Run/Pass Balance, Game Theory, and the Passing Premium Revisited

A few years ago I wrote some of my most popular posts, entitled the "Run/Pass and a Little Game Theory," with follow-up responses to comments One, and Two. (Some of my best ideas are in the responses.)

Although I can't say exactly that they were inspired by my work - though these posts were released in mid-2006 - there has been much serious work done in the areas since.

First, one of the phenomena I identified was that in a world without risk, coaches ought to be neutral between running and passing, and so should call them in whatever mixture produces the most yards per play. But I identified a "passing premium," which refers to the fact that in the real world, passes tend to average more yards per play than runs, and coaches generally do not throw the ball more to correct for this perceived imbalance. I argued that this made sense because passes are generally riskier than runs, but teams might still be out of wack one way or another. The other side of the coin was that supposedly imbalanced teams, be they run first or pass first teams, were often very much balanced in their play selection than people give them credit for.

Well, this idea has engendered much recent scholarship and commentary, including two articles in the Journal of Quantative Analysis in Sports:

- Benjamin Alamar, The Passing Premium Puzzle.

- Duane Rockerbie, The Passing Premium Puzzle Revisited.

- Sabermetric Research, NFL Passing Premium Puzzle Revisited.

The other phenomena I touched on in those articles was that the choice between running and passing, in terms of maximizing your expected gain, was not absolute. Instead it was a game theory problem. In other words, just because passes tends to average more than rushes does not mean that you should call 100% passes. If you pass more and more, the other team will shift their strategy. But even more importantly, the other team will adjust its strategy based on your intrinsic payout structure: If you are an excellent passing team, they will obviously call more pass defenses (or add an extra defensive back, etc) but if your payout structure changes - i.e. an excellent running back returns from injury - that does not mean that you should automatically run more and more, because the other team, knowing that he is back, will be forced to counter your running back. The exact change in optimal run/pass balance can change, but the upshot is that your passing game will often become more attractive when a great running back comes back, because the defense must shift its strategy. So when TV announcers say that just because you have a new or better running back, then that team must automatically run the ball more, do not believe it.

This idea too has engendered commentary (again, not necessarily as a direct result of my posts, but I wrote about it some years ago and I'm happy to see the ideas proliferate):

- Advanced NFL Stats, Game Theory and Run/Pass Balance.

- Advanced NFL Stats, Passing Paradox. (I mention this article too because it cites some of my older work, which attempted to account for the riskiness of runs and passes and find their optimal mix by using the Sharpe ratio from financial economics. See also here, and here.)

I look forward to more and more analysis on these topics. Football is by far the most interesting sport to analyze, but also the most difficult. So, so many variables. Each play is discrete, but interconnected to the others in intricate ways (hence, game theory). Further, to analyze it requires a certain basic competency in football, statistics, probability, and economics (along with time) that few possess. As great as Football Outsiders is, they have produced very little that is useful to the typical coach. But the ideas here transcend the fan and the practitioner. I am sure there is more to come.

Links to my past articles:

Run/Pass Balance and a Little Game Theory
Run/Pass Balance - Response to Comments I
Run/Pass Balance - Response to Comments II
The Sharpe Ratio for Football - I
The Sharpe Ratio for Football - II
The Sharpe Ratio for Football - III