Quarterback Productivity

Football fans are familiar with the "passer rating" (aka quarterback rating) that attempts to measure the efficiency of quarterbacks. Unfortunately, every component of the rating is normalized to pass attempts. Thus, while it does do well what it purports to do (measure per attempt "efficiency"), it is useless as a measure of what I'll call quarterback "productivity." If a quarterback rarely throws, he'll rarely face nickel and dime packages and consquently have an "efficiency" advantage. The real trick is a quarterback who throws a lot and still does it well.

For this reason, I was curious to find a simple modification to the quarterback rating that would measure just how heavily a team depends upon its quarterback for its offense and how well that quarterback delivers. Passing yards per game can be useful in this regard, but why not have a statistic that parallels the quarterback rating (i.e., considers TDs, INTs, etc.) but measures productivity.

My plan was to make it a simple variant of the quarterback rating as well as to try to keep it on roughly the same scale. Here is the result:

Quarterback Productivity (QP) =
Quarterback Rating (QR) * (Attempts Per Game / 30).

Basically, we've assumed a nice round number for typical attempts per game (30). If you revert to the original quarterback rating formula, you find that I'm basically converting all of its components (which are effectively per attempt) to a set of components that are instead "per game." Here are the recent leaders (no surprises):

2008 Graham Harrell (Texas Tech)
2007 Graham Harrell (Texas Tech)
2006 Colt Brennan (Hawaii)
2005 Colt Brennan (Hawaii)

A final note: While the average QP is on par with the average QR, the spread in the productivity is about double that of the rating, so numbers in excess of 200 are not uncommon. Thoughts? Suggestions?