Developing Air Yards Over Expected: A Look At Quarterback Aggressiveness

So, I started putting out data viz and the type about a year and a half ago now. For long, I stuck to the typical stuff: stats, tables, and graphs. I always wanted to make a model, develop a stat, or something along those lines but didn’t really know how. That changed for the better with my recent work that I’ll describe at length in this piece. Funny enough, after developing Air Yards Over Expected, I felt kind of dumb for not having done it earlier. It was pretty simple, yet informative!

Anyways, save the backstory, let’s get into what it entails. I’m certainly not the first to think about this or do it, but I’m glad I did it on my own. To understand AYOE (Air Yards Over Expected), we need to understand what expected air yards is. Essentially, expected air yards is a stat I worked through using a linear regression model. Mapping various inputs like down, yards to go, expected pass rate, and many more to air yards for each play allowed us to predict an expected air yards value. And with this expected air yards value, we simply subtract it from air yards to get a player’s AYOE.

A player’s AYOE can tell us quite a few things. Mainly, it gives us insight into how aggressive a quarterback is/was. Do they take shots? Do they play conservatively? Within structure? Gunslinger mentality? Additionally, using expected air yards, we can see which offenses scheme the most aggressively by what we expected of them. I’ll present a cool application later on.

Before I present the results, I just want to clarify a few things related to the data itself. I only modeled it for the regular season, as playoff stats are fluky and it seemed to be unnecessary. The data goes back till 2006, as that’s where expected pass rate started being applicable.

Additionally, I want to talk about the inputs I used and what my reasoning was, to be as transparent as possible. In total, I used 12 inputs. The main ones to know are the aforementioned along with the expected pass rate and the defense’s average air yards allowed. I used all 12 because I felt they gave me the best mix of relevant values that can have an effect on what we should expect of an offense’s pass length on any given play. And these thoughts were validated by my model’s performance, resulting in a p-value of 2.2e-16. The smaller the p-value, the better, so this was rewarding.

Now that the stat was developed, I wanted to check how stable it was. What good is a stat if it fluctuates every year?

As you can see above, it had a pretty stable relationship! Note that while an R-value of 0.54 isn’t perfect, working in an already variant sport like football, it’s still quite good. Having seen its stability, I moved on to other and more important things.

Up next was to test its correlation with other stats, to see if it had a positive relationship with stats like EPA per pass and PFF’s big-time throw rate. We can’t draw crazy conclusions, but it certainly bodes well for the stat if it tests well with key performance metrics.

0.27 was a solid number in terms of the correlation, and this held over other seasons as well. Solid! It’s not a widespread feeling I imagine, but it’s really nice to see that your stat does correlate a bit with key metrics. Now with BTT:

This was awesome, 0.67 was a great correlation. And the best part is that it makes sense intuitively. BTT rate measures the best throws a quarterback makes, the most aggressive and true star throws. AYOE measures how aggressive a quarterback is, so it was neat to see it line up.

Now that we’ve gone through the meat of the stat, let’s get into the actual results. (Thanks for sticking through that, lmao.) 2021 AYOE Leaders behold:

Really satisfied with how this came out. Denver Broncos’ legend Russell Wilson leads the way, which makes sense given how much he throws deep. Justin Fields came out chucking and Matt Stafford really stepped up the aggressiveness and play with Los Angeles. On the other hand, guys like Roethlisberger, Dalton, and Goff end up exactly where one would expect. The Coward Zone (trademarking that). Patrick Mahomes was a weird case though. In his first two years in the league, he really pushed the ball, with high AYOE values. This year though, as defenses started to give him more of the two-high safety look, the Chiefs started to play within structure and embraced the dink and dunk mentality, evidenced by his moderately low AYOE. Got to wonder if he tries to revert back to his old ways next year. In total, it’s not the smoothest correlation, but *deep breath in* the better quarterbacks at worst weren’t cowards.

The cool thing about creating a dataset going back to 2006 is that I can see AYOE trends over a quarterback’s full career. Take a look at Aaron Rodgers for example:

While his play’s sustained, his aggressiveness levels have absolutely shifted, which has been seen in the decrease in interceptions, so again, nice to see through AYOE. On the other hand, we can see career members of The Coward Zone, like Alex Smith:

That plummet is just MAN. Even Andy Reid couldn’t fundamentally change him. If you’d like to see this for any other quarterback, just shoot me a message on Twitter.

Overall, AYOE gives us a further look into what makes a good quarterback and their tendencies. Aggressiveness has often been thought of as a mental trait, but this was a decent first step in quantifying that. I’m sure there are more sophisticated methods of quantifying this, with different models too, but with public data, this came out really well.

Relatedly, I think it’s worth investigating how the big names traded at quarterback grade out highly in AYOE. Matthew Stafford last year unlocked that Rams offense like Jared Goff couldn’t, which actually was that cool application I wanted to mention, summing it up here:

Jared Goff never played with the gunslinger mentality Stafford did last year. Like, you and I both know for a fact he wasn’t making those throws Stafford made in the playoffs. Those sick no-look throws. It evidently paid off too. Maybe we something similar with the Broncos trading for Russ? One of the most aggressive quarterbacks ever by AYOE, he gives the Broncos a new dimension after spending a year with Teddy Bridgewater, who’s never been extraordinary in the metric. Definitely worth revisiting at the end of the 2022 season.

In the end, AYOE gives us a deeper look at what goes into an offense and its quarterback. We can take a look at which quarterbacks play with an air-it-out mentality and those that prefer to play conservatively. I’d love to evolve it with new data eventually, perhaps factoring in scheme and the receivers targeted (coming soon?). I did go into seeing if it had any predictive value for a bit but came up short-handed as it proved too similar to air yards to make a meaningful conclusion. For now, though, let’s appreciate the quarterbacks that stayed out of The Coward Zone.



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Ajay Patel

Ajay Patel

Undergraduate student at University of Rochester. Writes about sports.