This post at Football Outsiders caught my eye today. The IgglesBlog noticed something odd with their team rankings. I’ve notice the same phenomenon in my own systems—that team ranking methods that adjust for opponent strength tend to produce rankings that correlate (inversely) with a team’s strength of schedule. In other words, top ranked teams appear to have weaker schedules and low ranked teams appear to have stronger schedules.
The problem is, assuming that a ranking method properly adjusts for opponent strength, it ostensibly should produce no correlation between each team’s ranking and its opponents' average ranking. In fact, we might expect the opposite result because of the two “strength of schedule” games each season—Last year’s 1st place teams play other 1st place teams, and so on.
In 2011 FO’s “DVOA” method correlated with opponent strength at -0.66, which is considerable. Here at ANS, Generic Win Probability correlated with Average Opponent GWP at -0.60 this season. FO notes that in other years the correlation isn’t nearly as strong, but there is an apparent tendency for negative correlations for most seasons.
This phenomenon was first pointed out to me a couple years back by a reader, and I too thought it was either a) randomness, or b) a flaw with my methodology. But I soon realized this is exactly what we should expect given the NFL’s scheduling rules. It’s neither luck nor a flaw. In fact, it's a sign the method is doing something right.
Consider a fictional four-team football league. Presume we have a perfect team ranking system that can peer omnisciently into each team’s soul to know its True Winning Probability (TWP). The Sharks, Knights, River Dogs, and Jack Rabbits each have a TWP of 0.75, 0.60, 0.40, and 0.25. (Notice the TWPs average to 0.50, as they would have to.)
Now, suppose this league plays a schedule where each team plays each of the others twice. The top team Sharks, who have a TWP of 0.75, would have an average opponent TWP of 0.42: [.6+.4+.25]/3. And if we calculate the average opponent TWPs for all the teams, we’d get the chart below, which plots average opponent TWP vs. team TWP.
The better the team, the easier its schedule. In fact, the correlation is a perfect -1. The reason that strength of schedule will always tend to correlate inversely with team strength is that a team can never play itself. Scheduling is not a random draw.
Although NFL scheduling system isn’t a four-team round robin, the 6-game intra-division part of the schedule is. So each year we should expect an inverse correlation between team strength and average opponent strength to some degree. This year’s strong correlation is likely a random outlier, and the FO guys can rest assured it’s not due to a weakness in their system.