Random-dot cinematograms in which each dot’s successive movements are randomly drawn from a Gaussian distribution of directions can produce a percept of global coherent motion in a single direction. Discrimination of global direction was measured for various exposure durations, stimulus areas, and dot densities and bandwidths of the distribution of directions. Increasing the duration produced a greater improvement in performance than did increasing either the area or the density. Performance decreased as the distribution bandwidth increased. An ideal-observer model was developed, and the absolute efficiency for human direction discrimination was evaluated. Efficiencies were highest at large distribution bandwidths, with average efficiencies reaching 35%. A local–global noise model of direction discrimination, based on the ideal-observer model, containing a spatial and temporal integration limit as well as internal noise, was found to fit the human data well. The utility of ideal-observer analyses for psychophysical tasks and the interpretation of efficiencies is discussed.