The New Orleans Saints’ Jimmy Graham lost an arbitration hearing Wednesday in which he sought classification as a wide receiver rather than a tight end. Graham’s desire to be a wideout might seem counterintuitive to fantasy football players used to a game where being a tight end makes Graham even more valuable. But in the NFL, Graham will lose money as a result of the decision. He’s been designated with the Saints’ franchise player tag, which means that his compensation is determined by the top salaries in the NFL at his position. The five highest-paid NFL wide receivers make an average of about $12 million per season — more than the $7 million the top tight ends do.The arbitrator’s decision might seem unfair to Graham. Over the past three NFL seasons, Graham ranks eighth in the NFL in receiving yards, fourth in receptions and first in receiving touchdowns. He’s put up stats comparable to the best wide receivers — but he won’t be paid like one.But there’s a catch, and it has nothing to do with Graham’s position. Instead it involves his quarterback. Over the past three NFL seasons, Saints’ quarterback Drew Brees has ranked first in the league in passing yards, passing touchdowns and completions. Graham has been a big part of that. But even if we subtracted Graham’s receiving statistics from Brees’s totals, Brees would rank seventh, third and sixth in those categories.So we can say Brees’s numbers would still be very strong with an average tight end (or even with no tight end at all). But what would Graham’s numbers look like with an average QB?We can come to some reasonable estimates by using ESPN’s Total Quarterback Rating. Unlike most other quarterback statistics, Total QBR seeks to isolate the contribution of the quarterback as opposed to his receivers and his offensive line. It does so by using play-by-play tracking to account for things such as misthrown balls, yards after the catch and defensive pressure.Unfortunately, there’s not yet any analog to QBR for wide receivers and tight ends. But we can use QBR to estimate the effect a quarterback has on his receivers’ statistics. The next couple of paragraphs, which detail the method, are going to be a little dry; scroll down if you want to see just the results.To come up with these estimates, I used a subcomponent of QBR called Pass EPA, which focuses on a quarterback’s passing performance (as opposed to Total QBR, which also accounts for his rushing statistics and his propensity to avoid sacks and draw penalties). I ran a series of regressions on team totals from the 2011-13 NFL regular seasons, which estimated a team’s receiving yards, receptions and receiving touchdowns as a function of its Pass EPA. In essence, this reflects what a team’s passing statistics would look like given average receivers and pass protection but its actual quarterbacks. For example, a team with the quarterbacking of the 2013 Dallas Cowboys (mostly Tony Romo) would project to about 360 receptions, 4000 passing yards and 29 touchdowns given average receivers and offensive linemen.We can then divide a team’s projected statistics by league-average figures to estimate what effect its quarterbacks had on its receivers. For example, the average team since 2011 has had 24 passing touchdowns. Since the 2013 Cowboys projected to 29 touchdowns instead based on their QBR — about 20 percent higher than average — this implies that Romo boosted his receivers’ touchdown totals by 20 percent. Thus, we can reduce the touchdown totals for Dez Bryant, Jason Witten and other Cowboys receivers by 20 percent to estimate how they would have done with league-average quarterbacking.Let’s return to Graham. His quarterback isn’t the good-but-not-consistently-great Romo; it’s the spectacular Brees. Here’s what I estimate Graham’s numbers would have looked like with an average quarterback instead of Brees:In the table above, REC, YDS and TD represent a receiver’s unadjusted receptions, receiving yards and receiving touchdowns.Graham has been averaging about 90 receptions and 1,200 yards per year under Brees. I estimate that his totals would be more like 75 receptions and 900 yards with an average QB. And he’d go from having about 12 touchdowns per season to seven or eight instead. (Quarterbacks have an especially large impact on their receivers’ touchdown totals, in part because it requires consistent quarterbacking to get a team into the red zone.)These revised totals would still qualify Graham as an exceptional tight end — but they’d only be very good by the standard of a wide receiver. In the next chart, I’ve listed the actual and QB-adjusted receiving statistics for the top 50 players in the NFL as ranked based on a fantasy football scoring system of one point per reception, one point per 10 receiving yards and six points per receiving touchdown. (Fantasy football scoring systems place too much emphasis on touchdowns rather than yardage, but I’ll leave that argument for another day.)Based on his average fantasy points (FP) per season since 2011, Graham ranks third among all receivers and tight ends. But his FPs decline by almost 25 percent using his QB-adjusted statistics, so he falls to 14th place instead.Graham has benefited as much from his quarterbacks as any player in the NFL. Other pass-catchers for the Saints have been helped almost as much. So has Wes Welker, who left the New England Patriots and joined the Broncos just as Patriots quarterback Tom Brady began to show some signs of age. In Denver, Peyton Manning, apparently ageless, had perhaps the best QB season of all-time.The biggest gainer is the Browns’ Josh Gordon, who has posted excellent statistics despite a horrible quarterbacking situation in Cleveland. If Johnny Manziel lives up to the hype, Gordon could be a fantasy football monster next season (if he plays; Gordon failed a drug test and will be suspended for a yet to be determined number of games).For most other players, the effects are not so dramatic. Calvin Johnson and Brandon Marshall rate as the No. 1 and No. 2 receivers according to both raw and QB-adjusted statistics.But the league’s best tight ends tend to fall with the adjustment for quarterback quality. Rob Gronkowski drops from No. 20 to No. 39, for instance. Witten falls from No. 21 to No. 31 and Antonio Gates from No. 42 to No. 48.This could be a fluke — it’s a small sample of players. But it could also mean that tight ends are especially dependent on having good QBs. Along with slot receivers like Welker (it might be best to think of tight ends like Graham as being analogous to slot receivers), they tend to rely on routes based on precision and timing rather than beating their man downfield. Running those routes — and catching passes in traffic — requires a lot of skill. But the quarterback’s impact may be proportionately higher. That may be part of why NFL teams do not pay the best tight ends as well as the best wideouts.