Fitts Law as a Restrained Random Walk

Fitts law, one of the rare quantitative relations in psychology, describes the time it takes for a human being to aim at and hit a target of a given size, starting from a given remote position. We provide here a new interpretation of this law, not invoking a discretization of space and time as in the original information theory representation of Fitts, but involving a simple restrained random walk on a continuum, in space and time. We not only predict that the pointing time is proportional to the logarithm of the starting distance relative to the target size (which is Fitts law), but also describe the complete probability of presence of the pointer in its route to destination. In particular, we quantify the pointer large time overlapping efficiency with the target from the comparison of a new length-scale intrinsic to the motion, with the target size.