“Pythagorus Algebraic Separated” by John Blackburne. Licensed under Public Domain via Commons.

This is the second part of a five part series. Check out Part 1, Part 3, Part 4, Part 5 here. You can view the series both at Hockey-Graphs.com and APHockey.net.

In Part 1, I looked at some of the theory behind Pythagorean Expectations and their origin in baseball. You can find the original formula copied below.

WPct = W/(W+L) = Runs^2/(Runs^2 + Runs Against^2)

The idea behind the formula is that it is a skill to be able to score runs and to be able to prevent them. What isn’t a skill, however — according to the theory — is when one scores or allows those runs. Teams over the course of weeks or months may appear to be able to score runs when they’re most necessary, to squeak out one-run wins, but as much as it looks like a pattern, it is most often simple variance. If you don’t fully buy into that idea, or you don’t really understand what I mean by variance, read this and then come back. Everything should be a lot clearer.

When applying Pythagorean Expectations to hockey, there are a couple of factors that complicate the matter. First of all, the goal/run scoring environment is very different. Hockey is a much lower scoring sport. That means that a team is more likely to win, say, 10 one-goal games in a row than in baseball. The lower the total goals, the closer the average scores, the more variance involved. Second, not all games are worth the same number of points. In baseball, you either win or lose, so you use run differential to figure out a winning percentage. But winning percentage doesn’t really work as a statistic in hockey since you can lose in overtime and get essentially half a win, while your opponent gets a full win.

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