Passing efficiency, work load, and Rookie (Quarterback) of the Year

I'm told that many SB Nation readers have their ballots ready at hand, eagerly awaiting a quantitative analysis to show whom they should select as Offensive Rookie of the Year and what name should go in the little box below labeled "in the conversation" (because apparently that's a thing).

Three quarterbacks-- Andrew Luck, Russell Wilson, and Robert Griffin's grandson-- are all poised to lead their respective teams into the playoffs. There may be other deserving candidates, but fairness and thoroughness are the hallmarks of paid writers, which I am not. So let's talk about the quarterbacks.

Andrew Luck was the long-anticipated #1 overall pick in the draft. He's led his team to nine wins in 14 games, seven more than the Colts had all of last season. But he's played against softer competition and committed 23 turnovers.

Russell Wilson was initially overlooked by most teams because of his height (pun definitely intended). He's put up highly efficient numbers, especially in the last six weeks. But the Seahawks throw the ball less than any other team.

Robert Griffin was acquired by the Redskins in exchange for several draft picks, 5000 acres along the Potomac, and Daniel Snyder's left kidney. He's been impressive both running and throwing the ball. But he allegedly benefits from the brilliant planning of his head coach, and his running style has led to injury.

So: Can we quantify all of these factors to produce an objective comparison of the three?

No.

Can we quantify some of the factors, like competition level, surrounding talent and work load? Yes, obviously. Why else would I be posting this?

Surrounding Talent

Briefly and obviously, this is going to be subjective. The Indianapolis Colts posted a 2-14 record in 2011, but how much of that failure was purely on the quarterback, and how much is a general lack of talent? Kerry Collins and Curtis Painter combined for eleven losses, and neither is currently employed by an NFL franchise. By comparison, the Redskins' and Seahawks' starting quarterbacks from 2012, Rex Grossman and Tarvaris Jackson, are at least holding down backup jobs. It's not hard to improve on a very low baseline. With the reasonably-competent Dan Orlovsky (NFL QB rating 82.4 in 2011) starting, the Colts were 2-3, suggesting that their non-quarterback offensive talent is not so dismal.

Wins are what matter, but "wins" is the laziest and least-informative stat available. For a more thorough, play-by-play, opponent-adjusted measurement, we can use Football Outsiders' DVOA (defense-adjusted value over average). Comparing the 2011 numbers and the 2012 numbers, we see that the Redskins, Seahawks, and Colts have all improved with new quarterbacks. (Note that these are numbers through week 14, as Football Outsiders is currently suffering an outage because an upline supplier had to throw out a lead-tainted shipment of html tags.)

A good quarterback improves the running game by preventing opposing defenses from stacking the box. So it's not surprising that all three teams are improved in both passing and total offensive efficiency. The Redskins get an additional boost in total offense thanks to Griffin's own running (6.7 yards per carry). The Seahawks show the biggest improvement in both passing and total, some of which can be credited to having their top wide receiver and tight end come back from injuries.

Opposition Quality

A few weeks ago I analyzed Russell Wilson's improvement over the course of the season by measuring his per-game performance against each opposing team's pass defense, all using an omnibus passing statistic affectionately known as "Anya". ANYA stands for "adjusted net yardsperpassing attempt", and it's computed as follows:

(Passing yards + (20 X touchdowns) - (45 X interceptions) - sack yards) /
(pass attempts + sacks)

In essence, ANY/A is the average number of yards gained (or lost) on each drop back, measuring touchdowns and interceptions with a yardage bonus/penalty. If you're curious, the league average is around 5.9 adjusted yards/attempt (if you're not curious, the league average is "banana"). And because ANY/A is a simple, single-value measurement, we can then make a linear adjustment for each quarterback's performance versus each opponent. For example,

Andrew Luck vs. Green Bay Packers: 5.76 ANY/A
Green Bay defense season average: 5.2 ANY/A (0.7 below league average)
Luck's opponent-adjusted ANY/A for his game against Green Bay: 5.76 + 0.7 = 6.46

Robert Griffin vs. Tampa Bay Buccaneers: 8.92 ANY/A
Tampa Bay defense season average: 7.1 ANY/A (1.2 above league average)
Griffin's opponent-adjusted ANY/A for his game against Tampa Bay: 8.92 - 1.2 = 7.72

I'll show those numbers in a bit. But first,

Efficiency, Shmefficiency -- Look How Often That Guy (Doesn't) Throw

Let's accept as axiomatic that it's easier to throw the ball if the opposing defense is playing to defend the run. So we need to account for the added difficulty when a quarterback is expected to throw more often. We could multiply his efficiency (Anya) by the percentage of pass plays, but it turns out that's a silly option. If quarterback A throws 100% of the time on ten plays for 80 yards, his ANY/A will be 8 yards/attempt. If quarterback B throws 50% of the time on ten plays for 80 yards, his ANY/A will be 16 yards/attempt. We cannot discount quarterback B by the direct proportion of 50%, because that would equalize the performances, and the second is clearly better (quarterback B got the same production with half as many throws).

Instead, we will calculate the throwing percentage for each quarterback and each game as a ratio of the league average (57.88%), then take the square root of that number for reasons I cannot possibly explain without boring you to tears. Confused? Here's how the contribution modifier looks across a few numbers:

The most pass-heavy game among these rookies is Andrew Luck versus the Chicago Bears in week 1, when he had 48 dropbacks versus 13 (non-quarterback) runs, for a raw percentage of 82.8%. That's 143% of the league average, which means his ANY/A for that game will be multiplied by 1.196.

On the opposite side, Russell Wilson's game against the Dallas Cowboys in week 2 included just 22 dropbacks versus 39 (non-quarterback) runs, for a raw percentage of 38.6%. That's 66.7% of the league average, which means his ANY/A for that game will be multiplied by 0.817.

Wait, what's that about excluding quarterback runs?

Ah, we have a question from my bold-faced alter ego. If we wanted to do this perfectly, we'd count quarterback scrambles as passing plays (which would lower the ANY/A for all three whilst raising the contribution modifiers). Then we'd also have to go through and figure out how to count designed QB runs (which are often for very short yardage), measure opposing run defense quality, rework the concept of contributions ratio, etc. But I only have a few hours to get this posted before the world ends, so that's not going to happen.

Instead, I've excluded all quarterback runs when counting the contribution modifier. That means Griffin's pass percentage is only calculated against runs by his running back teammates, giving him slightly higher numbers for it. And we can also assume that effective scrambling has already been measured by improved passing efficiency as it's likely to tie up an opposing defender as a QB spy.

Putting It All Together

The "raw" season ANY/A is per-attempt. The other numbers weight each game equally, so a quarterback's poor 20-attempt performance against a tough defense will count the same as his excellent 40-pass performance against a bad defense.

Things we haven't accounted for:
* Russell Wilson has played 6 home games and 8 away games. Luck and Griffin have each played 7 home games.

* Griffin has already missed an entire game due to injury. If we compensated by throwing out each of Luck's and Wilson's worst games, they would have adjusted ANY/A's of 6.24 and 7.32, respectively.

* Running:

Conclusion:
Ignoring his status as a rookie, Griffin's running has been his most historical accomplishment. Heck, 748 yards in 13 games at 6.7 ypc would be enough to earn a hefty contract for a rotational running back. But even if we throw out his running contribution, Griffin's passing is enough to put him at the top of the list for rookie quarterbacks.

If anyone ought to "be in the conversation", it's Russell Wilson. He's played a tougher schedule of opposing defenses with nearly the same efficiency as Griffin, fumbled less, and already played one more game. Seattle fans can also be excited by the fact that Wilson has outplayed Griffin over each quarterback's past six games, even if they have to accept that "Rookie of the Year" does not equal "Best Rookie Right Now".

Andrew Luck has simply been outplayed by his NFC counterparts. An objective measure of surrounding talent and team improvement shows no reason to believe that Luck has "done more with less". Even accounting for opponent quality and increased passing, his efficiency trails Wilson by as much as Wilson trails Griffin.

So is Luck a slow learner? Just not as good? In fact, he's playing quite well for a rookie, but I believe he's lagging behind Griffin and Wilson for a comparative lack of running. For every 100 non-running dropbacks (sacks and passing attempts), Andrew Luck has run the ball just 8 times. By that same measure, Wilson has run the ball 21 times and Griffin has run it 30 times. So Luck is less likely to keep a quarterback "spy" in the box, (presumably) less able to scramble for extra time, and more likely to throw incompletions or interceptions (by a staggering coincidence, each of the three quarterbacks have been sacked on 5.7% of the plays in which they passed or ran; so Luck isn't struggling to get rid of the ball).

We've heard that Luck has good athleticism and mobility for a quarterback. And I'm sure that's true... for a quarterback. But at 6'4", he just can't have the speed and acceleration available to the 6'2" Griffin or the 5'10.625183423" Wilson (they measure his height with a laser before every game). But Colts fans should not be worried. Extra mobility helps a rookie quarterback from the first snap he takes; whereas Luck's height and vision should pay off when he's had more experience reading NFL defenses at NFL speed. They just have to accept that "Rookie of the Year" does not equal "Projected Quarterback of the Future".