Advanced NFL Coaching Stats: How to quantify coaching

One of the great mysteries in sports statistics lies in quantifying just how much a coaching staff helps the team. Surely there are cases in which coaching and physical training helps individuals improve, but without a 24/7 webcam in teams’ facilities and players’ offseason homes, it’s hard to know how much of a player’s improvement or decline can be attributed to the coaching staff. In baseball and hockey, all the coaching staff can really do to affect the actual game results are set the proper lineup, make good substitutions, and set proper strategy for certain points in the game. Basketball has some set plays, but not all the time. Football is different, in that each play involves play calling between the offensive and defensive coaches. Certainly, there are differences between good play callers and bad ones, and this should be able to be quantified. I recently stumbled upon a site that does just that, called QuantCoach.

 The proprietor of the site (he calls himself “QC”) has developed a way to extract coaching efficiency from the yards per pass attempt (YPA) of each team, based on an economic concept called Endogenous Growth Theory. In simple terms, the theory states that growth in any competitive process is a combination of technological progress and the application of labor. QC breaks this labor part down into “labor used in play calling” and “labor used in playmaking”. The “labor used in playmaking” is obviously the players on the field, while the “labor used in play calling” is obviously the coaching staff, and sometimes the quarterback.

QC explains his football philosophies in what he calls his “Ten Commandments” here. They are a very good read, and help explain the ideas behind the equations below. In developing the equations, QC takes the total on-field contributions of all parties, which is simply YPA compared to the average, and subtracts Hy (labor used in playmaking), which is YPA multiplied by the constraints of the football field. What’s left is the contributions of the coaching staff. Pretty neat, huh? There are also productivity equations, which involve the constraint of needing 10 yards to get a first down, along with yards per rush.

Here are the main equations:

1. Total: H = (YPA-6.692) / 6.692
2. Playmaking: Hy =[ [120(YPA/10)] – 100] / 100
3. Playcalling: Ha = H – Hy
4. Player Productivity: (.1*YPA)/[(1-.1*YPA-.01*YPR)(.1*YPA+.01*YPR)]

Anyway, what you’d like to know is how the Steelers and their coaching staff of Mike Tomlin, Bruce Arians, Dick LeBeau, etc. have done according to this model.

Glad you asked! In the past three years, the Steelers have ranked first (2008), seventh (2009), and third (2010) in the NFL in playcalling contribution. That’s an interesting result, and I’m sure it’s surprising to the people who end up causing one Steelers blogger who’s more popular than we are to constantly tweet sarcastic “Fire Bruce Arians” remarks.

Another key novelty that QC has introduced is a new way of calculating yards per pass attempt. Traditionally, it is simply total passing yards divided by the number of pass attempts. QC accounts for sacks and touchdowns by adding an extra 10 yards for each passing TD and by taking sack yardage lost, dividing that by pass attempts, and subtracting that from the traditional YPA number, creating a number that more accurately represents passing efficiency than traditional YPA.

One thing I find interesting with the formulas QC uses (and I think it might be a big drawback) is that, unless I’m missing something, the productivity formulas are entirely related to offense. The trademark of the Steelers teams has been LeBeau’s defensive schemes, and while QC does track defensive YPA, it doesn’t appear to be used in the above formulas related to playmaking and playcalling. In fact, the defensive YPA rankings seem to correlate better with the Steelers’ playoff ranking. They were first in 2008, 13th in 2009, and first in 2010.

All things considered, the website is one I wholeheartedly recommend, and I’ll be tracking QC’s stats all year, along with many others, in a weekly advanced stat roundup that will make its debut this week.