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Adjusting Plus-Minus For Team, Part I

Adjusting Plus-Minus For Team, Part I
Photo: USA Today Sports Images

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
Year Name Pos Targets Recepts Raw +/- Team
Team +/- Team
+/- per Dif.
2009 Reggie Wayne WR 134 100 16.9 417 20.3 0.05 0.13 0.08 10.4
2009 Dallas Clark TE 129 100 12.9 422 24.2 0.06 0.10 0.04 5.5
2009 Joseph Addai RB 60 51 5.1 491 32.1 0.07 0.08 0.02 1.1
2009 Donald Brown RB 13 11 1.4 538 35.8 0.07 0.10 0.04 0.5
2009 Tom Santi TE 11 8 1.1 540 36.0 0.07 0.10 0.04 0.4
2009 Colin Cloherty TE 1 1 0.2 550 37.0 0.07 0.21 0.14 0.1
2009 Mike Hart RB 6 5 0.4 545 36.7 0.07 0.07 0.00 0.0
2009 Chad Simpson RB 4 3 -0.2 547 37.4 0.07 -0.06 -0.13 -0.5
2009 Sam Giguere WR 2 0 -0.9 549 38.1 0.07 -0.45 -0.52 -1.0
2009 Gijon Robinson TE 13 9 -0.5 538 37.7 0.07 -0.04 -0.11 -1.4
2009 Austin Collie WR 86 60 3.4 465 33.7 0.07 0.04 -0.03 -2.8
2009 Jacob Tamme TE 9 3 -2.7 542 39.9 0.07 -0.30 -0.38 -3.4
2009 Pierre Garcon WR 83 47 0.2 468 37.0 0.08 0.00 -0.08 -6.4

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

8 Re: Adjusting Plus-Minus For Team, Part I

My guess is Brian Westbrook

This is a very interesting piece of research that seems to come very close to the holy grail of viewing individual performance independently of the team. As far as I can tell, teh only factor that is left out is how much of a spotlight a defense puts on a particular receiver, which is probably impossible to realise. Great stuff. (I still hate the name +/- though, surely there must be something more descriptive that gives nubes a better idea of what the stat represents.)

12 Re: Adjusting Plus-Minus For Team, Part I

If the plan is to use team adjusted plus-minus to compare different wide receivers across the league (I don't have the book, so I don't know), doesn't that assume each team has the same type of receivers? That is, if one team had a wide receiver corps filled with guys who have great hands, and another team was filled with speedy guys that dropped every pass, all the players are going to be around 0 plus-minus. But that doesn't mean they all have the same catching ability.

Put another way, this doesn't tell us that Pierre Garcon had below average hands. It tells us that (last season, at least), Pierre Garcon had below average hands for a Colts receiver. It doesn't necessarily tell us how he stands in relation to the rest of the league.

I'm not trying to diminish the point of the article; it seems pretty obvious that having Peyton Manning as a QB is going to help a WR without reflecting his true skill, and I could well be missing something. But using this to compare across teams could be problematic if the teams are constructed differently.

49 Re: Adjusting Plus-Minus For Team, Part I

IMO I'm not sure it can be used to compare recievers across teams. It helps compare players within teams though -- quite a bit!

Imagine a team with 5 HOF recievers: Jerry Rice x 5.

Their stats might all be different, since JR1 and JR2 will be on the outside, JR3 in the slot, etc, but after these adjustments ideally they all end up at 0.0 team-adjusted +/-.

Now, you have another team, full of Heyward-Bey's. This team similarly will have a team-adjusted 0.0 for its WR's.

There is no way you could compare the two sets of team-adjusted numbers to each other and conclude that the players are equally skilled.

At least, that is what the math looks like to me.

151 Re: Adjusting Plus-Minus For Team, Part I

Maybe. But what if the team of JR's had Jamarcus Russel throwing to them and the team of HB's had Joe Montana?

I guess what I'm saying, is Its unclear to me how this disentangles QB from WR play. The average +/- of the players on the team is affected by BOTH the QB and the skill of the average receiver on the team.

How that affects one player is even affected by how good the QB is on different kinds of throws and the distribution of types of throws to said player.

152 Re: Adjusting Plus-Minus For Team, Part I

Dumping the ball to the HB in the flats is a hell of a lot easier than throwing a deep out. For most QBs at least (I'm looking at you, Henne). The deep out is going to be on a rope, maybe behind or in front of the WR if the QB isn't so good. A check down is a check down.

156 Re: Adjusting Plus-Minus For Team, Part I

But the numbers are given relative to league-average QB's. So if you're QB is average at throwing the ball to a HB in the flats but slightly better than average at the deep out, then your RBs will be undervalued by this measure, and your deep receiver will be overvalued.

You're dealing with such small sample sizes that it would make any results very questionable, but ideally you'd take every QB and find his unique rate for each type of pass, and then use that rate when calculating your plus-minus figure for each player on the team. This would then be used to compare teammates.

16 Re: Adjusting Plus-Minus For Team, Part I

Hey -- not saying if any of the above answers are right or wrong, but:

a) You'll need to give a player and a season in question.
b) The only qualifying guess, 2006 LT, is wrong.

26 Re: Adjusting Plus-Minus For Team, Part I

As for the article I think it highlights what a lot of people are missing about the colts for this season and are similar (although way more detailed) to the findings i came through going through play by play data. And that is that you can't forget about Anthony Gonzalez. Yes Collie and Garcon played well but if you take into consideration their situation they weren't all world beaters where as Gonzo was actually above average last year and still has an elite 1st round pedigree. Whether he is 100% healthy is another question and I am sure that will play a big factor in the whole process but to completely dismiss him like a lot of people have done may be a mistake.

30 Re: Adjusting Plus-Minus For Team, Part I

I will say this much: No one has come even close yet. I wouldn't run a trivia contest where the answer was something as obvious as Chris Johnson or LaDainian Tomlinson.

32 Re: Adjusting Plus-Minus For Team, Part I

And for reference, I'll even give spots 2-5:

- 2: Brian Leonard, Bengals, 2009: +.11 plus-minus per pass vs. -.05 for rest of team
- 3: Ronnie Brown, Dolphins, 2006: +.10 plus-minus per pass vs. -.05 for rest of team
- 4: Chester Taylor, Vikings, 2008: +.11 plus-minus per pass vs. -.03 for rest of team
- 5: Jamal Lewis, Browns, 2007: +.08 plus-minus per pass vs. -.06 for rest of team

40 Re: Adjusting Plus-Minus For Team, Part I

Great work. It's been hard to reign in the enthusiasm of Colts nation about Garcon and Collie because they had good playoff games, but both had critical mistakes in the Super Bowl that are largely forgotten.

Anthony Gonzalez, if healthy, is just a flat better player than either one.

51 Re: Adjusting Plus-Minus For Team, Part I

Im going with 2009 Lex Hilliard. 100% catch rate. Closest player on Miami was Ronnie Browns 70% rate in the same amount of passes for less yards. I compared catch rates on teams and saw Lex's 30% difference and also saw that Lex was also about as good on a per play distance basis as Brian Leonard.

Hope I didn't blow my guess on a guy who doesn't qualify because of lack of targets.

69 Re: Adjusting Plus-Minus For Team, Part I

2006 Tiki Barber. He was reliable with a likely high catch rate, while surrounded by a team of WRs that was always overthrown by a still-erratic Eli. Right?

71 Re: Adjusting Plus-Minus For Team, Part I

Great research Bill.

If this had been around 15 years earlier it might have been in time to stop Dave Wanstedt from shelling out massive money to get Michael Timpson off the Bledsoe QBed Patriots. Then again Dave the Dunce would probably have ignored it.


Marion Barber, 2008 (Dallas)

97 Re: Adjusting Plus-Minus For Team, Part I

I can't believe I wasted my guess on someone Bill had already said was wrong because I think found the answer and it was not someone I was expecting.

106 Re: Adjusting Plus-Minus For Team, Part I

Ray Finkle, 1984. Soccer style kicker graduated from Cauler high June 1976, Stetson University honors graduate class of 1980, holds 2 NCAA division 1 records one for most points in a season, one for distance, former nickname "The Mule," The first and oly pro athlete to come out of Cauler County and one hell of a model American.

108 Re: Adjusting Plus-Minus For Team, Part I

With my reguess I'm taking Lamont Jordan of the 07 Raiders. Similar numbers to Leonard and an absolutely horrible Oakland offense run by Culpepper Russel ad Josh McCown.


JERIOUS NORWOOD, 2007. already bought FOA 2010 and KUBIAK, but wouldnt mind reimbursement on the previous!!

114 Re: Adjusting Plus-Minus For Team, Part I

2006 Kevin Jones, Detroit Lions, Mike Martz Offense, FTW!
If I hit a grand slam on this hole-in-one the dominoes will fall like a house of cards. Checkmate.

124 Re: Adjusting Plus-Minus For Team, Part I

No one has got it yet. I'll give one more big hint: One person actually named a different running back from the team and season of the player in question.

134 Re: Adjusting Plus-Minus For Team, Part I

i already used up my guess but he said unexpected... so pick a back that isn't really really well known for being a great receiver on a team with shitty hands at receiver.

143 Re: Adjusting Plus-Minus For Team, Part I


Noah Herron caught 93 percent of the qualifying passes thrown to him, 28 out of 30. That's a 93 percent catch rate, and a +/- of 4.58 on 30 targets. No other Packers receiver -- not even players with one target -- that year had a positive plus-minus; Brett Favre completed 56 percent of his passes.

I'm amazed that anyone got it. Peregrine, shoot me an e-mail at bill - at - to arrange your prize.