Global flow occurs when random dots, each selecting their direction of motion randomly each frame from a distribution of directions spanning up to 180°, appear to move as a whole in the mean direction of the components. This percept arises because the visual system integrates the many independent local motion signals over space and time. Through a series of direction discrimination experiments with random-dot cinematograms (RDCs), we show that varying the luminance of dots over a suprathreshold range profoundly affects perceived direction; the brightest dots appear to be weighted more and dimmer dots weighted less when determining perceived global direction. This effect is not observable if all dots in the display have the same luminance but only when the display contains dots with different luminance values. The results are consistent with energy models of motion detectors whose responses are contrast dependent. A Monte Carlo simulation of global direction discrimination employing a 12-mechanism line-element model that weighted the local motion vectors by the normalized squared contrast of the component dots (a proxy for contrast energy) captured well the features of the experimental data.