# A New Derivation and Dataset for Fitts' Law of Human Motion

### Ken Goldberg, Siamak Faridani and Ron Alterovitz

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2013-171

October 22, 2013

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-171.pdf

Human motion models for reaching tasks facilitate the design of many systems such as computer and cellphone interfaces, cockpits, and assembly lines. Fitts' Law species a logarithmic two-parameter relationship between motion duration and the ratio of target distance over target size, and more recent models consider square root and modied logarithmic relationships. This paper contributes new theory and new experiments. For the former, we provide a succinct derivation of the square-root model based on optimal control theory. Our derivation is intuitive, exact, makes fewer assumptions, and requires fewer steps than prior derivations. We present data from two experimental user studies, one a controlled (in-lab) study and the second an uncontrolled (online) study with a total of 94,580 timing measurements. We consider three two-parameter models that relate motion duration to the ratio of target distance over target size: LOG (the classic logarithmic function), SQR (square-root), and LOG' (logarithmic plus 1.0). We find that: (1) the data from the controlled and uncontrolled studies are remarkably consistent; (2) for homogeneous targets, the SQR model yields a significantly better fit than LOG or LOG', except with the most difficult targets (i.e., the ratio of target distance over target size is large) where the models are not significantly different; (3) for heterogenous targets, SQR yields a significantly better fit than LOG for easier targets and LOG yields a significantly better fit than both LOG and SQR on more difficult targets.

BibTeX citation:

@techreport{Goldberg:EECS-2013-171, Author = {Goldberg, Ken and Faridani, Siamak and Alterovitz, Ron}, Title = {A New Derivation and Dataset for Fitts' Law of Human Motion}, Institution = {EECS Department, University of California, Berkeley}, Year = {2013}, Month = {Oct}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-171.html}, Number = {UCB/EECS-2013-171}, Abstract = {Human motion models for reaching tasks facilitate the design of many systems such as computer and cellphone interfaces, cockpits, and assembly lines. Fitts' Law species a logarithmic two-parameter relationship between motion duration and the ratio of target distance over target size, and more recent models consider square root and modied logarithmic relationships. This paper contributes new theory and new experiments. For the former, we provide a succinct derivation of the square-root model based on optimal control theory. Our derivation is intuitive, exact, makes fewer assumptions, and requires fewer steps than prior derivations. We present data from two experimental user studies, one a controlled (in-lab) study and the second an uncontrolled (online) study with a total of 94,580 timing measurements. We consider three two-parameter models that relate motion duration to the ratio of target distance over target size: LOG (the classic logarithmic function), SQR (square-root), and LOG' (logarithmic plus 1.0). We find that: (1) the data from the controlled and uncontrolled studies are remarkably consistent; (2) for homogeneous targets, the SQR model yields a significantly better fit than LOG or LOG', except with the most difficult targets (i.e., the ratio of target distance over target size is large) where the models are not significantly different; (3) for heterogenous targets, SQR yields a significantly better fit than LOG for easier targets and LOG yields a significantly better fit than both LOG and SQR on more difficult targets.} }

EndNote citation:

%0 Report %A Goldberg, Ken %A Faridani, Siamak %A Alterovitz, Ron %T A New Derivation and Dataset for Fitts' Law of Human Motion %I EECS Department, University of California, Berkeley %D 2013 %8 October 22 %@ UCB/EECS-2013-171 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-171.html %F Goldberg:EECS-2013-171