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Saturday, June 28, 2008

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


Phil said...

I looked at this a while back

I looked a run pass balence after the 2003 season and what I found was that there was no correlation between a higher pass/run ratio and a higher yeards per play average

What there was a correlation for was between a lower pass/run ratio and a higher yards per pass average

that year Detroi had the highest pass/run ratio and one of the lowest yards per pass ratios, where as Green Bay and Denver had two of the lowest run pass ratios and 2 of the highest yards per pass averages (if I remember right Atlanta was an outlier having one of the lowest pass/run ratio yet a relatively pedestrian yards per pass average)

2 explainations came to mind, one that runnning the ball more allows your o be more effective through the air, or two that if you were effective through the air you built up a big lead early and ran the ball the rest of the game

I think that if you were able to just do 1st half run pass ratio to yards per play and yards per pass that would lend insight, but that was more work than I was willing to do then or now

Anonymous said...

I, too, read the original article and gave some thought to the notion of passing premiums and what they mean to the game. In my opinion the issue holds very sound dependent on the quality of execution and quarterback play. I am sure we can all agree that there is no substitute for solid quarterback play in terms of offensive production. But there is also something to be said for the element of surprise within a play and the idea that an offense may not attempt to gain as many yards as possible on every play. That could certainly skew an analysis of the inferential statistics regarding the passing premium. A team may not want to incur the risk of going for 12 in the air if they only need 3 on the ground.

For two examples I would look at the Colts and Patriots as they have that outstanding quarterback play. The element of surprise within the passing play has never been more prolific (in my rather brief 25 years of watching football) than it was with Peyton Manning and Edge James. In 04 and 05 Manning had an average of 9.2 and 8.5 despite what had been a very steady 7.4 average before and since. Seeing a lot of the Colts, I believe that this was specifically because of the savvy of the Manning/James duo in the play action deception and the very crisp and veteran receiving staff of Harrison, Wayne, and Stokely. I pose that the well placed threat of playaction was able to enhance the passing premium of the Colts during these years. As you stated in the original post, you must pick your best weapons and play them. The threat of James enhanced the accuracy of Manning and the route running of the receivers.

As for the other example, I pose that the awesome deep weapon that is Randy Moss was without equal when paired with extremely sound quarterback play from Brady. Perhaps in no other system has the theory of a passing premium been proved more true. One could extend this comment to greater lengths to cover that tandem, but suffice it to say that the deep ability of Moss opened up the underneath for Welker and that their overall effectiveness made the running game moot. Brady could throw the 5 yard out to Welker as safely as Maroney could carry it for 3 so why not throw to Welker? There is simply no reason to disguise it. Ironically, it was good pressure from the front four without the risk of excessive blitzing that finally overcame them. A good lesson for GMs in the future? Perhaps Jacksonville was not foolish in taking two pass rushers in the first round? THey do have to play Manning twice a year.

Zennie said...

One aspect to consider: time. A team that passes 100 percent of the time uses less of the clock but suffers simply tiring out the offense, thus making it less effective in maintaining block over time.

An effective run play can serve to strategically shorten the game. Thus the genius of Coach Walsh's approach, where he passed early to establish a large lead, then ran the ball to run out the clock.