Two Large Open-Access Datasets for Fitts’ Law of Human Motion and a Succinct Derivation of the Square-Root Variant

Fitts' law specifies a logarithmic relationship between motion duration and the ratio of target distance over target size. This paper introduces two large open-access datasets from experimental user studies: first a controlled (in-lab) study with 46 participants, and second an uncontrolled online study using a Java applet. We present a succinct derivation of the square-root variant of Fitts' law using optimal control theory and compare three models that relate motion duration to the ratio of target distance over target size: LOG (Fitts' original logarithmic function), SQR (square-root), and LOG' (McKenzie's logarithmic plus 1.0). We find that: 1) the data from the controlled and uncontrolled studies are consistent; 2) for homogeneous targets (with fixed size and distance), the SQR model yields a significantly better fit than LOG or LOG', except with the most difficult targets (where the ratio of target distance over target size is large) where the models are not significantly different; and 3) for heterogeneous targets (with varying size and distance), SQR yields a significantly better fit than LOG for easy targets and LOG yields a significantly better fit for targets of medium difficulty, while the LOG' model yields a significantly better fit than both LOG and SQR on very difficult targets. The anonymized datasets including 94 580 human reaching motion timing measurements are, to our knowledge, the largest collected to date.