigenic characteristics of new viral variants remains an exceptionally difficult task. A complementary approach to disease control would be to guide the dynamics of a virus into an evolutionary regime that could be more effectively managed. This approach seems plausible as different viruses exhibit different evolutionary patterns and these patterns appear to be shaped, at least in part, by modifiable ecological factors. However, the feasibility of this approach is currently limited because we lack an understanding of which factors are key to shaping these evolutionary differences. With this as an overarching goal, I will present a theoretical framework that probabilistically anticipates patterns of viral antigenic diversification. This framework is based on a dimensionless number, whose value depends on epidemiological parameters. While similar in spirit to the basic reproduction number, which quantifies a pathogen's reproductive potential, our dimensionless number quantifies an antigenically variable virus's evolutionary potential. As such, it offers new perspectives on viral evolution by linking well-known ecological factors to the less well understood, long-term changes in viral antigenic diversity. I further detail how this framework can be applied to empirical viral systems, using influenza A/H3N2 as a case study.