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Offensive Holding and the Run/Pass Ratio

This football season, the NFL has made a change in the rules that is causing the offensive holding penalty to be more stringently enforced, especially on run plays. Josh Hermsmeyer at FiveThirtyEight argues that this new rule could incentivize teams to attempt pass plays more often as the increased likelihood of a holding call will decrease the expected value of a run play for the offense:

NFL teams hardly need further incentive to call more pass plays, but nevertheless, here is potentially another reason to move away from the run game. Teams that pass more often than they run would stand to benefit the most from the new emphasis on back-side holding. Perhaps the officials will do what analysts have been unable to do all these years; that is, finally convince the NFL to reevaluate the frequency with which they run the ball.

Even prior to this season, it has seemed illogical how infrequently teams pass the ball when you look at the expected yardage gain for each type of play. So, why are there still so many run plays? Clearly it would be a poor strategy to pass the ball for every play, as the defense would quickly adapt to that. But, shouldn’t teams be passing much more frequently than they currently are?

If we vastly simplify the play-calling process into a two-strategy game-theoretic model where the offense can either run or pass the ball and the defense can more heavily guard against either the run or the pass, we can see that maybe there is some reasoning behind the run-heavy offenses that we have observed. Often in mixed-strategy Nash equilibria (which is what we have) players will use their most effective strategy (the pass) less frequently then we might intuitively think. This is because, again, if a team passes too much, the defense will begin to expect it. If they only occasionally pass, they are likely to be successful when they do, as the defense will be unprepared for it.

We should also consider that, even if the defense is expecting it, a run play can often get a yard or a few yards, as the gain depends on how far the runner can go before getting tackled. Compare this to a pass play, where a major component of the play’s success is whether the pass is complete or incomplete—the play can either gain some number of yards, or gain nothing at all. As such, perhaps it is advantageous to run more often and save the pass for those occasional game-changing plays.

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