Do you also account for margin of victory?
Affirmative. I took some inspiration from the soccer ratings, which account for goal differential in addition to the game result. But this is one of the more complicated parts.
For the NFL, I start by adding one point to team’s margin of victory and then take its natural logarithm. Then I multiply that result by the K value. That means I’m more moved by big wins than narrow ones, although there are diminishing returns. I’m not so impressed by the fifth touchdown when a team is ahead 28-0.
That seems simple enough.
It would be, but that isn’t all there is to it. We haven’t talked about my autocorrelation problem. It’s a little embarrassing.
Go on. “Autocorrelation”? Was that the weird David Cronenberg movie?
Autocorrelation is the tendency of a time series to be correlated with its past and future values. Let me put this into football terms. Imagine I have the Dallas Cowboys rated at 1550 before a game against the Philadelphia Eagles. Their rating will go up if they win and go down if they lose. But it should be 1550 after the game, on average. That’s important, because it means that I’ve accounted for all the information you’ve given me efficiently. If I expected the Cowboys’ rating to rise to 1575 on average after the game, I should have rated them more highly to begin with.
It’s true that if I have the Cowboys favored against the Eagles, they should win more often than they lose. But the way I was originally designed, I can compensate by subtracting more points for a loss than I give them for a win. Everything balances out rather elegantly.
The problem comes when I also seek to account for margin of victory. Not only do favorites win more often, but when they do win, they tend to win by a larger margin. Since I give more credit for larger wins, this means that their ratings tend to get inflated over time.
Is this also a flaw with the soccer Elo ratings?
Possibly. You may want to reconsider what you wrote about Germany.
So, how do you correct for this?
It isn’t complicated in principle. You just have to discount the margin of victory more when favorites win and increase it when underdogs win. The formula for it is as follows:
Margin of Victory Multiplier = LN(ABS(PD)+1) * (2.2/((ELOW-ELOL)*.001+2.2))
Where PD is the point differential in the game, ELOW is the winning team’s Elo Rating before the game, and ELOL is the losing team’s Elo Rating before the game.
It’s a little ugly, but we all have our vices.
http://fivethirtyeight.com/datalab/intr ... o-ratings/
