Random dot motion (RDM) displays have emerged as one of the standard stimulus types employed in psychophysical and physiological studies of motion processing. RDMs are convenient because it is straightforward to manipulate the relative motion energy for a given motion direction in addition to stimulus parameters such as the speed, contrast, duration, density, aperture, etc. However, as widely as RDMs are employed so do they vary in their details of implementation. As a result, it is often difficult to make direct comparisons across studies employing different RDM algorithms and parameters. Here, we systematically measure the ability of human subjects to estimate motion direction for four commonly used RDM algorithms under a range of parameters in order to understand how these different algorithms compare in their perceptibility. We find that parametric and algorithmic differences can produce dramatically different performances. These effects, while surprising, can be understood in relationship to pertinent neurophysiological data regarding spatiotemporal displacement tuning properties of cells in area MT and how the tuning function changes with stimulus contrast and retinal eccentricity. These data help give a baseline by which different RDM algorithms can be compared, demonstrate a need for clearly reporting RDM details in the methods of papers, and also pose new constraints and challenges to models of motion direction processing.