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.

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).

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):

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 sacks ^[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 … Continue reading 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.