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Yards per Attempt is the basic statistic around which the passing game should be measured. It forms the base of my favorite predictive statistic (Net Yards per Attempt) and my favorite explanatory statistic (Adjusted Net Yards per Attempt). But it’s not perfect.

In theory, Yards per Attempt is a system-neutral metric. If you play in a conservative, horizontal offense, you can have a very high completion percentage, like David Carr in 2006. But if you’re not any good (like Carr in 2006), you’ll produce a low yards-per-completion average, dragging down your Y/A average. You can’t really “game” the system to get a high yards per attempt average; the way to finish among the league leaders in Y/A is simply by being very good.

Courtesy of NFLGSIS, I have information on the length of each pass (or Air Yards) thrown during the 2012 regular season. I then calculated, for each distance in the air, the average completion percentage and average yards per completion. In the graph below, the X-Axis shows how far form the line of scrimmage the pass went (or, as Mike Clay calls it, the depth of target). The blue line shows the average completion percentage (off the left Y-Axis) based on the distance of the throw, while the red line shows the average yards per completion (off the right Y-Axis). For example, passes four yards past the LOS are completed 69% of the time and gain 5.4 yards per completion, while 14-yard passes are at 50% and 17.6.

Cmp vs. YPC2

We can also follow up on yesterday’s post by looking at Air Yards vs. YAC for each distance or depth of throw. Air Yards is in red and on the right Y-Axis, while average yards after the catch is in blue and measured against the left Y-Axis. Initially, there is a pretty strong inverse relationship, just like with completion percentage and yards per completion. On a completion that is one yard past the line of scrimmage, the average YAC is 5.5; on a completion 10 yards downfield, the average YAC drops to 3.0. This is why players like Percy Harvin and Randall Cobb will rack up huge YAC numbers. But once you get past 13 or 14 yards, YAC starts to rise again. This makes sense, as that far down the field, a player is just one broken tackle away from a huge gain (I suspect using median YAC might paint a different picture).

Air Yards vs. YAC

But now, let’s take a look at straight old yards per attempt based upon the distance of the throw relative to the line of scrimmage. Remember, this includes incomplete passes (i.e., this is not yards per completion):

Yards per Attempt by depth

Whatever the theory, this chart makes it clear that Yards per Attempt isn’t really system-neutral. Deep throwers have an advantage, because the dropoff rate in completion percentage — at least in 2012 — wasn’t disproportionate to the increase in yards per completion. This also makes sense in light of two of the surprise finishers in the top 12 in yards per attempt last season: Cam Newton and Josh Freeman.

The list of the top 12 leaders in Y/A from 2012 is a who’s who of the top quarterbacks in the league, Newton, Freeman, and Matt Schaub (and to the extent that Schaub’s presence surprises you, that’s nothing to do with Y/A and everything to do with his performance down the stretch; he ranked 7th in Y/A through the first eleven weeks and then 15th in Y/A and 19th in AY/A over the final six weeks). And for those who didn’t already know, Newton and Freeman finished first and second in yards per completion.

Newton actually finished third in the league in yards per attempt last season. But no one would say he was the third most efficient quarterback last season, which is a sign that his Y/A is inflated by the fact that he throws deep passes. To be fair, Newton drops to 7th in NY/A and 11th in ANY/A, so perhaps there’s nothing wrong with Y/A (after all, there’s a reason we prefer NY/A and ANY/A to Y/A). And as a deep thrower, Newton takes more sacks1 and is more likely to throw interceptions, so perhaps using ANY/A solves this “problem” about how Y/A isn’t system-neutral. And just to make the problem even more complicated, while Newton was a big downfield thrower (he ranked 5th in Air Yards/Completed Pass), he also ranked 1st in YAC per completed pass, which obviously helped raise his yards per completion average. Freeman ranked 3rd in AY/CP and just inside the top ten in YAC per completion.

Still, I’m not convinced that ANY/A solves the problems inherent in Y/A. Some deep-throwing quarterbacks don’t take sacks — Eli Manning finished 2nd in Air Yards per completed pass and 1st in sack rate in 2012. And we know that interceptions are really random (and that Joe Flacco is immune to them) so they may not serve as a good way to offset the artificial inflation involving with quarterbacks who make deep throws.

One solution would be to just change the equation. Yards per attempt is simply completion percentage multiplied by yards per attempt. If you instead multiply Y/C by the square of completion percentage, you get a much straighter line, although the units no longer have meaning. But since I don’t place much value on completion percentage alone, I’m hesitant to do that.

Another school of thought would say that this isn’t a problem at all. Throwing down the field is harder than dinkin’ and dunkin’, so who cares if Y/A overstates how good the downfield throwers are? In fact, we should want yards per attempt to be biased towards the quarterbacks who make the most difficult throws. There’s something to be said for that view, although I’m not sure I fully support it.

I do have another thought. We can use first down data to help smooth out this issue, at least a little. If we modify Y/A by giving a bonus for passing first downs, that would help out Tom Brady and the Patriots. Brady ranked only 8th in Y/A last year (although he was 6th in NY/A and 3rd in ANY/A), but the Patriots were second in passing first downs per attempt last year, so that would bump them up. And I’m okay with bumping up Matt Ryan, too, as his Falcons were first in first downs per pass attempt but 7th in Y/A. (Of course, Matt Ryan is just a proxy for Matt Ryan playing on the Atlanta Falcons with Julio Jones, Roddy White, and Tony Gonzalez).

Of course, to do that, we need to assign a value to a first down. That’s a topic for another day.

Finally, let me close with the data above presented in table form. One note: keen observers may have noticed that the number 0 was missing from the X-axis in the above graphs. That wasn’t an accident: spikes and passes batted at the line of scrimmage are marked down as going for zero air yards, so the data on 0-yard passes is misleading. In any event, here’s how to read the table below. There were 4,526 passes thrown behind the line of scrimmage last year. 3,554 of them were completed, for an average completion percentage of 78.5%. The average yards per attempt on passes thrown for negative air yards was 5.09. The average amount of Air Yards was -3.16 and the average amount of YAC was 9.64, making the average yards per completion 6.48.

CategoryAttCmpCmp%Y/AAir YardsYACYPC
  1. Although this issue is complicated. As my buddy Jason Lisk likes to say, many plays that go down as rushing attempts for a quarterback are really sacks avoided. In that case, Newton and other scrambling quarterbacks will actually have their sack rate be artificially inflated by the fact that their scrambles do not count in the denominator when calculating sack rate. []
  • Sunrise089

    I don’t think there is much wrong with Y/A. As you say we already have the superior NY/A, so Y/A isn’t the end-all stat anyways. I think your first down bonus fixes whatever issue remains – the advantage of short passes is lower variance, which is very useful in a game where plays stack together to make up a possession.

    I will say your graphs, particularly the second, sort of horrify me. You have a non-linear scale on the X axis, and it makes your red line have bends when the scale changes. I can look past it, but a casual reader might think there was a rate change not really present if they don’t carefully check the scale. Not to mention you don’t even need the red line in your second graph – it’s the same as the axis 🙂

    • Chase Stuart

      Thanks Sunrise089. I agree with you on the graphs, although the non-linear scale was necessary (I suppose I could have inserted breaks or something, but again, good enougher) – but yes, the casual reader could be misled. The red line was necessary in the same graph for the X values outside of 1 to 15 (and helps to solve your other point!), but yeah, it’s mostly overkill.

  • Red

    What about giving a bonus to QB’s who are above a certain threshold in both C% and YPC (and penalizing those who are below the threshold in both)? This will give extra credit to the QB’s who are both accurate and aggressive, while not rewarding those who live at the extremes like David Carr or Newton/Freeman. I first started thinking about this while comparing two historic playoff performances: Tim Tebow’s 2011 game vs Pittsurgh and Kurt Warner’s 2009 game vs Green Bay.

    Using Y/A, NY/A, ANY/A, or VALUE, Tebow’s game always comes out significantly ahead. But that seemed wrong to me. Having watched both games closely, Warner’s felt like a better performance, because he was consistently good on nearly every play, while Tebow was erratic and just happened to connect on a handful of long bombs:

    Tebow: 31.6 YPC, 47.6%, 15.1 NY/A
    Warner: 11.5 YPC, 87.9%, 11.0 NY/A

    This is where variants of Y/A fail, at the extremes. Looking at games retrodictively, I don’t think any of this matters, because outcome trumps process. However, when trying to predict future outcomes and/or assessing the “true” skill of a past performance, we have to separate what’s sustainable from what’s not. In the above case, 31.6 YPC is clearly not sustainable, not even close, so we can presume that Tebow’s performance was largely a fluke (the rest of his career backs that up) and has little predictive value. Meanwhile, Warner’s game may have been an outlier in its greatness, but it didn’t feel fluky. His longest gain was 33 yards and he still averaged 11 NY/A . That has predictive value (again, the rest of his career, particularly his playoff run with the Cardinals, backs that up).

  • Chase Stuart

    Great stuff.

    In the Denver-Pittsburgh game, Tebow had 9 passing first downs (including the TDs), while Warner threw for 21 first downs against the Packers. Tebow threw 21 passes, while Warner threw 33.

    Side note: How ridiculous is that? Warner picked up a first down 21 times on 33 attempts. That’s insane (and ignores two more first downs on pass plays that didn’t count because the penalty was accepted).
    Also, you would probably enjoy this post by Neil: http://www.footballperspective.com/checkdowns-adjusted-net-yards-per-attempt-fip-for-quarterbacks/

    • Richie

      Why is this blue?

  • Long passes will average more yards per play than short passes. Defenses are rational: they are not seeking to minimize the number of yards per play they are surrendering; they are seeking to minimize something more like the number of points per drive they are surrendering.

    Other things equal, an offense that averages 6 yards per pass attempt with a 75% completion percentage will score a lot more points than an offense that averages 6 yards per pass attempt with a 25% completion percentage. (If it’s not obvious why, think about which team will have to punt more often.)

    If an offense is gaining 6 yards per pass attempt on both short (high-percentage) and long (low-percentage) attempts, it will gain more points per drive (but not more yards per attempt) by throwing more short attempts than long attempts. The defense will therefore shift more of its effort into defending short attempts, and the new equilibrium will result in more yards per attempt on long passes than on short passes.

    That’s why the NFL passer rating is correct to include completion percentage separate from (and in addition to) yards per attempt. I don’t know if they’re weighting those inputs correctly, but they’re right to give completion percentage a weight greater than zero. For any given number of yards per attempt (adjusted, net, or otherwise), a higher completion percentage is better for the offense.

    (Including something like success sate may be even better than including completion percentage; but either way, considering only net adjusted yards per attempt, without additionally considering completion percentage or success rate, leaves out an important component of a passer’s true efficiency.)

    • Chase Stuart

      Thanks Maurile. There are many reasons I don’t like completion percentage. One of them is that it teams with leads tend to throw safe passes. This inflates their completion percentage, and it feels like you start getting close to giving quarterbacks credit for wins once you give credit for completion percentage.

    • Chase Stuart

      Some thoughts from Jason Lisk on completion percentage: http://www.pro-football-reference.com/blog/?p=6158

    • Red

      When Y/A is high, a solid completion % is important. As you mentioned, completing passes consistently implies picking up first downs and keeping drives alive. However, I disagree that completion % is important at the low end of Y/A. In fact, I’d almost argue the opposite, that a weak passing offense is better served to employ a boom-or-bust strategy. Let’s say a QB can only muster 5 Y/A. The chances of him driving his team 80 yards for a touchdown are pretty low, so it would make more sense to gamble with a few deep bombs and hope lady luck smiles on him that day. This touches on one of the principles of game theory – the superior player should use a low variance strategy, and the inferior player should use a high variance strategy. That’s how the Ravens won the SB this year without having the best team, by utilizing a very high variance passing offense.

      Here is my rule of thumb on this issue:
      When Y/A is between 6 and 8, comp % doesn’t matter either way
      When Y/A is above 8, high comp % is better
      When Y/A is below 8, low comp % is better

      One of my favorite weird player seasons in NFL history illustrates this point: Chris Chandler’s 1998. In leading the Falcons to a SB appearance, Chandler led the league with 9.6 Y/A, which is historically rare. Even more astonishing is that he did it with a ho-hum 58% completion rate (plus his sack rate was a horrendous 12%). His Y/C was a meteoric 16.6, probably four standard deviations above average. That performance was a big reason why Atlanta went 14-2, but it had fluke written all over it. In fact, Chandler finished his career at 7.1 Y/A, and never even broke 8 Y/A in any other season in his long career. Why? His 1998 success was almost entirely a product of hitting deep passes, which are notoriously random from year to year. Once his long balls stopped connecting, he immediately regressed to being a mediocre QB.

      Compare Chandler to other QB’s who had a season over 9 Y/A. Marino, Montana, Peyton, Warner, and Rodgers each accomplished the feat, but they all completed 65-70% of their passes while doing so. So, even when their deep passes stopped hitting in subsequent seasons, these QB’s could still move the ball down the field with consistent, accurate throws. Not coincidentally, all will probably be in the HoF.

      • Red, I agree with the principle that you state, but I disagree with your rule of thumb.

        Let’s say that a quarterback is averaging 5 yards per pass attempt. If it is 1st and 10, 2nd and 7, or 3rd and 4, his ideal variance would be zero. If it is 1st and 20, 2nd and 15, or 3rd and 10, his ideal variance would be significantly positive.

        I’d say that the former situations are a lot more common in the NFL than the latter, and that for a QB averaging 5 yards per attempt, variance is therefore generally his enemy rather than his friend.

        In other words, even at the very low end of the realistic Y/A range, a higher completion percentage is better.

        • Red

          maurile, I understand where you’re coming from, and agree that manageable down-and-distances are more common than long ones. But to me, a drive is analagous to a chain, and each link in the chain must connect in order to score a touchdown. The low variance strategy may be superior for 3/4 of all plays, but all it takes is one third down failure and the drive is over. Stringing together a long chain is difficult if you’re only moving one link at a time. Conversely, a 50 yard heave may fail 80% of the time, but the 20% of time it succeeds will almost always yield a field goal or touchdown. If a pedestrian offense gets 12 drives in a game, and can get “lucky” on three of them and score 21 points, they have a real chance of winning a game they’d have NO chance of winning with a dink-and-dunk strategy.

          Anecdotally, when I think about low Y/A, low variance passers, their teams are usually bad (Joey Harrington, David Carr, Trent Edwards, Jason Campbell, etc) and don’t score very many points.

  • Aaron Di Silvestro

    I think you’re short changing the deep throw without cause to do so. Every play comes with a risk of a turnover. Deep plays may be riskier than screen passes but a single completed downfield bomb is less risky than the sum of the 10 slants you’d need to complete to equal the bomb’s production.

    Also it doesn’t take a great deep thrower to work the ball down field during a drive, just a relatively lucky play sequence. The shorter thrower isn’t as likely to experience that luck because the skill shines through more in a higher sample of attempts.

    Guys with effective deep looks may not have the same ineffable ability to play QB like a ballerina but that shouldn’t matter if they’re as effective

    Stuff like suggesting that a modification would help Tom Brady reads like the stat produced some results that don’t jive with your perception of reality and you’re blaming the stat instead of your perception – which is fine, but first you have to prove that the stat didn’t jive with reality instead of your perception.

    I may just be looking at it differently since I never had the perception that Y/A cut across systems or stood on it’s own. I always thought that it’s special because it stabilizes quickly and tracks well with more complicated or indirect measures of QB value.

    • Richie

      a single completed downfield bomb is less risky than the sum of the 10 slants you’d need to complete to equal the bomb’s production.

      I believe Bill Walsh disagreed.

  • Chase, good stuff. Where on NFL GSIS can you find Air Yards?

    • Chase Stuart

      In “Individual Ranking Reports.”

  • gmopro

    The main issue I have with YPA is that it doesnt take into account the First down %. You can throw a long pass and then the O avgs a couple yards per play and is done. The YPA looks good , yeah, but the team loses possession. YPA is just one thing to examine. You need to check yards differential, points differential, yards per drive, points per drive, First Downs, DSR.. drive success rate. Ypa is a nice lil stat ,but doesnt tell u how consistent the yards are. Also, i recommend the %differences where you look at the % team A is better vs the teams that played team A’s opponents. Lots to examine. Points differential, net adjusted YPA, yards differential, home/away impact, momentum, injuries,etc. No one stat gets it done IMO.