In this week's Varsity Numbers, Bill Connelly revisits some measures and concepts: Adjusted Scores, Covariance, and momentum (or whatever you choose to call it).
23 Jul 2010
by Bill Barnwell
Just like any other receiving statistic, catch rate is dramatically affected by both the scheme a receiver plays in and the quarterback throwing him passes. Even our new plus-minus statistic isn't immune; in the second part of our introduction to plus-minus last year, we noted how the plus-minus of receivers on a given team tends to flock together. That suggests that quarterbacks are the dominant factor in determining the catch rate of most players.
To get a true glimpse into which players are catching passes at a rate above or below expectation, then, we need to add another layer of adjustments to the process. Accounting for pass distance and the yards needed for a first down -- as we do in Football Outsiders Almanac 2010 -- isn't enough; we also need to account for the laundry a player's wearing. In this piece, I'll explain my methodology for doing so, and in Part II of our team analysis (or Part V of the ever-expanding plus-minus trilogy), I'll analyze what it tells us about the past few seasons and the upcoming 2010 campaign.
(Right about now, you might be asking why this research wasn't included in the numbers you've seen/will see in Football Outsiders Almanac 2010; the answer is that, unfortunately, ideas and research times don't always coincide with book schedules. The idea for how to perform the adjustments, as simple as it is, didn't actually come to me until the book was all but done.)
The process of getting the team-adjusted figures is actually reasonably simple. With plus-minus calculated for each player already, it's a few short steps:
1. Divide the player's plus-minus by his target total to get a per-play figure
2. Divide the combined plus-minus of every other player on the team by their target total to get a team per-play figure
3. Find the difference between the two figures
4. Multiply the difference by the player's target total to get a re-constituted, team-adjusted plus-minus
As an example, let's use a player whose figure is heavily affected by context: the Colts' Austin Collie.
After stripping out plays defined as uncatchable, our database figures that Collie caught 60 of the 86 targets thrown to him last year, which yields a catch rate of just under 70 percent. Plus-minus suggests that he caught 3.4 more passes than an average receiver would, given the raw distance of his routes as well as the relative down and distance they came on. Divide that on a per-target basis, and Collie was just about 0.04 catches above average each time he was thrown the ball.
Of course, Collie doesn't play in an average offense; he plays for the Colts, and he has Peyton Manning throwing him the ball. There were 465 qualifying targets thrown to the remainder of the Colts' players. On those plays, the rest of the team accrued 33.7 catches above expectation. On a per-play basis, that's 0.07 catches above average; because that's higher than Collie's average, it means that Collie was worse than his teammates.
Subtract the difference and multiply it by Collie's 86 targets and you'll find that the tune of his numbers has changed. While Collie was catching passes at an above-average rate according to both catch rate and plus-minus, adjusting the figure for his team context produces a plus-minus figure of -2.8, a figure below what his Colts teammates were producing.
Below, we've provided a table with these statistics for every Colts player in 2009 (except for Hank Baskett, whose numbers are a little more complicated because he played for two teams). As you might expect, the overall success of the offense drags each individual receiver's plus-minus down.
|Plus-Minus For The Indianapolis Colts, 2009|
Pierre Garcon is another excellent example of how context can make a player with below-average hands look good. Garcon's plus-minus was about league-average relative to the distance and nature of his routes, but once you factor in the context of his offense, he was actually pretty mediocre at catching the ball in 2009. That blends well with DVOA, which saw Reggie Wayne and Collie well ahead of Garcon a year ago.
The change in Wayne's figures is also very interesting. Wayne led the league in raw plus-minus in 2009, but some of that is thanks to a high target total and the presence of Peyton Manning. He drops to the middle of the top ten in scaled plus-minus, and because a lot of the passes that weren't thrown to him were also completed, his team-adjusted plus-minus was only the league's sixth-best. (We'll cover the 2009 leaders in Part II of this piece.)
Team-adjusted plus-minus tells a distinct story for the 2009 Colts -- Wayne and Dallas Clark caught a lot of passes at a well-above-average level, and everyone else was average or worse -- but the team's statistical signature isn't always so similar. In 2008, for example, Wayne's raw numbers declined, and his plus-minus figures were no different. He had a raw plus-minus of 10.4 on 124 targets; adjust that for the team rate, though, and he was only at 2.1. Anthony Gonzalez led the team, with a team-adjusted plus-minus of 4.4 catches above average on 77 targets.
In Wayne's dominant 2007 season, well, he was a one-man wrecking crew. His 18.3 raw plus-minus was met with mostly mediocre performances by the rest of the offense, producing a team-adjusted plus-minus of 16.7 that led the league. It's the second-best figure of the four-year stretch we have plus-minus available for, having been narrowly beaten out (16.74 catches above average to Wayne's 16.72) by a receiver in 2009. One of the main reasons why Wayne's figure is so high is because the only other Colts receiver with more than 50 qualifying targets that year was Dallas Clark, who had a raw plus-minus of -5.6 on 94 targets. After adjusting that for the team context, Clark was at a very disappointing figure of -9.5 catches, the worst figure in the league that year.
2006, of course, was the last gasp of Wayne and Marvin Harrison as anything close to equals. It's borne out in their plus-minus figures. After adjusting their figures for the Colts offense, Wayne was at 7.9 catches above expectation on 128 targets, while Harrison was at 8.2. (Clark, in part of a two-year stretch with a strangely low raw catch rate, was at a dismal -8.7 catches on just 55 targets.)
In Part II, we'll expand the focus to the rest of the league, breaking down the most bizarre out-of-context performances from the past four seasons while providing the numbers on who did the best job, relative to their teammates, of catching passes.
As a teaser, here's a quick contest. The player with the biggest per-play difference between his personal plus-minus and the plus-minus of the rest of his teammates in a given season over the past four years is a running back. I'll give everyone a lone guess at who that back is; the first person to guess correctly gets a free PDF of FOA 2010.
162 comments, Last at 26 Jul 2010, 11:25pm by Nathan