About this time last year, I made several attempts at coming up with an equivalent to baseball's "Pythagorean Expectation." For those of you unfamiliar with the term, it was invented by baseball stat guru Bill James, and it describes the relationship between runs scored/runs allowed and wins/losses, then derives "standings" from a simple equation. In this post, I attempt to do the same thing for hockey. For those of you that I haven't lost with the words: Pythagorean, stat, derive, equation and James, a table and full explanation follow after the jump.
For those uninterested in the process behind all this, here are the standings.
For the sake of comparison, here are the standings based on actual points, note that these may not correlate to the NHL's standings because they don't account for tiebreakers.
Finally, since the most interesting part of Pythagorean systems is to see which teams are getting "lucky" and which are "unlucky," here's a table of the teams ranked from unluckiest to luckiest, based on delta between their expected points and their actual points - the higher the number, the luckier the team has been.
From a Caps perspective, this is sort of typical good news/bad news. The Caps have been getting somewhat "lucky," but in actuality, this is likely due to several lopsided defeats that the Caps have suffered (vs. ATL, NJD and NYR). The good news is that Tampa has been getting even luckier, and though they suffered a 6-0 drubbing at the Caps' hands, I'm not sure that they had a spate of awful play similar to the Caps' recent skid. They did, however, have awful goaltending for much of the season to date. The other bad news is that Atlanta and Florida have both been playing better than their records would suggest.
For those of you interested in the process behind all this, read on...
The first problem encountered with creating a Pythagorean system for hockey is that, unlike baseball, hockey results aren't binary. There are wins, losses, and overtime/shootout losses, so the James equation won't work. The NHL further muddies the water with the points system: two for a win, zero for a loss and one for an OT/SO loss. The NHL standings aren't based on Win-Loss records, they're based on the points that teams accumulate. This actually proved to be a saving grace.
Going back over the years since the lockout, I determined that there were several key numbers that were constant enough to be used as the basis for a possible Pythagorean Expectation for the NHL. First, the average number of points earned by teams in the NHL since the lockout is remarkably constant at 91.3. This means that the average team playing 82 games would earn 1.1134 points per game. Moreover, the "average" NHL team also scored exactly as many goals as it let in since, by definition, there are exactly as many goals scored every year as there are allowed. Armed with these two numbers, I calculated that to move one standings point away from the mean (91.3 points), a team would need to either score or not allow a combination of around 2.64 goals.
For this iteration of Pythagorean standings, I decided to subtract empty net goals from the goals for and against totals. The reasoning behind this is simple - empty net goals aren't a great barometer of skill disparity. They're simply a great barometer of which teams happen to enter the late stages of the 3rd period with a one to two goal lead.
The final equation ends up being:
Pythagorean Points = [(Goals For - Empty Net Goals For) - (Goals Against - Empty Net Goals Against)]/2.64 + (Games Played * 1.113414)
Here's the resultant table in alphabetical order.
Thoughts, suggestions and corrections all welcome. Any data entry errors are my own.