Quantitative analysis of football play calling suggests that NFL coaches do not choose their strategies optimally. They tend to be overly cautious. One possible explanation for this finding is that NFL coaches are averse to risk and loss. We propose a prospect theory based model of coaches' utility and estimate the model's parameters using kickoff data from the 2009 NFL season. Using an outcome measure of points scored on the initial post-kickoff possession we analyze two strategic kickoff decisions that involve risk-reward tradeoffs: the decision to kick a surprise onside kickoff or a regular kickoff, and the decision to accept a touchback or run the ball out of the endzone. Surprise onside kickoffs may yield a more favorable mean points scored value for the kicking team than a regular kickoff, yet surprise onside kickoffs are infrequently used (and thus the same size is small and the p-value of significance test is 0.68). Coaches appear averse to the possible loss involved in the surprise onside kickoff. Running the ball out yields a higher mean points scored for the receiving team than accepting a touchback, but it entails some risk (fumbles are lost in 2 percent of returns). Nevertheless, declining the touchback option and running the ball out is very common. Coaches do not appear excessively risk averse when presented with this choice over possible gains. Prospect theory models allow for risk aversion over possible gains, as in traditional expected utility theory, and in addition they permit an asymmetric aversion to losses. A prospect theory model therefore seems suitable for our analysis of kickoff strategies. We estimate a risk aversion coefficient value of 0.66 and a loss aversion coefficient value of 1.55, where values <1 and >1 indicate risk and loss aversion, respectively. Our analysis supports the notion that NFL coaches are both modestly risk averse and loss averse. In other words, coaches display diminishing sensitivity to changes in scoring outcomes as they move further from a reference point (zero), and for scoring gains and losses of equal magnitude they suffer more from a loss than they enjoy from a gain. This result may explain their propensity for making conservative strategic choices that, at first glance, appear sub-optimal.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston