Does Spreading the Ball Around Make a Passing Attack More Efficient?

Part of analyzing an NFL team’s passing game is measuring the distribution of passing stats among its receivers: targets, yards, touchdowns, etc. A good way to do this is looking at the percentage distribution to different receivers, i.e. the WR1 received 25 percent of receiving yards, the WR2 got 15 percent, and so on. This is useful when projecting stat lines for receivers, but doesn’t give us an easy way of comparing generally how concentrated one passing game is versus another.

A commenter at Chase Stuart’s Football Perspective gave him an idea from the finance world for calculating portfolio concentration, which Stuart used to conclude that teams are spreading it around more these days. The formula sums the squared passing yard ratios for each receiver to form a single number, or what Stuart calls the concentration index. The more spread out a passing game, the lower the concentration index, and vice versa.

I decided to dig into concentration index a bit more to see if we can learn anything about the benefits or costs of have a diversified passing game.

A look at 2016

There isn’t really any correlation between a quarterback’s total passing yards and his concentration index. You can see a consistent spread in the concentration index from around 0.125 to 0.185, until the range narrows for the top three passers: Drew BreesMatt Ryan and Kirk Cousins.

How to the top quarterbacks compare?

One of the issues with concentration index is the lack of an adjustment for injuries. If a quarterback’s WR1 is injured mid-season and account for 20 percent of passing yards in the eight games he plays, then the replacement WR1 accounts for 20 percent of the yards in the next eight games, the concentration index sees this the same way as if two receiver had 10 percent share and played the entire season. Unfortunately, my ability to adjust the numbers for these circumstances is limited by the lack of play-by-play participation data available to the public. I tried to make some adjustments with snap counts, but without knowing exact formations on each play, snap-count adjustments tend to over emphasize the relative performance of part-time players.

But there is something to be learned by looking directly at the concentration indexes of the top quarterbacks over time.

The passers included in the chart include the quarterbacks will be in the Hall of Fame, might not but should be (Rivers), and excludes those who may make it but haven’t been efficient enough to deserve it (sorry, Eli).

A quick glance reveals that even the top passers see quite a bit of fluctuation year-over-year in their concentration indexes. Brees stand out as the only passer to maintain a relatively low concentration index since 2006. Philip Rivers has been right around Brees since 2010, but his concentration index has likely been artificially low as top receiving option Keenan Allen consistently missed time. Brees is known for spreading the ball not only among wide receivers and tight ends, but also his running backs.

If we group all the top passer above to one index and compare them against the league average, you’ll see that there isn’t a huge difference between the two averages.

Top passers have spread the ball out more in seven of the 11 years, but I wouldn’t call that conclusive that better passers spread the ball around more often. You’ll also see a little of what Stuart was pointing to in his post: the league-wide concentration index is trending down over time.

Who drives passing concentration? Quarterbacks or receivers?

Seeing how these quarterbacks have been successful despite differing concentrations in their passing presents a chicken-or-egg questions: Is passing distribution driven by the quarterback or the differential in talent of his receivers?

We can get a better historical picture by plotting all passers’ concentration indexes from 2006 t0 20116.

The trend line is fairly weak in the direction of more concentration leading to better passing efficiency. The highlighted name near the top of the graph illustrate how efficient season can be produced with a wide variety of passing concentration.

I think the correlation between concentration and passing efficiency, while slight, could be a function of the fact that you need to have stud receivers to have a concentrated passing game. I doubt Aaron Rodgers couldn’t have spread the ball around more in 2014 if he chose. But why target less efficient options when you have Jordy Nelson and Randall Cobb at your disposal?

The fact that there hasn’t been a single 0.20+ concentration index quarterback with an indexed yard per attempt under 85 (or 85 percent of league average that year) probably means something. First, you likely had healthy receivers to achieve that level of concentration. Second, you had to have at least one receiver who was good enough to get consistently open. Last, you likely had less reliance on less efficient passing options, like running backs. Brees may use his running backs efficiently in the passing game, but many quarterbacks primarily use them as secondary or tertiary dump off options.


While it makes intuitive sense that spreading the ball around will help a passing games efficiency, it isn’t certain when looking at the numbers. In fact, there is evidence pointing the other direction. But our ability to rely on a single number like concentration index is complicated by its inability to incorporate important factors like injuries and formations.

Would you rather have a concentrated passing attack like Aaron Rodgers in 2014, or spread the ball around like Drew Brees? As long as your receivers stay healthy, there doesn’t seems to be anything wrong with staying concentrated. But as we saw with Rodgers in an atypically inefficient 2015, relying too much on your top receivers can leave a passing game fragile in the face of a injuries. Brees, on the other hand, continues to lead the NFL in passing as his top receiving options rotate consistently.

Leave a Reply