Because the retinal activity generated by a moving object cannot specify which of an infinite number of possible physical displacements underlies the stimulus, its real-world cause is necessarily uncertain. How, then, do observers respond successfully to sequences of images whose provenance is ambiguous? Here we explore the hypothesis that the visual system solves this problem by a probabilistic strategy in which perceived motion is generated entirely according to the relative frequency of occurrence of the physical sources of the stimulus. The merits of this concept were tested by comparing the directions and speeds of moving lines reported by subjects to the values determined by the probability distribution of all the possible physical displacements underlying the stimulus. The velocities reported by observers in a variety of stimulus contexts can be accounted for in this way.