A couple of weeks ago, I wrote about interceptions per incompletion, or POPIP. In that article I showed how a player’s completion percentage is a better predictor of his future interception rate than his actual interception rate. And in this article by Brian Burke, one comment stuck with me:

Griffin has thrown deep, defined as attempts of greater than 15 yards through the air, on only 13% of his attempts, 30th among league quarterbacks. This is also likely the largest factor in his very low interception rate.

That makes sense — quarterbacks throwing short, safe passes should throw fewer interceptions. But this statement is a more important one than you might originally think, thanks to some great research by Mike Clay.

Clay came up with a metric he calls ‘aDOT’ — average depth of target — which measures exactly what you think it does. For each targeted or aimed pass, Pro Football Focus tracks how far from the line of scrimmage the intended target is. What’s makes this stat particularly appealing to me is that it’s very predictable as far as football statistics go. That’s not all that surprising because aDOT is based on a large sample of plays and basically frames how an offense operates.

Clay posted the 10 passers with the largest and smallest aDOT in 2011, which I’ve reproduced below. Note that there are some passes — spikes, throwaways, passes tipped at the line (these are grouped together as ‘other’) — with no target, and therefore are excluded when calculating aDOT. In the far right column, I’ve shown how the player’s aDOT compares to the league average rate of 8.8.

That’s just some flavor for how aDOT works. What really interested me was getting a precise understanding on the relationship between length of pass and interception rate. And thanks to Pro Football Focus and aDOT, I was able to discover some interesting results.

As you might suspect, there is a very strong relationship between the length of the throw and the likelihood of an interception. To measure this effect, I grouped all throws from behind the line of scrimmage together, and all passes of over 50 yards together, and analyzed the results. The correlation coefficient between interception rate and distance was 0.86, and the best fit formula was 0.0071*DOT^0.6757. This means that for every additional five yards from the line of scrimmage the ball travels, the likelihood of an interception increases by almost one percent.

But there’s a simpler way of showing the results, one that requires no math geekiness at all. I grouped all passes since 2008 into eight categories based on the length of the pass, and the correlation between the length of the pass and the interception rate was striking:

And, of course, it’s not just interception rate that’s highly correlated with aDOT. Take a look at how completion percentage falls as aDOT rises:

I really like aDOT as a metric because it really helps us visualize a player’s statistics. A quarterback with a high completion percentage and a high aDOT is a more accurate passer than one with a low aDOT; these are the sort of adjustments that advanced statisticians should do when analyzing a player’s numbers.