An objective (mathy) look at the improvement of the Seahawks passing offense

Kirby Lee-USA TODAY Sports

Having made the subjective observation that Russell Wilson (or more precisely, the Seattle passing offense) has improved over the course of the season, I thought it would be fun to take a more scientific approach. I quickly devised an experiment whereby I would stick my head in an MRI, establish a baseline, and then compare subsequent brain scans while watching (a)video of the Seahawks passing offense in recent weeks, and (b)video of sexy women.

Unfortunately, this experiment was stymied by lack of access to the necessary equipment. I'd planned to sneak in to a hospital at night to make use of the MRI machine, but wouldn't you know it, they're open all night long. Still, we can guess what the results would be. This is one sexy offense.

Adjusted Net Yards Per Attempt

Moving on, then, I settled for a mathematical analysis. I wanted a single, comprehensive number assigned to each week's performance. The best candidate for that is ANY/A, or "adjusted net yards per passing attempt". To get an ANY/A, we first add up the "adjusted" net passing yards, which includes a bonus for touchdowns and a penalty for interceptions:

Passing yards + (20 X touchdowns) - (40 X interceptions) - sack yards

We then divide that by the number pass attempts, including sacks. Simple enough? Wilson's numbers so far:

vs ARI ... 3.51
vs DAL ... 7.68
vs GNB ... 7.68
vs StL ... 1.41
vs CAR ... 5.89
vs NWE ... 12.1
vs SFO ... 3.2
vs DET ... 6.74
vs MIN ... 9.28
vs NYJ ... 9.74
vs MIA ... 9.03
vs CHI ... 8.28

These raw numbers, however, do not account for the differences in opponent quality. So I referenced each opponent's defensive ANY/A on the season, courtesy Pro-football-reference: [1]

ARI ... 4.6
DAL ... 7.0
GNB ... 5.3
StL ... 5.4
CAR ... 5.9
NWE ... 6.7
SFO ... 4.6
DET ... 6.0
MIN ... 6.1
NYJ ... 5.8
MIA ... 5.9
CHI ... 4.1

No surprises there, as New England and Dallas are relatively weak, but Chicago, Arizona, and San Francisco are all near the top of the league (the league average is 6.0; and Seattle is currently running 5.2 ANY/A, 6th in the league, in case you were wondering).

With that data at hand, we have a more honest look at the offense's performance, which I measured by subtracting the opponent's average ANY/A from Wilson & Seattle's actual ANY/A. The Dallas performance then becomes less impressive (+0.68 vs expected), the game against Arizona is not so awful (-1.09 vs expected), and the matchup with Chicago is outstanding (+4.18 vs expected). Preantepenultimately (yes, that's a word) this is all tied together with a linear regression (I used an online calculator because I was feeling lazy) to produce a "line of best fit". That should give us an objective, homer-prejudice-free measurement that shows improvement (or not). And it looks like this:

Cool, huh? The Mean y, 1.429something, indicates the average margin by which Wilson has outplayed opposing defenses (versus each opponent's expected performance) over the course of the entire season, and that by itself is a pretty good number. The positive slope, 0.427449..., shows the rate of improvement.


We can see from a casual glance that the data points are pretty scattered. And that small number near the upper right, the correlation coefficient, indicates how well the data fit the line. The cc is always between -1 and +1, so 0.5598 can be considered a pretty strong correlation, but for a data set this small it's kind of iffy.

Away Games vs Home Games

A lot of the scattering, we know, comes from the disparity in performance between home and away games. Doing a separate linear regression for each yields:

The improvement during away games has been far more dramatic, and also far more consistent with a correlation coefficient of .8135 (very high). But that shrinks the sample size even further, and poses another disturbing question: Are Wilson and the passing offense improving in a way that can be expected to continue, or is the steep slope merely a reflection of bad play early on (i.e., interceptions) that has been cleaned up?

So to tie that all together, I created a site-adjusted value for each of Wilson's performances. In the season-average away game, Wilson's ANY/A has beaten opponent's expected by 0.224 yards/attempt. In the season-average home game, Wilson's ANY/A has beaten the opponent's expected by 3.12 yards/attempt. So I went through and subtracted .224 from each away-game ANY/A and subtracted 3.12 from each home-game ANY/A. Recomputing,

Notice that this time the Mean y is essentially zero (.0000833, if you aren't sure how to read the exponential shorthand). That's because this chart is strictly Wilson vs Wilson over time. But it takes us back up to 12 data points and produces a much better correlation coefficient (0.7444), something that you can see from the reduced scattering. And that means our conclusion is more certain. Yay!

Projecting the Remainder of the Season

Although the last chart is zeroed out in terms of absolute performance, we can apply the slope (+0.478) as a valid measure of improvement. Wilson's season-long average of +1.429 is the midpoint for game 6.5 (the San Francisco Patriots, I presume). So based on linear extension, he started the season at -1.2 vs. opponent's expected ANY/A, and is now playing at a level of +4.058 vs opponent's expected ANY/A (all relative to a neutral site). Continued linear improvement is well-nigh impossible, of course, unless Wilson figures out how to throw a negative number of interceptions (and hey, I wouldn't put it past him to come in as a nickel back, but we'll exclude that possibility for now). So going forward, I'm going to use +0.418, which is the slope we get if the 3-interception Rams game is excluded.

And of course, there will still be differences in home and away performance. Even if the entire offense is cool as liquid hydrogen when traveling, opposing defenses will tend to play better in their home stadiums and worse on the road. Meanwhile, the difference in slope between home- and away-game performances suggests that the season-average gap of 2.89 ANY/A should now be closed down to 1.3855 ANY/A, or +0.693 at home and -0.693 on the road. Using that, we can now make a highly speculative projection for the remaining games:

vs. ARI (4.6 defensive ANY/A) + 4.476 (Wilson projection) + .693 (site modifier) = 9.77 ANY/A
vs. BUF (6.1 defensive ANY/A) + 4.894 (Wilson projection) - .693 (site modifier) = 10.3 ANY/A
vs. SFO (4.6 defensive ANY/A) + 5.312 (Wilson projection) + .693 (site modifier) = 10.6 ANY/A
vs. StL (5.4 defensive ANY/A) + 5.730 (Wilson projection) + .693 (site modifier) = 11.8 ANY/A

Continuing the trends, the good news is that we'll win at least two of the next three Super Bowls. The bad news is that the Wilson era will be brief owing to his acsension to a higher plane of reality.

[1] Note that uses -45 yards per interception, but I decided the small difference was not worth recomputing everything.

[note: This post edited on 15 June to replace images after hosting site went away]

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