Decisions in everyday life are prone to error. Standard models typically assume that errors during perceptual decisions are due to noise. However, it is unclear how noise in the sensory input affects the decision. Here we show that there are experimental tasks for which one can analyse the exact spatio-temporal details of dynamic sensory noise and better understand variability in human perceptual decisions. Using a new experimental visual tracking task and a novel Bayesian decision making model, we found that the spatio-temporal noise fluctuations in the input of single trials explain a significant part of the observed responses. Our results show that modelling the precise internal representations of human participants helps predict when perceptual decisions go wrong. Furthermore, by modelling precisely the stimuli at the single-trial level, we were able to identify the underlying mechanism of perceptual decision making in more detail than standard models.