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Five years ago, in one of the first posts at Football Perspective, I looked at league-wide passing distribution in terms of what percentage of receiving yards were gained by the WR1, WR2, WR3, TE1, and RB1 for each team. Today I want to examine passing distribution in a different way: how much are teams spreading it around than ever before?

In the comments to Wednesday’s post, Quinton White described one way economists measure how concentrated industries are, using a relevant football example:

If you wanted to incorporate more than just the #1 guy, then you could sum up the squared shares for all a QBs receivers. For example, say a QB threw to 7 guys, and the first guy caught 30% of the yards and the second 20% and the remaining 5 guys each caught 10%, then he would have a concentration index of .3^2 + .2^2 + .1^2 + .1^2 + .1^2 + .1^2 + .1^2 = .18. The higher the number, the more concentrated the passer is. The max is 1 (Brees threw all his passes to Cooks then 1^2 = 1). If he threw 10% to ten guys each, then the index would be .1.

Let’s say we did that for the 2016 Falcons, who had the best passing game in the NFL last season. Atlanta’s skill position players gained 4,960 receiving yards last year. In the table below, column 2 shows the number of receiving yards gained by each player, column 3 displays their number of receiving yards divided by 4,960, and column 4 shows the squared result of what is in column 3. The bottom right cell in the table is the sum of all the numbers in column 4, or 14.14%.

PlayerRec YdsPercSqrd Perc
Julio Jones140928.41%8.07%
Mohamed Sanu65313.17%1.73%
Taylor Gabriel57911.67%1.36%
Devonta Freeman4629.31%0.87%
Tevin Coleman4218.49%0.72%
Aldrick Robinson3236.51%0.42%
Austin Hooper2715.46%0.30%
Levine Toilolo2645.32%0.28%
Jacob Tamme2104.23%0.18%
Justin Hardy2034.09%0.17%
Nick Williams591.19%0.01%
Patrick DiMarco521.05%0.01%
Joshua Perkins420.85%0.01%
Terron Ward110.22%0.00%
D.J. Tialavea10.02%0.00%

What does 14.14% mean? Maybe not much in the abstract, but it is a pretty small number. It ranks just 26th among all teams last year, which is consistent with the narrative that Ryan really spread it around last year. On the other end of the spectrum are the Dolphins, who had the most concentrated passing attack in the NFL last year. Miami’s top 3 receivers were responsible for 70% of the team’s receiving yards last season:


The league average last season was 0.155, which in the historical context is pretty low. How low? The numbers the last two years were the two lowest seasons since 1983. The graph below shows the pro football concentration index for each year (except 1987) since 1946:

What do you think? What would you like to see in a follow-up post?

  • Quinton White

    This was a cool thing to wake up to this morning 🙂

    • AgronomyBrad

      This was an awesome idea. I had never heard of this before you mentioned it yesterday.

  • Joseph Holley

    As a follow-up post idea(s):
    Percentage using top 7 receivers (prob. would be 3 WR, 2 TE, 2 RB–but not necessarily)
    Percentage using only players to have 10+ catches, or 50+ yds, to filter out a practice squad player that played in week 17.
    Percentage using only players on the week 1 roster or who played in at least 8 games.
    Quinton’s idea is great–and definitely shows its value–but to really view how M. Ryan spread the ball around, the top 10 guys on the chart + DiMarco are the ones who truly made up ATL’s pass catching corps last year.

  • Wesley Brandemuehl

    Perhaps how well past great passing offenses spread it around?

  • Dan

    I’d expect teams to spread it around more when they pass more – this is basically the pattern that you looked into in the post How Many Extra Receiving Yards Should Come on Extra Passes? and incorporated into True Receiving Yards.

    It would be interesting to see how closely the concentration index tracks the number of passing attempts per game, to see what else might be influencing it. Increasing the number of games in a season should also lead to a lower concentration index (for the same reasons that a single game should have a higher concentration index than a whole season), although I’m not sure how big that effect is.

  • Tom

    This is really cool. For follow up post, it would be neat to see what this means as far as the overall success of a team’s offense…do the better offenses spread it around or concentrate? Or maybe it doesn’t​ make a difference?

  • LightsOut85

    Very cool. I wonder if this could be incorporated into one of the “adjusted WR value across the eras” formulas. (I know TRY incorporated measures to account for the fact that more-passes=/=more-targets-for-top-WR, but perhaps this could further refine it). Accounting for the fact that modern “extra passes” are going more towards non-primary receivers, and perhaps for the “playing with other talented receivers” effect (since one team may lean heavily on one receiver because they don’t have much depth of receiving talent, but another may spread it between 2 great talents, leading neither to have impressive (relative) totals).

    • The thing I can’t quite figure out how to handle is certain teams have used the short passing game to replace running plays. If you hand the ball to the RB, that’s a handoff. If you throw it to the TE behind the line of scrimmage one second after the snap, that’s a pass. But in reality, they are pretty similar.

      Some teams use a lot of short throws to replace runs. But not every team does. The teams that don’t, I suspect, will have more concentrated passing games. So I’m not surprise to see Carolina near the top, because they have a power running game — maybe that changes with Christian McCaffrey. I think Miami is similar, with a power runner in Ajayi and a running QB. The Giants are a little trickier.

      OTOH, seeing BUF and SF at the bottom kind of goes against this line of thinking.

      • LightsOut85

        That’s very true. Screens, check-downs, & the-like definitely throw a wrench into the gears. Looking back at my screenshots of PFF’s “QB project” back in 2013, screen-% (among individual QBs) ranged from 3.7% to 17.5%! (the latter being Nick Foles) and an average of 9.7. And in the passing-by-route breakdown, they had “HB non-screens” (which I assume were behind the LOS or in the flat, otherwise they’d be classified as the traditional routes), which ranged from 7.7% to 18.6% (average 13.4%). If we add those numbers for each QB, the range of “essentially a run” passes is from 15.4% (Ryan Tannehill) to 30.2% (Nick Foles), and 23.1% for the NFL as a whole. That’s a lot of variation in “traditional passing” rates.

  • Vincent Verhei

    So the Falcons are in the top ten for most diverse passing attack in 2016. Which is amazing, because if I’m doing this right, than the 2015 Falcons come in with a score of 22.3%, which would have just lapped the field last year. The 2015 Falcons really were just Julio Jones and nothing else.

    • Yep — the Falcons were at 22.3% in 2015 and 14.1% in 2016. Jones went from 40.7% to 28.4%, which when squared, goes from 16.5% to 8.1%, which actually exceeds the amount by which Atlanta’s concentration index declined. It’s a little counterintuitive because the Falcons #2 and #3 receivers in 2015 were Tamme and Freeman (so they weren’t WRs) but they each had a larger share of the pie than the Falcons #2 and #3 receivers in 2016. But the 2016 Falcons #5-#10 guys each had about 2% more than their counterparts in 2015.

      Said another way: Atlanta had TEN players gain at least 200 receiving yards in 2016, compared to just FIVE in 2015. Justin Hardy had 194 receiving yards in 2015 and 203 receiving yards in 2016, yet he dropped from 6th to 10th on Atlanta’s receiving list.

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  • I find it interesting that 1956 has a spike in the data, because that was one of the worst passing seasons ever:


  • Using fftoday ppr scoring – i matched up the WR1(based on fpts) from each team and compared them to the teams ratio – is this chart better with the player specific ratio or does it work with team ratios? https://uploads.disquscdn.com/images/43bd9c109fdf2ebb273a6a7682fd56dff1bd103c0b3fc84bf17ebf8c05e4486a.jpg

    • Good stuff. It’s crazy how bad much the Panthers passing game dropped off last year. And it’s weird seeing Benjamin right next to Britt there.

      • Matt Aitken

        I had to look the name up, but the economic metric you allude to in the post is called the “Herfindahl index”:


        As for this chart: both WR1 fantasy points and the Herfindahl index partially depend on WR1 receiving yards, so there’s automatically a built-in correlation. Plotting the data like this tends to just separate receivers by how many touchdowns they score and/or how good of an offense they play in. For example, the players way above the regression line (Brown, Nelson, Evans, Beckham) led the league in TDs last year. The players way below the line either didn’t score a lot of touchdowns (Jordan Matthews + Benjamin) or play in a horrible offense (Britt + Enunwa).

        Rather than comparing the Herfindahl index to WR1 fantasy points, I wonder if it might be more illuminating to compare the Herfindahl index to team variables, such as total passing yards or team wins or offense efficiency rating, to see if there’s a correlation. Do teams that spread it around more tend to gain more yards or win more
        games? If so, why? That would be a cool follow up post.

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