## Defense Adjusted YPA Efficiency for Playoff QBs

Joe Nicholson-USA TODAY Sports

Kenneth Arthur's great piece on passer rating got me thinking about different measures that would make a better passer rating stat. Y'know, nothing crazy, just wondering if anyone has ever tried to find the Holy Grail yet. Well, I didn't. My head nearly exploded, but I did learn something very interesting: I realized that I am not that smart. After I decided to quit trying to brew a cauldron of statistics to boil down into a perfect QB index, I did hatch a plan to weight QB passing yards per attempt efficiency for each game, relating the yardage for each attempt by the strength of their opponents' pass defense. And it goes something like this...

PROJECTING EXPECTED PASSING YARDS PER GAME

Recognizing that defensive units have varying degrees of vulnerability to pass plays, let's first look at the yards per attempt that each defense yielded over the course of the season. The league average for pass yards per attempt yielded by defenses was just over 7.1, but that number ranges from 5.8 to 8.1.

With that information, I then analyzed each of the starting QBs for the 2014 playoff teams that advanced past the wild card round, which seemed like a great sample of the most interesting QBs. Aaron Rodgers would be interesting as well, but since his sample size for this season wasn't consistent with the rest of them, I left him out. Knowing how many yards each defense gave up on average per attempt this season, I was able to project an expected yardage per game output by multiplying that number by the number of attempts each QB made in the games where they faced a given defense. Let me show you... for example, in the Seahawks' first game, Wilson threw a season high 33 passes against a Carolina defense that would average 8.0 yards per pass over the course of their season. This projects to an expected 264 yards for Wilson in this game. In theory.

COMPARING PROJECTIONS TO PERFORMANCE

To check our projections, or better yet to throw them out the window, we put players on the field for a few hours and yell things we will regret. That's where the magic happens. Against Carolina, Russell Wilson actually threw for 320 yards. That's 121.2% of our projection. Impressive? Well it's too early to say, but that right there is something we can talk about. Should we call this measure "defense adjusted yard-attempt efficiency" (DAYAE?). I don't know. Discuss. Naturally, the league-wide QB average for this measure against every defense will be 100%, so a number below that would suggest a performance less than the defense would be expected to yield given the QB's number of attempts, and numbers higher than 100% illustrate to what degree that the QB outplayed his peers against that defense.

These were the average performances for each (post-wild card) playoff QB during the regular season:

 QB Season avg Manning 126.14% Wilson 123.39% Rivers 119.11% Kaepernick 117.45% Brees 116.01% Newton 108.61% Luck 102.59% Brady 95.95%

Yes. Tom Brady's attempts yielded fewer yards per attempt against the defenses he faced than the average QB facing the same defense. Now, these numbers are a little bit gooey, because--well, I'll use Wilson as an example again. Wilson had two bad games by this measure, and both would be losses if not for a memorable play by Richard Sherman to score a TD when it counted, salvaging one of them. Against Houston, Wilson only threw for 123 yards, 69.5% of his 177 yard projection against their defense, given 23 attempts at their average of 7.7 yards per attempt.

Against Arizona he was only able to muster 108 yards, or 61.5% of the 175 yards their average would project for Wilson's 27 attempts. These numbers are so far below his typical game that it drags down the middle substantially. No matter how bad these games were, they were losing efforts, and we can contain the influence of outliers so that they don't bleed into the effectiveness of other performances. On the flip side, without Brady's outstanding performance against Pittsburgh, where he went off at a 221.8% clip, his regular performance was significantly worse than his average suggests.

So let's look instead at the median, the figure arrived at for the game at the center of this set of numbers:

 QB Median Wilson 130.35% Manning 123.74% Kaepernick 122.94% Rivers 120.94% Brees 117.54% Newton 107.48% Luck 103.33% Brady 87.52%

What this means is that in his most typical game, Wilson's yards per attempt was over 30% higher than his opposing defense typically yields given his number of passes thrown. Comparing these numbers to the averages above, we can see that a couple bad games according to this measure from Wilson--and Kaepernick to a significant degree--weigh down their average and skew their typical performance. Brady sees a boost of 8% projected to his average for all games if we let the outliers work their magic. Impressive.

How many yards is that, you ask? Well, it depends on which defense they are throwing into, but compared to their opposing defense's average yield per attempt, you can expect these QBs to throw for this many extra yards relative to the league average for each attempt:

 QB PaYd/Attadjusted Manning +1.55 Wilson +1.29 Rivers +1.16 Brees +0.99 Kaepernick +0.96 Newton +0.45 Luck +0.26 Brady -0.82

These numbers fit each player's schedule, such that comparable raw yards per attempt for two players will show a different relation to their expected production. Andrew Luck faced the most stout defenses of this lot, averaging 6.63 yards per pass attempt, while Tom Brady's opponents yielded the most, at 7.38. That would suggest that if Luck played Brady's schedule and produced identical numbers, he would produce -0.49, while Brady's production against Luck's difficult schedule would improve his average to -0.07, or very close to league average. In fact, comparing these number without adjusting for defense we would see Brady ahead of Luck by 0.26 yards per attempt (separated by Kellen Clemens, Christian Ponder, and Geno Smith). But check this out...

BIG GAME EFFICIENCY

Sure, a good QB can pick apart a bad defense at a torrid pace, and although every week is a championship opportunity, not all games are created equal. So how did these QBs fare against other teams that were headed to the playoffs? Looking at these percentages against future playoff opponents we get a little more separation:

 QB Vs. Playoff teams Wilson 124.08% Manning 118.67% Rivers 115.62% Luck 104.88% Newton 92.84% Brees 90.36% Kaepernick 83.72% Brady 83.72%

As you might expect, most of these QBs struggle more against quality opponents. This normalizes the data significantly, and brings the average among these elites to just over 101%. Luck and Wilson do actually get a bit better against tough opponents, but where we see the biggest change in the face of tough opponents is--woah!--Holy Moly, Mr. Kaepernick! Hang on, lemme check that a sec...

Okay yeah, looking a little deeper into these numbers we see that Colin Kaepernick goes from an astounding 137% against ten non-playoff teams, to just 83.72% defense adjusted yard-attempt efficiency against playoff-bound opponents. Thankfully for the 49ers, he actually stepped it up in the playoffs, averaging 98.56% by this measure, and this says nothing of his outstanding rushing performance. However, unfortunately for them, Wilson's 25 attempts in the NFC Championship Game against the 5.8 yards per pass average 49ers, should have meant just 145 yards, but he instead netted 215, for over 148% in a game where pass defense made all the difference.

Also. Tom Brady throws TDs, and he's lean for interceptions. But when it comes to throwing for yardage, just ... wow. That is all.

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