Our ability to predict upcoming events is a fundamental component of human cognition. One way in which we do so is by exploiting temporal regularities in sensory signals: the ticking of a clock, falling of footsteps and the motion of waves each provide a structure that may facilitate anticipation. But how strong is the effect of rhythmic anticipation on perception? And to what degree do people vary in their ability to capitalize on these regularities? In 2015, Hickok et al. introduced a behavioural paradigm to assess how a rhythmic auditory stimulus affects perception of subsequent targets (Hickok G, Farahbod H, Saberi K. 2015 The rhythm of perception: entrainment to acoustic rhythms induces subsequent perceptual oscillation. Psychol. Sci. 26, 1006–1013. (doi:10.1177/0956797615576533)). They tested five listeners and found that perception (target detection accuracy) fluctuated rhythmically just like the sound rhythm. Here, we replicate the original finding, assess how likely the finding is to be observed for any individual, and quantify effect size in a large sample of adult listeners (n = 149). We introduce a model-based analysis approach that allows separate estimates of amplitude and phase information in target detection responses, and quantifies effect size for individual listeners. Together our results strongly support the presence of oscillatory influences on target detection accuracy, as well as substantial variability in the magnitude of this effect across listeners.