Influenza virus evades prevailing natural and vaccine-induced immunity by accumulating antigenic change in the haemagglutinin surface protein. Linking amino acid substitutions in haemagglutinin epitopes to epidemiology has been problematic because of the scarcity of data connecting these scales. We use experiments on equine influenza virus to address this issue, quantifying how key parameters of viral establishment and shedding increase the probability of transmission with genetic distance between previously immunizing virus and challenge virus. Qualitatively similar patterns emerge from analyses based on antigenic distance and from a published human influenza study. Combination of the equine data and epidemiological models allows us to calculate the effective reproductive number of transmission as a function of relevant genetic change in the virus, illuminating the probability of influenza epidemics as a function of immunity.