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#1 Posted : Sunday, March 3, 2013 11:37:35 PM(UTC)
Although Denver Broncos quarterback Peyton Manning posted an excellent season in 2012, it wasn’t the best performance of his career, according to the Complete Quarterback Rating System (CQBR).
Although Denver Broncos quarterback Peyton Manning posted an excellent season in 2012, it wasn’t the best performance of his career, according to the Complete Quarterback Rating System (CQBR).

Not another rating!
Considering how vocal I am in my insistence that quarterbacks get too much of the credit for wins and too much of the blames for losses, it might seem a tad hypocritical to release yet another quarterback rating system into the wild.

What can I say? I am addicted to this rating business. Besides, I think it’s high time that budding football analysts like ourselves had access to a complete quarterback rating that takes into account a quarterback’s actual numbers on the field, one that doesn’t rely on mystical concepts like “clutch factor” and “expected points.”

Concepts like those are undoubtedly interesting, and they may even be very useful. The problem is they are also inherently subjective, based as they are on value judgments of what is “good” and “bad” and how “good” or “bad” they are.

There is definitely a place for those kinds of rating systems. They do an excellent job of provoking debate and discussion, which is what they are designed to do.

On the other hand, there is also a place for a rating system that takes an objective, dispassionate look at a quarterback’s production, one that doesn’t care how he gets the job done but simply paints a picture of where his performance ranked with respect to that of his peers.

Complete Quarterback Rating (CQBR)
The Complete Quarterback Rating System (CQBR) fills just such a niche. It looks at everything a quarterback does between the white lines — both passing and rushing — and takes into account how well he maintains ball security. Rather than trying to weight a quarterback’s passing and rushing by how much of an effect each has on winning, however, CBQR simply weights them by the number of respective attempts.

This exciting approach means that the CBQR doesn’t care whether a particular quarterback is a pass-first quarterback or a run-first quarterback. As long as he does what he does best, he can have a high rating.

An immobile quarterback like Peyton Manning of the Denver Broncos can have a very high CBQR despite being an ineffective rusher, because he hardly ever scrambles and his low rusher rating doesn’t affect his overall rating much. By contrast, a quarterback like Michael Vick of the Philadelphia Eagles, who for most of his career was far and away one of the greatest rushers in league history (at least in terms of yards per attempt) but was never an elite pocket passer, can also shine. A quarterback who can do it all, like Aaron Rodgers of the Green Bay Packers, is going to look good no matter what he does.

In other words, the beauty of the CQBR is that there is more than one way to skin a cat.

That being said, protecting the football is paramount to attaining a high CQBR. Because the NFL lumps all quarterback fumbles together instead of separating passing fumbles from rushing fumbles, we were forced to give fumbles their own sub-rating. No matter how good a passer or rusher a quarterback is, therefore, if he can’t hold on to the football, his rating will suffer.

A quarterback like Aaron Rodgers of the Green Bay Packers, who can both pass and run, fares very well in the CQBR.
A quarterback like Aaron Rodgers of the Green Bay Packers, who can both pass and run, fares very well in the CQBR.

How it’s calculated
We assembled quarterback statistical data from 2012 dating back to the divisional realignment in 2002. All quarterbacks with at least 100 passing attempts were included, comprising a dataset of 486 quarterback-seasons. We broke down the complete quarterback rating into three sections: passer rating (PR), rusher rating (RR), and fumble rating (FR).

Passer rating
Passer rating consists of the following statistical categories:

  • Completion percentage (CMP%): percent of passing attempts that resulted in a completion
  • Touchdown percentage (TD%): percent of passing attempts that resulted in a touchdown
  • Yards per dropback (YPD): average net passing yardage per dropback (passing attempt or sack)

Anyone familiar with the NFL passer rating formula will see that there is a close relationship between the two passer ratings. Whereas NFL passer rating is based on yards per attempt (YPA), however, CQBR better reflects passing efficiency by taking into consideration the number of times a quarterback was sacked. A quarterback’s YPD will typically be lower than his YPA. The more times a quarterback is sacked, the lower his YPD will be.

An interesting effect of using YPD instead of YPA to calculate PR is that it accounts for quarterbacks who are either too immobile to avoid sacks or who choose to take sacks instead of throwing the ball away. Quarterbacks like Aaron Rodgers cannot artificially inflate their PR by holding on to the ball longer, as they can with NFL passer rating.

It’s also worth noting that whereas the NFL passer rating was developed from passer data of the 1960s and early 1970s (a period Cold Hard Football Facts so colorfully calls the “Dead Ball era”), PR is based on data from the past decade and thus provides a better assessment of the modern passing game.

Rusher rating
Rusher rating consists of the following statistical categories:

  • Yards per carry (YPC): average yardage per rushing attempt
  • Touchdown percentage (TD%): percent of rushing attempts that resulted in a first down

The reason we created a rusher rating specifically for quarterbacks instead of using the rusher rating system (WRR) by which we evaluate running backs is twofold: First, the conditions under which a quarterback rushes are usually quite different from those under which a running back rushes; it tends to be much easier for a quarterback to have a higher YPC than a typical running back. (For most of his career, Michael Vick had the highest average of any back in history at over 8 ypc.) Second, FUM% is built into the WRR, so breaking out fumbles requires us to adjust the formula; it only makes sense to recalibrate the scale to the cohort of quarterbacks themselves.

Fumble rating
Fumble rating consists of fumble percentage (FUM%), defined as the percentage of total plays (passing attempts, rushes, and sacks) on which a quarterback fumbled.

Putting it together
PR and RR are weighted by their respective attempts and added together. So if, for example, a quarterback dropped back to pass 300 times (including sacks) and rushed 100 times in a season, his PR is multiplied by 0.75 and his RR by 0.25. This prevents a quarterback’s passing or rushing attempts from disproportionately affecting his CQBR, helping to make the rating system more scheme agnostic — in other words, ensuring it favors neither pass-first nor run-first quarterbacks. (The reality, of course, is that passing will almost always be heavier weighted than rushing, since seldom, if ever, does a starting quarterback attempt more rushes than passes in a game, much less a season).

The weighted sum of PR and RR is then multiplied by two so that the weighted average of PR, RR, and FR can be calculated to produce the final CQBR.

Because the system is not weighted by how “good” or “bad” we think any of the categories are, FR can (for better or for worse) have a fairly significant impact on final rating. For example, in 2012, rookie Seattle Seahawks quarterback Russell Wilson had a superb PR (76.97) and RR (80.06), but his high FUM% (2.82%, FR = 25.94) brought his CQBR down to a still respectable 60.41. By contrast, Denver Broncos quarterback Peyton Manning had a stellar PR (87.71) and a terrible RR (21.98), but because he attempted so few rushes, his outstanding FUM% (0.33%, FR = 85.22) helped keep his final CQBR up at 85.27 — highest of any quarterback that season.

In this regard, CQBR reflects the idea that there is more to being an all-around quarterback than slinging the ball and making plays with the feet. Protecting the football is important too. A quarterback can throw can throw as many touchdowns and scramble for as many yards as he wants, but a pair of untimely turnovers can still be enough to doom his team against an opportunistic opponent.

The scale
To create the scale for for each of the sub-ratings, we first calculated the means and standard deviations for all relevant statistical categories in the 2002-2012 data set. The scale for each category was then bounded as follows:
   0 = μ - 2σ
  50 = μ
100 =  μ + 2σ 

where μ is the mean and σ is the standard deviation for that category.

The scale was of course inverted for FR, such that a high FUM% produces a low FR.

To put it another way, 100 on this scale equates to roughly the 98th percentile of efficiency -- an elite level of efficiency -- while 0 equates to roughly the 2nd percentile, an extremely low level of efficiency. A rating of 50 represents an exactly average degree of efficiency.

The highest possible CQBR is 655.30, which would occur if the quarterback averaged 99 yards and a touchdown per dropback, threw no interceptions, ran for 99 yards and a touchdown on every rushing attempt, and never fumbled.

The lowest theoretical CQBR is -1,325.16, which would require a statistical impossibility: a quarterback would have to intercepted on every pass and yet somehow still complete the attempt and have the wide receiver run backwards to average -99 yards per dropback; average -99 yards per rushing attempt and never score; and fumble on every single play.

Negative CQBRs are possible, however, and have occurred, one notable example being San Francisco 49ers quarterback Alex Smith (2005), who posted CQBR of -13.14 on the season!

The main weakness of the CQBR is that relies upon fumbles, which the NFL did not record before 1945. Fortunately, fumbles are only one element of the rating and are not intertwined with the rest of the formula, so all is not lost. With the use of statistical tools like the z-score, quarterbacks can be ranked based on how much they stood out from their peers, allowing us to make comparisons across eras. (A great example of a question that a z-score could answer is "Did Brett Favre's 1995-1998 campaigns really comprise the greatest period of dominance by any quarterback in history?")

Some might argue that the fact fumbles have such a significant impact on the final rating is also a weakness, but that is a matter for debate sure to be hashed out thoroughly here at PackersHome and elsewhere.

Others will find it displeasing that the CQBR is strictly a measure of efficiency and isn’t weighted to favor high-volume quarterbacks, and it will no doubt be debated endlessly.

Here is the formula for CQBR:
Equation 1. The equation for the WCSN Complete Quarterback Rating System (CQBR), which rates quarterback efficiency by a number of statistical measures. A mean efficiency produces a CQBR = 50.00.
Equation 1. The equation for the WCSN Complete Quarterback Rating System (CQBR), which rates quarterback efficiency by a number of statistical measures. A mean efficiency produces a CQBR = 50.00. (Click on image to enlarge.)

where ATTp = passing attempts, ATTr = rushing attempts, TD%p = passing touchdown percentage, and TD%r = rushing touchdown percentage. (Other variable names are explained above.)

Although the formula looks daunting at first glance, it is relatively easy to plug in to a spreadsheet. In fact, we’ve already done the legwork for you. Feel free to download this spreadsheet and use it for your own investigations.

Top-rated quarterbacks of 2012
Now that we’ve laid out the background in exhaustive detail, let’s look at how the quarterbacks stacked up in 2012. As a bonus, the passer rating (PR), rusher rating (RR), and fumble rating (FR) are included for each quarterback to give insight into how the final CQBR was obtained.

Top-rated NFL quarterbacks of 2012 per WCSN Complete Quarterback Rating (CQBR).
Top-rated NFL quarterbacks of 2012 per WCSN Complete Quarterback Rating (CQBR).
Table 1. Complete Quarterback Ratings (CQBR) for all NFL quarterbacks with at least 100 passing attempts in the 2012 regular season. (Click on images to enlarge.)

Due to space constraints, passing attempts, sacks, and rushing attempts were left out of the table. If you want to see how attempts affected the weightings of the sub-rating for each of the quarterbacks, check out this spreadsheet.

Remember that 100 represents an elite level of performance; 50 represents exactly average performance; and 0 represents extremely poor performance. To sustain a rating of 80 or above for an entire season is outstanding.

My thanks go out to Jon Vander Woude, who spent a great deal of time hammering out the details of the system. The final conceptual design is largely of his devising. I also wish to express my appreciation to Andy Froehle, who consulted on some of the finer structural points. Finally, I want to thank my longsuffering wife, Katie Decker, who patiently went character by character through the formula and rooted out any fundamental logic or algebraic errors I had made. She helped simplify the equation and make it readable. It turns out there are advantages to being married to a math teacher after all!

Any remaining errors are, of course, my own.
#2 Posted : Monday, March 4, 2013 5:48:30 AM(UTC)
In the future, after v2.0 is released as stable, posts marked with the "Blog" topic status will be displayed on the front page of the site.
#3 Posted : Monday, March 4, 2013 7:36:47 AM(UTC)
I can accept a stat computation based on tangible elements as raw statistics verse subjective insertions being added as part of the formula.

I like the format.. albeit that I am not sure that we will ever get to the point were any collection of statistics will really properly define the impact a player has upon a team. Many of the impacts, both positive and negative, are just not measurable.
#4 Posted : Monday, March 4, 2013 7:43:42 AM(UTC)
So the fumble rating goes into the final score but interceptions have no part of it? That doesn't really make too much sense.
#5 Posted : Monday, March 4, 2013 7:53:41 AM(UTC)
Zero2Cool said: Go to Quoted Post
posts marked with the "Blog" topic status

I didn't know what, if anything, that feature did. I just knew you used to beg people to write for the blog, so I thought it might have something to do with that and figured if you didn't appreciate it, you could take off the tag.

What I find perhaps most interesting about the CQBR is what it shows us about Aaron Rodgers. He still comes out as no. 2 in the league for 2012 (tops in the league for 2011) despite being sacked so many times. If he would just stop taking so many sacks, he would have the highest rating in the league, and it wouldn't be all that close. But by taking sacks, he lowers his YPD average and also opens himself to more hits, which increases his chances of fumbling. It's the fumbles that, season after season, have lowered his CQBR.

I have been insisting for years that, in terms of individual performance, Rodgers is a much better quarterback than Tom Brady. The Patriots have been smart and ensured that Brady is one of the best-protected quarterbacks in the league. But that knee injury still looms large in the back of his head, and in the rare games where opposing teams ball up and are willing to pass rush and stop worrying about giving up the big play, we have seen him get indecisive and even crumble. There is no way Brady could ever have accomplished behind the Packers the things that Rodgers has. That being said, Brady gets farther in the playoffs more consistently, partly because he is playing against such weak divisional opposition, but partly because he doesn't take so many hits. I am hoping that as Rodgers mellows a bit with age and stops being so cocky out on the field, he'll start taking what plays present themselves and stop getting blasted so often.

In that sense, I think Brady plays smarter than Rodgers, and I hope Rodgers learns to emulates his example. But in terms of toughness, skills, and abilities, Rodgers puts Brady to shame. It would be such a waste of a rare talent if the Packers are never able to win more than one Super Bowl with Rodgers at the helm.
#6 Posted : Monday, March 4, 2013 8:07:37 AM(UTC)
Nonstopdrivel said: Go to Quoted Post
I didn't know what, if anything, that feature did. I just knew you used to beg people to write for the blog, so I thought it might have something to do with that and figured if you didn't appreciate it, you could take off the tag.

Yes, I always encourage people to write blog type posts because I believe it offers a lot to the members and to the site.

#7 Posted : Monday, March 4, 2013 9:24:37 AM(UTC)
It looks interesting. I have to wait until tonight when I have more time to study it closer.

Any calculations that involve Mu needs more time than I can offer at the office.
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