Inspired by a tweet from Chris Brown a.k.a smartfootball on this interesting but largely meaningless article from Rivals I decided to put together a post on offensive balance. This is going in place of my normal Monday post and I should be back in a week or so with Brian’s requested special teams primer.
Game Theory and Play Calling
Game theory suggests that teams will adjust their choices so that the average value of each choice (run or pass) will be equal. We also know that not all coaches are rational decision makers and there are likely very few who understand what game theory is. That is where nerds like myself come it to explain on blogs and help them understand.
The thinking goes like this: a team is really good at running the ball and really bad at passing the ball, but they are perfectly “balanced,” half their plays are rushes and half are passes. Since there is more value on a running play than a passing play, it doesn’t make sense to be calling so many pass plays, so the first adjustment happens and this team starts calling more rushes to take advantage of their more efficient running game. At some point, the defense responds to the new strategy and begins to stack against the run which of course makes success in the passing game easier. If the offense is playing optimal strategy, their final mix will be one that garners the same value for each play, regardless of whether it is a run or a pass, even if the distribution of plays is not 50/50.
This is how every team in the country fared on a per down basis in both rush and pass. The diagonal line represents balanced results on a per play basis. Teams on the top right are balanced and successful, teams on the bottom left are balanced and unsuccessful. Teams to the left of the line (Northwestern, Iowa, Michigan St, Notre Dame, Penn St, Wisconsin, Indiana and Minnesota) should pass the ball more to become more optimal where teams below the line (Michigan, Ohio St and Illinois) have the opportunity to run the ball more to become more optimal. Purdue sits right at the intersection of all lines, balanced and mediocre. Most of the teams in the Big 10 where within reach of balance with the notable exceptions of Michigan St and Notre Dame, two teams that couldn’t get their rushing outputs to match their passing success. Time for another chart.
In this chart you can see how balance in calls does not necessarily equal balance in output. In fact, some of the least balanced play callers, on both ends of the spectrum no less, produced the most balanced results in output. Teams who rushed over 80% of the time like Georgia Tech, Navy and Army got almost the same value from passes as they did form rushes. On the other end, pass happy squads like Texas Tech, Kansas and Houston saw similar production on a per play basis from their running games as they did from their passing games. These teams are still running or passing teams, but their play calling balance has found an equilibrium where they are maximizing their total points by finding balance, even if they are calling a lot more of one type of play than another.
You can see that Michigan St and Notre Dame are both outliers in their respective deviations in success between run and pass, despite being towards the middle (especially MSU) when it comes to run pass selection.
This data does not include games for any team versus non D1 opponents (Baby Seal U). Only plays when the lead is 2 TDs or less or if the game is still in the first half are counted. Points per play uses my expected points model and is adjusted based on opponents played. Interceptions are included in this analysis but fumbles, fumble returns and interception returns are not. Including fumbles pushes the balance to passing as fumbles are more likely to occur on running plays than pass plays. Most of that difference is negated if you include returns as interceptions are much more likely to be returned than fumbles and the total value of interception returns is nearly equal to the difference between fumbles on running plays versus passing plays. The net of it all is that excluding fumbles and returns does not materially affect any of the data above.