This week's Varsity Numbers revisits the concept of Covariance and what it can tell us about teams and their personality.
In math terms, covariance basically measures the strength of the correlation between variables. In football terms, covariance can tell you which teams play their best games against their best opponents, and which play their best against their worse opponents. At least, that's how we will use it here. I discussed it in Varsity Numbers just over a year ago, and I utilized it in each of this summer's statistical profiles at SB Nation.
We tend to look more favorably on the teams that play the best against the best, but that doesn't necessarily signify a better team. Plenty of teams go in the opposite direction and win a lot of games. The trick, of course, is balance. If you play your best against the best teams, then you run the risk of both losing a lot of close games to good teams and suffering letdown losses against lesser teams.
This year, Washington State is a lovely example of this. The Cougars fared as well as just about anybody against Oregon (third in the F/+ rankings), lost by 13 to Oregon State (11th), stayed within seven points of Stanford (12th) and almost completed a ferocious comeback in an eight-point loss to UCLA (30th). They were perfectly respectable against those four teams but went 0-4. Meanwhile, they collapsed and lost to lowly Colorado (123rd), got their doors blown off by Utah (56th), and tried really hard to lose to both Eastern Washington (FCS) and UNLV (86th). As you'll see below, Wazzu is on the extreme "best against best" pole of the Covariance scale, with a 2-8 record to show for it. Play well against the worse opponents and take blowout beatings against the best, and they're probably 4-6 right now.
At the same time, you could end up like Louisville, playing just well enough to beat most of the better teams on their (rather weak) schedule (34-31 over Cincinnati, 45-35 over Pittsburgh, 39-34 over North Carolina) and barely beating some of the lesser opponents (28-21 over FIU, 21-17 over Southern Miss in a downpour). Until last week's blowout loss to Syracuse, the Cardinals were actually undefeated through nine games despite what wasn't even a top 40-level performance.
And yes, UCLA is as high on the Standard Deviation list as you would imagine.