On the Packers' Statistical Sorcery

Watched the saintly, darling Bears play the evil, awful, no good Packers on Sunday and was struck by this graphic (if you'll pardon the glare):

This is kind of a fun fact, right? A team can be 11th in rushing yards allowed and 10th in passing yards allowed, but when you combine them (to make total yards) they're suddenly 6th! This is, as my friend W. put it, a cousin of Simpson's paradox.

I actually think we can cook up a more extreme example. For the sake of the exercise, let's abandon team names and just call them Teams 1-32:

Imagine that Teams 1-15 have allowed 0 rushing yards, Team 16 has allowed 1 rushing yard, and Teams 17-32 have allowed 100 rushing yards. Now imagine that Teams 17-32 have allowed 0 passing yards, Team 16 has allowed 1 passing yard, and Teams 1-15 have allowed 100 passing yards. Team 16 would be ranked 16th in rushing yards allowed (behind Teams 1-15), and Team 16 would be ranked 17th in passing yards (behind Teams 17-32). And yet, despite being in the middle of the league in both stats, Team 16 would be 1st overall! They've only allowed 2 total yards, while every other team has allowed 100 total yards. In table format:

If I'm not mistaken, we can establish a more general rule here as long as rushing rank + passing rank are >32:

Best Possible Overall Rank = Rushing Rank + Passing Rank - 32.

If Rushing Rank + Passing Rank <32, then the best possible overall rank is 1st.

So a team could be dead last in rushing, 1st in passing, and 1st overall. Or they could be 31st in passing and 2nd in rushing and 1st overall, and so on. And if we're dealing with a different number of teams, as in a college football conference, we can just replace the 32 in the formula with the number of teams being ranked.

Is this interesting? Folks, I don't even know if it's right!!