How Football Players Determine where to Run to Tackle other Players: A Mathematical and Psychological Description and Analysis

Dennis M. Shaffer1, *, Thomas B. Gregory2
1 Department of Psychology, The Ohio State University-Mansfield
2 Department of Mathematics, The Ohio State University-Mansfield, USA

© 2009 Shaffer et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Psychology, The Ohio State University, Mansfield, USA; E-mail:


Players in American football must be able to competently and quickly intercept and tackle an opponent who has the ball. We developed a mathematical model that describes the use of a constant target-heading angle between the pursuer and ball carrier. We found that players in American football maintained a constant target-heading angle across changes in initial angle, direction, and speed of the players being pursued. Players more often evaded capture by running toward the chaser and then changing direction, than by running faster and farther away from the chaser. Our mathematical model made several testable predictions that were supported by our data. It also makes several testable predictions that may be investigated in future work. The act of maintaining a constant target-heading angle seems to be a strategy that is used generically to pursue and intercept moving objects.