While humans are very reliable (i.e. give highly reproducible answers) when repeatedly judging the direction of a moving random-dot pattern (RDP) we find that their accuracy (i.e. the direction they so reliably report) shows systematic errors. To quantify these errors, we presented a complete set of closely spaced directions and mapped the directional misjudgments by asking subjects to compare the perceived direction of a moving RDP with the direction of a test line. The results show misjudgments of up to 9 degrees, which are best accounted for by a tendency of the subjects to overestimate the angle between the observed motion and an internal reference direction. A control experiment in which subjects had to judge the spatial distance between a point and a line demonstrates that these misjudgments are not confined to motion stimuli but rather seem to reflect a general tendency to overestimate the distance between a stimulus and a reference when they are close to each other.