Tuesday, December 15, 2009

Did Ohio State Run Too Little This Year???

Amazingly, the answer to my provocative question is maybe.  Bear with me and I will try to explain why.  Earlier this year, I mentioned in response to complaints regarding the Buckeyes running too often that tpeople were not getting the full picture.  The key question was not "balance" in the sense of how many runs vs. how many passes, but rather whether Ohio State's run-pass equilibrium in terms of yards per carry versus yards per pass attempt was efficient.

Now we have some data from which we can assess this question   As alluded to above, I am basing my determination of this on Chris Brown's discussion of run-pass balance and game theory here, here, and here.  I highly recommend it all, but if I could boil down Brown's position on run-pass balance it would be the following:

[A] football game is a series of Nash Equilibriums: Every down is a little contest and each side must figure out its best strategy using a mixture of runs and passes or different defenses (a "mixed strategy") and should pick the mixture of runs and passes that maximizes (or minimizes, if on defense) average gain per play, subject to the "passing premium," which requires that passes yield more than runs because of their greater risk.
 I will not try to fully restate Brown's position but will give this further synopsis.  The goal is not to shoot for a particular run/pass 'balance' be it 60/40, 50/50 or the like.  Rather the goal is to maximize yards per attempt.  (Note that, like Brown, I am focusing on yards per pass attempt, which counts an incompletion as '0' and a sack as negative yards.).  To do so, you want to get to a point where your yards per run play and yards per pass attempt equal out to the nearly the same thing--if they are not then you are leaving yards on the field by doing one or the other too often, meaning the defense is able to too fully focus on one to the exclusion of the other.  So if you are gaining 15 yards per pass attempt and 5 yards per rush, you should keep passing until the defense has to focus on your passing game more, which will increase your yards per rush attempt and decrease your yards per pass attempt until they reach an equilibrium.  So theoretically a team could pass 80% of the time and rush 20% of the time and be perfectly balanced if they are maximizing their yards per attempt.

But, as Brown argues, the run and pass numbers should not be identical--instead their should be a built-in "passing premium."  To make this point, he cites an old adage that Buckeyes fan will recognize:

 Three things can happen when you pass, and two are bad.
Basically, because loss of field possession, long third downs, (harder to convert) and turnovers are so costly, passing is riskier than rushing.  As such, teams should average more yards per pass attempt than yards per carry.  If they do not have a "passing premium" they are passing too much relative to running under game theory and opening themselves up to mistakes.  Brown acknowledges that it is unclear what this premium should be, but it seems it should be anywhere from 1-2.5 yards per attempt (Brown notes the NFL had a 2.5 yard per premium, and I personally tend to defer to NFL coaches in making such run/pass determinations because they have the most time to study these issues, but for now the exact premium is irrelevant).

In sum, as Brown says:

Balance, then is not a matter of how many runs and how many passes, but how good you are at both and making sure you are rewarded for passing's increased risk as this is the way to more first downs, more points, and more wins.

Taking this framework as a given, we can now assess Ohio State's run-pass "balance"  this year.  Basically we are trying to assess whether Ohio State took a maximal or inefficient strategy under Game Theory based on yards per carry vs. yards per pass attempt.  Fortunately, TheOnlyColors.Com put together a great scatterplot graph plotting each Big Ten Team's yards per carry and yards per pass attempt in Big Ten play (MGoBlog discusses the same graph here):

As we can see here, in Big Ten play, Ohio State rushed for 5.2 yards and passed for 5.4 yards per attempt .  That means that Ohio State rushed too little because they do not have a sufficient pass premium built in!   According to Nash Equilibrium, Ohio State should have ran more in Big Ten play until they established a sufficient yards per attempt balance (by contrast Penn State has about the optimal balance; Iowa should have passed more).  If anything then, Jim Tressel was inefficient by not running the ball enough.

Two caveats apply.  The first , as Brown notes, is that such a study should ideally focus on First and Second down, because the goal on Third Down is not to maximize yards, but to gain a First Down.  This may make the above data not as refined, but my own intuitive sense is that because rush plays on Third Down are often short yardage plays, this may actually skew the stats in favor of passing, only further establishing the point.

The second, more important caveat, is that (I do not believe) this yards per pass attempts include Terrelle Pryor's rushing yards from scrambling on called pass plays (though I could be wrong, the study does not say).  Because this ability is a clear benefit to Ohio State's passing game, these numbers should be included in the yards per pass attempt.  However, I do not believe that those yards are sufficient to point the statistics in the other direction; very likely it would instead create a sufficient passing premium for Ohio State and  demonstrates that Ohio State came close to a Nash Equilibrium.*


Jim Tressel gets a lot of flak for being too conservative, and he would probably not argue the point too vigorously.  But, using Brown's position as a baseline, statistics from Big Ten play, and the caveat I state above, Ohio State was not "too conservative" in its playcalling.  Instead, it appears OSU wasentirely rational in their playcalling and perhaps did not run the ball enough.  Under Game Theory, Ohio State's run/pass balance was nearly spot on.  I would not be surprised if, following the Purdue game, the Ohio State staff studied similar statistics and saw they needed to run the ball more, leading to their late season gameplan.    

*By contrast, note that Brown's study of 2005 Texas included Vince Young's rushing stats in the rushes per carry--including his scrambles into the yards per pass attempt would have only increased the sub-optimal nature of the run-pass play calling for Texas that year).


  1. First I want to say thank you very much for the post. It was very insightful. I hadn't considered the trade-offs involved between RYA and PYA. My question is to what extent are the RYA and PYA's structural in nature. In other words is the tradeoff a function of players (i.e. Pryor) or does the playing calling that Tressel is making influence these numbers. If we assume that Tressel's play calling is reducing PYA's specifically then the play calling is in question and the running heavy is a crutch given Tressel's initial shortcomings in increasing PYAs (more or less introducing a 2 level game theoretic model).

    Anyway thanks for the post. I really enjoyed it.

  2. Great post. As an ops-research guy, I really got a kick out of this analysis from a game theory standpoint. Looking forward to the pre Rose Bowl breakdowns if you're making them.

  3. Boulderbuck, thanks so much for the awesome site. I come back to it every day looking for new posts. Though I've been a lifelong Buckeye (born in Columbus!) I've never gotten deeper into the game than simple run play pass play key down etc, and you've been tremendously instrumental in helping me appreciate the Xs and Os (since I watch every OSU game). Best of luck with the site and keep up the good work!!

  4. Love the site. Awesome analysis, keep up the good work.

  5. Mighty Mike-

    That is a great point; one would have to assume that the actual plays called would have some effect, but I am unsure how one could structure a study to figure it out. But I think your basic point is sound, that being that the overall yardage gained may be sub-optimal because, to take your example, perhaps defenses can overly commit to stopping the run because the OSU pass offense is not maximized by the play calling, thereby in turn bringing down the run yards.

    On the other hand, over the course of the season, one may also think that good and bad decisions regarding play calling would even out and, relatedly, that it would get to the point where a defense would 'gang up' so much against the run that even a poorly designed passing game would succeed.

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