This project was a collaboration with Rob Warendorf, a junior Chemical Engineering student at the University of Delaware. You can find Rob on Twitter.
Julian Edelman sprints upfield before making a sharp cut towards the sideline. The ball arrives as he reaches the sideline, and his catch gives the Patriots another first down.
New England turned Edelman, who is white, from a college quarterback playing in the Mid-American Conference to one of the NFL’s best receivers. As an encore, they signed Chris Hogan, who played lacrosse for most of his time in college, and turned him into a white Jerry Rice (9 catches, 180 yards in the AFC championship game against Pittsburgh).
It’s not only New England that has productive white wide receivers. Cole Beasley, all five foot eight inches of him, has become one of the most effective weapons for the Dallas Cowboys.
Is there an NFL market inefficiency for white wide receivers? Rob Warendorf and I dug into the data to find out.
It’s a cautionary tale about not drawing conclusions based on data without considering the bigger picture first. Here’s what Tom Kislingbury said about it on Twitter.
This is the sort of article I love. Clear data and results combined with awareness of its own limitations. Chapeau. @TomDegenerate
Let’s dig into it.
Team Pass Efficiency
To look for market inefficiencies for white wide receivers, we first asked whether teams with a white wide receiver performed better than teams without one. This required making a list of white wide receivers, a project we crowd sourced.
We decided to look at teams in which a white wide receiver had a minimum of 8 games played and 20 targets. From 2007 through 2015, this gave us 20 white wide receivers who played in 75 seasons.
Based on these seasons, we looked at how the pass offense performed compared to the NFL average based on yards per pass attempt. These pass offenses with a white wide receiver performed 3.5% better than the NFL average. (Over these 75 data points, the error in this estimate is 1.4%.)
To determine the statistical significance, we decided on a 90% certainty that these results did not come about due to randomness. An analysis showed that these offenses were 1% better than the NFL average with this 90% confidence.
We also ran numbers for yards per game, finding that these offenses with white wide receivers performed 7.6% better than the NFL average. These results were also statistically significant.
Second guessing this approach
So we can conclude that there’s a market inefficiency for white wide receivers, right? Another team just has to dig up these hidden gems to become a better offense.
Not so fast. Players such as Jordy Nelson, Julian Edelman and Eric Decker played many of the seasons in our raw data set of 75 seasons.
Who was throwing the ball to these white wide receivers? Aaron Rodgers, Tom Brady and Peyton Manning (in his prime). Not every season featured an elite quarterback. The data also includes two seasons of David Garrard’s passes to Matt Jones.
However, the presence of so many seasons with elite quarterbacks made us expand our analysis. To determine an actual inefficiency in the market for wide receivers, we looked at another source of data: salaries.
Salary Data on NFL Wide Receivers
The analysis of wide receiver salaries required some assumptions. In 2015, NFL teams spent about 7.6% of their salaries on wide receivers. Without full data on previous years, we’ll assume that this rate holds for all seasons in our sample.
Also, a player’s contract usually includes both a base salary and bonuses. We decided to split the entire value of the contract evenly over the years of the contract.
Based on these assumptions, we calculated that white wide receivers received 28% of the total salary spent on wide receivers in our sample of 75 seasons.
How does this fraction of salary compare with the production of white wide receivers? We’ll quantify production as the fraction of yards gained by these white wide receivers compared with other wide receivers on their team.
Determining this fraction of yards gained by white wide receivers requires another simplifying assumption, as tight ends and running backs also make contributions to passing yards. In 2015, wide receivers gained 67.8% of all receiving yards, a fraction we will assume constant for each season in our sample.
For our sample of seasons, white wide receivers gained 18.7% of the team’s passing yards. To determine the fraction of yards for white wide receivers compared to all wide receivers, we divide this 18.7% by the 67.8% average. This implies that white wide receivers gained 27.6% of the passing yards of all wide receivers.
In summary, white wide receivers make about 28% of the salary of all wide receivers on their team and gain 27.6% of the yards by wide receivers. This suggest the lack of a market inefficiency for white wide receivers.
New England Patriots
While there is no market inefficiency across the NFL, maybe some specific teams are good at finding undervalued white wide receivers. Let’s look at New England.
From 2007 through 2016, the Patriots white wide receivers made 41.4% of the salary for wide receivers but produced 30.5% of the pass yards. This suggests the Patriots have possibly overpaid for their white wide receivers.
The salary analysis makes a two assumptions for all teams:
- the fraction of salaries for wide receivers compared to all players is constant
- the fraction of pass yards gained by wide receivers is constant
One could do a more specific analysis by finding the salary and yards for every wide receiver on the 75 teams in our data set. However, the results here suggest this more detailed analysis will not change the conclusion about the efficiency of the market for wide receivers.
This study of white wide receivers in the NFL shows how one must be careful about drawing conclusions from data.
From watching players like Cole Beasley and Julian Edelman in the playoffs, I thought there might be a market inefficiency for white wide receivers. An increase in pass efficiency by yards per attempt for the 75 seasons in which a white wide receiver made a contribution seemed to confirm this.
However, the quarterback and other wide receivers make a significant contribution to the pass efficiency of these offenses. We turned to salary data and found that white wide receivers contribute pass yards in accordance to how much they get paid. This suggests no market inefficiency for white wide receivers.
I don’t think any sharp handicapper or NFL front office person would ever use raw receiving yards as a measure of WR value to a team. So I’m really not buying the yards = $$ assumption underlying your analysis.
That’s my point. Want to see a number jump off the page? Targets to catch ratios and % 3rd Down conversations and TDs. All the stats gathered by Pro Football Reference should make this interesting.
Interesting analysis. I wonder if you looked at short wide receivers (maybe under 6 foot or under 5 10) if you would fine a market inefficiency. It seems like outside of Gronk and Moss, that is all the Patriots have used in their run.
Dr. Ed Feng says
Great idea. Edelman is 5’10” and a low round draft pick, Jordy Nelson is 6’3″ and a 2nd round pick. Both are great players.
Sample size is small though.
James Greenberg says
Tom Brady was a 6th-round pick. Maybe there is a market inefficiency for HOF 6th-round QBs. Small sample size though.
Maybe the Patriots are a phenomenally well-run organization that does its due diligence year in and year out.
Maybe some things defy statistical analysis.
Maybe statistics suck all the fun out of sports.
I know there’s a large enough sample size to assert that!
How about an analysis of white reciever draft position compared with draft position of non white receivers with similar production?
Dr. Ed Feng says
That’s a nice idea, although the sample size is small.
From our data set, Beasley, Danny Amendola, Wes Welker and Chris Hogan were all undrafted free agents. Jordy Nelson was taken in the second round.
Dr. Ed Feng says