Comparing wide receivers across teams is tricky. Pierre Garcon led the NFL in targets, ^[1]All target data comes courtesy of Footballguys.com. but that’s partially because Washington didn’t have much help at wide receiver. ^[2]And in the offseason, Washington signed DeSean Jackson and Andre Roberts Vincent Jackson was 2nd in percentage of team targets (we’ll get to who was first in a few minutes) for a similar reason: Jackson is a very good receiver, but Tampa Bay had limited weapons in 2014. ^[3]And in the 2014 NFL Draft, the Bucs added Texas A&M wide receiver Mike Evans and Washington tight end Austin Seferian-Jenkins. At least in theory, the high target numbers for Garcon and Jackson should be considered in light of the fact that both teams had below-average passing offenses.

The flip side of that coin is a player like Demaryius Thomas. In 2012, while “competing” with another very good receiver in Eric Decker, Thomas saw 24.2% of Denver targets.  Last year, with the addition of Wes Welker and a breakout season from Julius Thomas, Thomas saw just 21.2% of Broncos targets. But the team’s passing game was better, so arguably Thomas should receive a “bump” in his target percentage because he played for a great offense.

That’s just in theory. The unspoken elephant in the analysis is the quarterback. It’s not just a player’s supporting cast of weapons that determines whether his team has a good or bad passing attack: Thomas obviously benefited greatly from playing with Peyton Manning, too. Regular readers may recall that last year, for each team’s leader in targets, I compared their target percentage (defined as targets divided by all team targets) to their team’s passing efficiency (defined by Adjusted Net Yards per Attempt). I thought it would be fun to perform the analysis again, even if it may make more sense in theory than in practice. Take a look: the Y-axis shows percentage of team targets, and the X-axis respects Team ANY/A. In theory, the best WR1s should be up and to the right, with the worst WR1s (or tight ends masquerading as WR1s) in the bottom left corner of the chart.

Anquan Boldin really stands out here. If you look at the players to the right of him — i.e., those on better passing offenses — none of them came within 5% of Boldin’s league-leading 34% target percentage. After Boldin, four other players emerge to form a second tier: A.J. Green was a very highly-targeted player on an average passing attack, while Brandon Marshall saw slightly fewer passes but played for a slightly better offense. Moving further down that line, DeSean Jackson saw a still-respectable 25.5% of Eagles targets, which is impressive considering how effective Philadelphia’s aerial game was in 2013. And then at the far right is Thomas, dominant in ANY/A and posting a solid-enough 21.2% target percentage.

Putting aside the quarterback — which is a risky proposition, no doubt — the theory is that it’s easier to get a bigger piece of a pie when the pie isn’t very good (Vincent Jackson, Pierre Garcon) and it’s harder to get a big slice when the pie is great (Demaryius Thomas). This means, in theory, if we can control for those two variables, we can get a better estimate of receiver production.

One way to do that is to measure how many standard deviations from the rest of the group each player was in both target percentage and team ANY/A. By quantifying this relationship, Boldin’s dominance really stands out. He saw 34% of all 49ers passes in 2013, while San Francisco averaged 6.66 ANY/A. That 34% rate puts Boldin 2.22 standard deviations above average for these 32 wide receivers, and the 6.66 ANY/A is 0.69 standard deviations above average. Add those two together, and Boldin comes out at 2.91 standard deviations above average. Here’s how all 32 players fared:

So what can we learn from this?

• No metric is perfect, and this one has some drawbacks. Colin Kaepernick is very good, of course, but Boldin also benefits from San Francisco’s run-first attack. When the 49ers decide to throw, well, no team puts fewer wide receivers on the field than San Francisco. The counter-argument would be that if Boldin wasn’t so good, the 49ers couldn’t get away with that strategy, but I’m not sure I buy the argument that Boldin was the top receiver in the NFL last year. He ranked 16th in receiving yards in 2013, and certainly raw receiving yards is a terrible way to measure Boldin’s production. But I’m more comfortable with his 5th-7th place ranking in True Receiving Yards than his first-place ranking here. Also worth noting: using a similar method in 2012, Michael Crabtree came out as the top receiver in the league, likely for many of the same reasons.

• Brandon Marshall had an insane 39.9% target rate in 2012, but the Bears averageed just 5.1 ANY/A. The emergence of Alshon Jeffery put Marshall at 28.7% but the Bears at 7.12 ANY/A. In any event, for the second year in a row, Marshall comes in second place to the 49ers top receiver. The theory of this post breaks down from time to time, but the way it handles Marshall’s transition is kind of beautiful, and one of the reasons I enjoy this method.

• The Golden Tate/Calvin Johnson rankings are interesting, and not just because the duo will be on the same team in 2013. Both players saw just over 24% of their team’s targets in 2013. ^[4]Okay, let’s not just gloss over this. How many people would have guessed this to be true? Tate? Tate’s mom? Anybody else? But the Seahawks passing game was more efficient than the Lions passing game, so this formula likes Tate more. Some additional thoughts:

• How a player actually performs with his targets is ignored in this formula.  That’s a big issue for someone like Josh Gordon, who averaged 10.4 yards per target, because he gets “dinged” here by the terrible Browns passing game (and for missing two games).  But it isn’t as big of an issue as you might think: DeSean Jackson averaged an incredible 10.6 yards per target, but he still comes out third in this metric. As for Johnson and Tate, Megatron averaged a healthy 9.5 yards per target, but Tate was in the same ballpark at 9.1. The highest Yards per Target average, minimum 70 targets? Tate’s teammate, Doug Baldwin.

• So why is Tate ranked higher than Johnson? A few reasons. For starters, he gets to catch passes from Russell Wilson, and not Matthew Stafford. And while Tate and Johnson may have both been responsible for 24% of their team’s pass targets, they were certainly not making up the same percentage of their team’s offense.  Johnson maintained that rate on a pass-first offense, while Tate did it on a run-first offense.

• On the other hand, the question from 2012 persists: why don’t the Lions throw to Megatron more often? How come Kris Durham and Brandon Pettigrew saw 148 targets (gaining just 906 yards) and Johnson was targeted only 156 times (picking up 1,492 yards). ^[5]One reason: Johnson missed two games due to injuries last year. If Stafford doesn’t throw as frequently to Johnson because he’s always double teamed (which he’s not), then why are Stafford’s numbers so bad when throwing to other receivers? Perhaps with Tate in Detroit in 2014, we’ll get our answer. In any event, Stafford should be out of excuses with the additions of Tate and North Carolina tight end Eric Ebron: over the past two seasons, Stafford has averaged around 9.6 yards per attempt on passes to Megatron, and about 6.2 on all other passes.

• One other Detroit note: the Lions threw to running backs 157 times last year, the third highest number in the league behind Atlanta (161) and New Orleans (204!!!). I’m not sure what percentage of those passes were checkdowns versus designed passes (such as screens), but arguably a receiver shouldn’t get dinged for screen passes to running backs.  A team like Detroit might do that pretty frequently whereas the 49ers and Seahawks will just run the ball; in that sense, Boldin and Tate will be helped by this formula, while Megatron (and Jimmy Graham) would be disadvantaged.

• This formula finally answers the question of whether Jeremy Kerley could be a competent number one wide receiver. Glad we got that settled.

• True Receiving Yards champion Antonio Brown checks in at #6 on this list. Brown averaged a solid 9.0 yards per target last season, but Emmanuel Sanders mustered only 6.5 yards per target on 112 targets last year. I have a feeling that Sanders, now in Denver, will fare a bit better in that metric in 2014.

• Andre Johnson is pretty far down the list, and it’s almost entirely related to the play of the Texans quarterbacks in 2013. Playing with DeAndre Hopkins caused his target numbers to decline a bit, but it wasn’t balanced by an improvement in Team ANY/A.  Unfortunately, there’s no stats adjustment for your quarterback forgetting which team he plays for.