Rating Quarterbacks

by Jason Winter of Defensive Indifference

There’s no really good existing way to rate quarterbacks, from a statistical standpoint. Most people understand the flaws with the widely known statistic, though there are alternatives. Adjusted Yards Per Attempt is one of the simpler ones. To review, that’s:

AYA = (Passing Yards + 10*TD passes - 45*Interceptions)/(Pass Attempts)

It is, essentially, a QB’s “yards” (counting TD passes as 10 yards and interceptions as -45 yards) divided by his attempts. Seems logical enough, and fits with other generally accepted “average” stats (like yards per carry for running backs or yards per reception for wide receivers).

But it’s always bugged me how pretty much every stat ever used to rate quarterbacks only accounts for their passing numbers. Since the days of Fran Tarkenton, carrying forth into the days of Randall Cunningham, and, more recently, with Michael Vick and Vince Young, people have argued that rushing stats should play a role in whatever system exists to rate quarterbacks. It makes sense; how can you say a QB with a 6.5 AYA (or 88.7 passer rating) for the season who runs 40 times for 40 yards is the same, statistically as one with a 6.5 AYA who runs 40 times for 200 yards? Isn’t the second guy better?

But if we get into adding rushing yards to a quarterback’s numbers, why shouldn’t we add other things, as well? Isn’t it better if a QB takes 20 sacks instead of 50, or if he fumbles five times instead of nine (assuming identical attempts)?

Ah, but now that opens up another can of worms. Many people would argue that some sacks – not all, but a fair number – are the fault of the offensive line and not the quarterback. You could make similar arguments regarding fumbles, many of which occur as the result of sacks. Why should those numbers be counted against a quarterback in any “comprehensive” statistic?

My response is: Why should passing yards be counted? Or touchdown passes? If we’re going to credit the QB for a completed pass, and assign him positive stats based on his good play, why shouldn’t we blame him for a bad play, like a sack or fumble? True, the negative play might not have been his fault entirely. But no completed pass is ever completely due to his efforts – the receiver and offensive line likely had a role in it, as well – and nobody would suggest we not include passing yards in our rating of a quarterback. If we can’t determine what percentage of a quarterback’s “good stats” are due solely to his efforts and adjust his numbers downward as a result, there’s no reason we should exclude his “bad” stats just because some part of them wasn’t his fault. Just as it’s clear that some QBs are better at running than others, it’s clear that some QBs are better at not taking sacks or not fumbling than others? Why shouldn’t the QBs who are good at this be rewarded and the ones who are bad at it penalized?

Even if we accept that some guys are “just playing on a bad team” or behind a bad offensive line and want to make adjustments for that, why shouldn’t we make adjustments for players with good offensive lines or receivers? Would Tom Brady have thrown 50 TD passes in 2007 if he’d been playing for San Francisco instead of New England and been throwing to Arnaz Battle and Darrell Jackson instead of Randy Moss and Wes Welker? Of course not.

That comes to the heart of this system, however. It’s not meant to show who the “better” QB is, not from a strict interpretation of the word. Tom Brady would have been the exact same person and same player in San Francisco, but his stats would have been lower, due to having worse teammates and coaching. A quarterback who takes a lot of sacks puts up worse numbers than one who doesn’t, all other things being equal. He may or may not actually be worse, but his stats should suffer, just as a quarterback who has Randy Moss and Wes Welker to throw to should have better numbers than one who didn’t (and we might get a chance to see how Matt Cassel does when he doesn’t have those two to throw to). Rather, this system is meant to show which quarterback had the best statistical year, taking all available statistics into account and not biasing the results with any judgments based on credit or blame. If it’s on the player’s stat line, it counts, whether for good or bad.

We can use AYA as a baseline for our “new” stat, which I like to call Total Yards per Attempt (TYA). We can stick with the basic premise of Yards/Attempts, but we’ll need to add a few things to each side. Our numerator has to include:

Passing yards
Rushing yards *
Passing touchdowns
Rushing touchdowns *
Interceptions (negative)
Sack yardage (negative) *
Fumbles (negative) *

And the denominator includes:

Pass attempts
Rush attempts *
Sacks *

(* indicates new statistic. And yes, I know I could add receiving stats, but those are so rare for QBs that I think we don't lose much by leaving them out.)

Rushing yardage can be added easily enough. Rush TDs can have the same weight as passing TDs, 10 per. Sack yardage can simply be negative yardage. Pass attempts, rush attempts, and sacks present no problems, either.

What to do about fumbles, though? Not every fumble results in a turnover, so they should be weighed less than an interception (which is always a turnover). Yet I don't know of any easy place to find the stats on individual quarterbacks' lost fumbles, and I can't assign a -45 per lost fumble for each quarterback, some of which are recovered by the offensive team.

Looking at the last few years, I find that, overall, fumbles (by any player) are recovered by the defense about 2/3 of the time (usually 65-70% per season). That's a convenient enough result, since 2/3 of 45 is an even 30. Works for me. Thus, fumbles are worth -30 to a quarterback.

(I realize, too, that fumbles by a quarterback are generally worse than an interception, since they often occur on or behind the line of scrimmage, as opposed to downfield, but unless there’s something in The Hidden Game of Football (which I haven’t read) or anyone else has any other data out there to assign better values to fumbles, I’ll go with what I’ve got.)

So, putting it all together, we get the following formula:

TYA = (Passing Yards + Rushing Yards - Sack Yards + 10*TD passes + 10*Rushing TDs - 45*Interceptions - 30*Fumbles)/(Pass Attempts + Rush Attempts + Sacks)

Which appears to take pretty much every QB stat into account.

To close, here’s the leaders in TYA for 2008, along with their rank in passer rating. The average among these quarterbacks was 5.04; figuring the average for the entire league is difficult because it requires individually looking up rushing numbers for every quarterback, as well as excluding players who threw passes and whose rushing numbers would skew the results (like running backs).

Rank	Quarterback	TYA	PR Rank
1	Philip Rivers	6.6	1
2	Drew Brees	6.52	4
3	Chad Pennington	6.39	2
4	Peyton Manning	6.19	5
5	Jake Delhomme	5.86	18
6	Kurt Warner	5.82	3
7	Matt Ryan	5.8	11
8	Jay Cutler	5.8	16
9	Jeff Garcia	5.55	9
10	Aaron Rodgers	5.51	6
11	Matt Schaub	5.49	7
12	Donovan McNabb	5.46	14
13	Tony Romo	5.23	8
14	Matt Cassel	5.19	10
15	Kerry Collins	5.18	23
16	Seneca Wallace	5.11	13
17	Eli Manning	5.1	15
18	Jason Campbell	4.9	19
19	Trent Edwards	4.83	17
20	Shaun Hill	4.76	12
21	David Garrard	4.66	20
22	Tyler Thigpen	4.57	27
23	Kyle Orton	4.56	25
24	Dan Orlovsky	4.28	30
25	JaMarcus Russell	4.23	26
26	Joe Flacco	4.17	22
27	Ben Roethlisberger	4.03	24
28	Brett Favre	3.91	21
29	Gus Frerotte	3.83	28
30	Marc Bulger	3.81	31
31	Derek Anderson	3.24	33
32	JT O'Sullivan	3.12	29
33	Ryan Fitzpatrick	2.94	32