Are white wide receivers undervalued in the NFL?

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.

Podcast: Rufus Peabody and the NFL Conference Championship Games

Rufus Peabody, ESPN’s predictive analytics expert who makes his living investing in the sports markets, joins me on the Football Analytics Show to discuss the NFL playoffs. He’s also half of the excellent Massey-Peabody rankings and predictions for football.

Among other things, we discuss the following.

  • The balance between a quantitative model and subjective adjustments
  • The one factor for Massey-Peabody that tips the balance against the spread in Green Bay at Atlanta
  • The new results on home field advantage that impacts the NFC title game
  • How our models differ on New England’s pass defense
  • Rufus’s book recommendation for those interested in randomness
  • The perils of small sample size in sports

You’ll find Rufus incredibly humble for someone who has had his success in sports analytics, and I’m lucky to consider him a friend.

To listen on iTunes, click here.

To listen on the site, click on the play button.

NCAA is meeting with quants to make tournament selection process better

On Friday, January 20th, 2017, hell will freeze over, and the NCAA will meet with analytics guys like Ben Alamar, Jeff Sagarin and Ken Pomeroy. The conversation will revolve around making the tournament selection process better.

You can read about it here, but two points stand out for me.

First, they say the following about the RPI rankings the committee currently uses.

An even more powerful microscope to go with the time-honored RPI.

Time-honored my ass. The RPI is stupid for two reasons:

  • It lacks a solid mathematical basis (compare it with the least squares rankings that Pomeroy uses)
  • It uses wins and losses instead of margin of victory in its calculations

I discuss both of these issues in relation to college football here. Hence, RPI fails as a predictor for how teams fare in the tournament.

The NCAA should eliminate RPI from the selection process.

Second, Jim Schaus, the athletic director at Ohio State and committee member, said this:

I’m going to have to strap on in the meetings to stay up with all the calculus that’s going to be discussed, but I’m excited about it.

Calculus is so overrated in our society.

You want to hang with the quants, Schaus? Then let’s talk probability, or that no analytics ever says a team will beat another team with 100% certainty.

Want to get fancy, Schaus? Then let’s dig into linear algebra so you can understand the least squares method used in adjusting for strength of schedule.

I’m all for learning calculus. It’s just not as useful in sports analytics as probability and linear algebra.

Podcast: Ben Alamar on the ESPN Football Power Index and NFL Divisional Playoffs

On this week’s episode of the Football Analytics Show, I’m honored to have Dr. Ben Alamar, Director of Sports Analytics at ESPN. We dig into a host of topics, which includes:

  • The NBA executive that opened the conversation with “I don’t believe this analytics stuff”
  • How FPI (Football Power Index) makes adjustments for quarterback injuries
  • The surprising team to which FPI assigns the second highest Super Bowl win probability
  • The hidden factor that gives Dallas an extra point in the FPI prediction against Green Bay
  • Spread predictions for all 4 Divisional Playoff games for FPI (not available anywhere on the internet to my knowledge) and my member numbers
  • Ben’s 3 tips for breaking into sports analytics

You can check out the work of ESPN analytics team by clicking here.

To listen to the show on iTunes, click here.

To listen here, click on the play button:

How Andy Reid wins football games with interceptions

Andy Reid’s teams throw a low rate of interceptions. The visual shows how his teams in Philadelphia and Kansas City have had a lower than NFL average interception rate (interceptions divided by attempts) in all but 3 of 18 seasons.

Reid’s Eagles had a particularly good stretch of pick suppression from 2000 through 2004. Led by quarterback Donovan McNabb, Philadelphia never won fewer than 11 games in any of those 5 seasons.

Despite a decreasing interception rate across the NFL, Reid has continued to beat the NFL average over the past four years in Kansas City. Led by quarterback Alex Smith, the Chiefs have won 43 regular season games and never dipped below 9 wins in any one season.

The randomness of turnovers

The visual goes against the typical quant narrative that turnovers are random.

For example, I’ve shown this visual that shows the relation between interception rate the first 6 games of the college football season versus the remainder of the season.

The lack of correlation between these quantities shows that you can’t predict a team’s interception rate later in the season based on the same quantity during first 6 games.

This suggests interceptions are random, and a team has a 50% chance to have a better or worse than average interception rate. However, if you assume this for Andy Reid’s teams, there’s only a 0.37% chance his teams would have had 3 or fewer seasons with a below average interception rate.

Randomness certainly plays a role in interceptions. No one who has ever seen a tipped pass fall into the hands of a defender should doubt that.

However, the Reid visual suggests that some coaches can suppress interceptions over a very large sample of games.

Steelers at Chiefs

This has implications in predicting the outcome of the Steelers at the Chiefs playoff game this weekend.

Kansas City doesn’t seem like much of a Super Bowl threat with the 16th and 11th ranked pass offense and defense, respectively, by my adjusted yards per attempt. I use these pass efficiency numbers to evaluate teams for two reasons:

  • My research shows the importance of passing over rushing in the NFL.
  • Turnovers have little impact on yards per pass attempt.

However, if Kansas City is truly skilled at not throwing interceptions, then these pass efficiency numbers will underestimate their team strength.

Team rankings based on adjusted margin of victory might be a better way to evaluate Kansas City. Their low interception rate will impact margin of victory, as I’ve found that an interception is worth 5 points in the NFL.

My member numbers combine both pass efficiency and margin of victory to make Kansas City a 1.3 point favorite against Pittsburgh. However, my team rankings based on only points would make Kansas City a 3 point favorite.

I interviewed Ben Alamar on the Football Analytics Show this week, and his FPI (Football Power Index) makes the Chiefs nearly a 5 point favorite. They use an expected points added, a metric which accounts for interceptions but their own twist. To listen to that part of the discussion, go to 14:50 of my interview with Ben Alamar.