Lots of very good comments, insightful and thought-provoking. Thanks to all who responded to the blog, by email, or otherwise.
Before directly responding, I'll digress for just a moment. The interesting thing to me about football is its complexity. Baseball can essentially be modeled as a two-man game between pitcher and hitter and each's job never really changes throughout the game, it's simpler to identify the key baseball statistics that increase winning--on-base percentage, walks, and others that increase runs scored and decrease runs given up over time.
Football, on the other hand, is full of "noise." Twenty-two players on every play, different strategies, down and distance, leads, and even injury concerns all muddle the analysis. Further, there are only a handful of games each season, so we don't really get a large enough sample to know what works and what doesn't. All is not hopeless though. While baseball can maybe be thought of as a maximization problem for runs with a few variables, football is more like decision theory--many variables, changing circumstances, and lots of uncertainty.
This trait--that football decision-making is overwhelmingly complicated for what is otherwise a very simple game--leads many to throw their hands up and fall back on "common wisdoms" and truisms ("the only stat that matters are wins"). I argue, however, that the correct response is to try to be as objective as possible and get smarter about how you analyze those decisions, and then to use informed judgment. As Charlie Weis says, at some point, play-calling is more art than science, but the best artists have thought it all through.
Lastly, doing the kind of analysis I did in my last article is really just another way to attack the objective/subjective problem in football. Football games are wildly odd events; every single play in a half can be a statistical anamoly, and information is flies at you faster than you can process. Good teams adjust in-game, but the best adjusting teams have already thought of all the scenarios during the week.
In a previous post, I compared Thomas Schelling's work on decision theory to Bill Walsh and his progeny's gameplanning revolution--the real hallmark of the West Coast Offense. Walsh many times has discussed how important it is to make as many decisions as possible in the cool confines of the coaches office in order to be rational and objective rather than subjective and subject to human passions and biases.
The approach I set forth to rethinking balance and average output per play is just an attempt to do the same thing--pursue objectivity--in a different way. I think this idea is best illustrated with an example from New England Patriots coach Bill Belichick. According to several accounts, Belichick realized several rather simple facts. First, winning teams convert their third downs at a rate higher than the NFL average. Second, some teams are consistently better than others. Turning to league data, his own director of research (the fact that the Patriots have one should be a tip-off to the rest of us) and some academic work, he realized that good teams almost exclusively run in short yardage situations. In other words, on the whole, NFL playcallers--the highest paid most experienced coaches in the world--overvalued passing and undervalued running in short yardage situations. Play-callers simply didn't take into account how frequent incompletions were compared to stuffed run plays.
This result is not a total surprise, even from conservative coaches. On 3rd and 1 a QB rolls right, tosses it to the flat to the fullback . . . who drops it. On 4th and short the QB drops back, he has a guy in his face, but the Tight-end is wide open . . . and the ball sails high. Then, on 4th and 1, with the line stacked, the coach calls a dive . . . stuffed. Which one does he receive the media flak for? Criticism from other coaches? Is hardest on himself?
In the first scenario the fullback is the goat (he should have caught it!), on the second the QB (how hard is it to hit the open guy?) or the line (if the guy hadn't gotten through the QB would have thrown it fine), while on the run, it's unimaginative playcalling.
After doing his homework, however, Belichick had no choice but to conclude that all that was subjective bias: The bottom line is that runs work better in those situations, and he's run the ball to being a league leader in those situations over the last several seasons.
This is a perfect example of rethinking the entire approach to a situation in a way supported by theory and data to achieve greater success. Is it revolutionary? Is it upending all football? No of course not. But it was not a widely held belief and despite all the best and most well paid minds in the game preparing every week, he was one of the first to simply stop and say that running the ball simply works better in short yardage than does the pass. My hope is to start down the road of something like this kind of insight regarding our concept of balance on "bread and butter" downs like 1st and 10, 2nd and 5, and the like.