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. (more…)