Despite decades of research on the influenza virus, we still lack a predictive understanding of how vaccination reshapes each person's antibody response, which impedes efforts to design better vaccines. Here, we combined fifteen prior H3N2 influenza vaccine studies from 1997-2021, collectively containing 20,000 data points, and demonstrate that a person's pre-vaccination antibody titers predicts their post-vaccination response. In addition to hemagglutination inhibition (HAI) titers against the vaccine strain, the most predictive pre-vaccination feature is the HAI against historical influenza variants, with smaller predictive power derived from age, sex, BMI, vaccine dose, the date of vaccination, or geographic location. The resulting model predicted future responses even when the vaccine composition changed or a different inactivated vaccine formulation was used. A pre-vaccination feature ‒ the time between peak HAI across recent variants ‒ distinguished large versus small post-vaccination responses with 73% accuracy. As a further test, four vaccine studies were conducted in 2022-2023 spanning two geographic locations and three influenza vaccine types. These datasets formed a blinded prediction challenge, where the computational team only received the pre-vaccination data yet predicted the post-vaccination responses with 2.2-fold error, comparable to the 2-fold intrinsic error of the experimental assay. This approach paves the way to better utilize current influenza vaccines, especially for individuals who exhibit the weakest responses.