Passing and Rushing Plays in the NFL
https://thepowerrank.com/2018/09/24/the-surprising-truth-about-passing-and-rushing-in-the-nfl/
The article The Surprising truth about passing and rushing in the NFL discusses the effectiveness and ultimately the importance of passing and rushing plays to NFL teams. In football, there are three fundamental types of plays – passing, rushing, and play-action, a deception play where the offense fakes a rushing play although the article focuses primarily on passing and rushing plays. To measure the efficiency, we can use a statistic called team efficiency, which is calculated by subtracting the average number of yards given up by the defense per play from the average number of yards gained by the offense per play. As opposed to the team passing efficiency, the team rushing efficiency demonstrated little correlation with the number of games an NFL team won each season, suggesting that rushing plays have only a minimal impact on the game. A similar conclusion can be drawn by looking at a different statistic – expected points added (EPA). Although the calculations for EPA are more complex, the number itself reflects the value of each play. The average rushing play yielded an EPA of -0.04 while the average passing play yielded an EPA of +0.04. All in all, rushing plays would appear to be counterintuitive to employ in an offense by these statistics alone.
By looking at the decision-making between passing and rushing games through the lens of game theory, we can understand the reasoning as to why NFL teams do decide to employ rushing plays. Consider the payoff matrix of the game to include two players which are the offense and defense with payoffs equalling the average number of yards gained per play for the offense as its payoff and the average number of yards given up each play. The offense can either choose to run a pass or rush play and the defense can either choose to defend against a pass play or defend against a run play. Although the stronger strategy for the offense is to run a pass play, if the offense were to commit to running pass plays each time, the defense would choose to commit to defend against the pass each time, thus decreasing the payoff for the offense. This sets up a mixed strategy equilibrium in which the offense chooses to employ a pass play for some percent p and the defense chooses to defend against the pass for some percent q such that the expected value of passing and rushing is equal for the offense and the expected value for defending against the pass and defending against the rush is equal. Such an equilibrium demonstrates the importance of the run play despite its apparent lack of efficiency at times.
This simple analysis of the game ignores the third type of play, however: the play-action play. The EPA for a play-action play in the NFL comes in at 0.17, significantly higher than the EPA for either a purely pass or rush play. What is interesting, however, is that the success of the play-action play solely relies on the use of rush plays for its deception to be effective. Teams that have had a strong running efficiency do not necessarily excel at play-action plays. At the end of the day, NFL teams must vary the type of play run each time to ensure the maximum payoff for their offense to, in the end, win games, regardless of the effectiveness of the run play.