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DNA methylation clocks can accurately estimate chronological age and, to some extent, also biological age, yet the process by which age-associated DNA methylation (DNAm) changes are acquired appears to be quasi-stochastic, raising a fundamental question: how much of an epigenetic clock's predictive accuracy could be explained by a stochastic process of DNAm change? Here, using DNAm data from sorted immune cells, we build realistic simulation models, subsequently demonstrating in over 22,770 sorted and whole-blood samples from 25 independent cohorts that approximately 66-75% of the accuracy underpinning Horvath's clock could be driven by a stochastic process. This fraction increases to 90% for the more accurate Zhang's clock, but is lower (63%) for the PhenoAge clock, suggesting that biological aging is reflected by nonstochastic processes. Confirming this, we demonstrate that Horvath's age acceleration in males and PhenoAge's age acceleration in severe coronavirus disease 2019 cases and smokers are not driven by an increased rate of stochastic change but by nonstochastic processes. These results significantly deepen our understanding and interpretation of epigenetic clocks. Tong et al. construct simulations using DNA methylation data to quantify what proportion of the predictive accuracy of epigenetic clocks could be explained by stochastic methylation changes, suggesting that stochasticity contributes more toward the accuracy of chronological rather than biological age predictions.