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%.
|Player||Rec Yds||Perc||Sqrd Perc|
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?