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Random numbers are at the heart of every agent-based model (ABM) of health and disease. By representing each individual in a synthetic population, agent-based models enable detailed analysis of intervention impact and parameter sensitivity. Yet agent-based modeling has a fundamental signal-to-noise problem, in which small changes between simulations cannot be reliably differentiated from stochastic noise resulting from misaligned random number realizations. We introduce a novel methodology that eliminates noise due to misaligned random numbers, a first for agent-based modeling. Our approach enables meaningful individual-level analysis between ABM scenarios because all differences are driven by mechanistic effects rather than random number noise. We demonstrate the benefits of our approach on three disparate examples. Results consistently show reductions in the number of simulations required to achieve a given standard error with levels exceeding 10-fold for some applications., Comment: Updated title, improved abstract, and changed formatting