The aim of this paper is to develop a game-theoretic framework to study the impact of player personnel changes on offensive productivity in American football. We develop a new model, the improvement in passing model, which is used to determine the optimal proportion of run and pass plays that a team should call. The model determines the optimal run/pass balance in terms of parameters that reflect a recent change (generally, in our case, an increase) in efficacy of a team's passing offense. The model assumes a residual positive effect on the team's running game occurs as a result of the improved passing attack. Several conclusions are drawn, most surprisingly that improvements in a team's expected gains via the passing game imply that the team should, in fact, run more frequently to optimize their overall offensive productivity. We conclude with an example studying the 2009 acquisition of Jay Cutler by the Chicago Bears.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston