Pythagorean Expectation – Can it Tell us Anything About the Toronto Maple Leafs?

Last week I wrote an article about the Toronto Maple Leafs’ chances of making up 12 points in the standings to make the playoffs this upcoming season.  Today I thought I would look at Pythagorean expectation to dig a little deeper into the Maple Leafs’ disappointing 2011-12 campaign.

Pythagorean expectation was developed by long time baseball writer turned executive, Bill James.  The idea is fairly straight forward.  In baseball, if you compare runs scored with runs allowed over an entire season you should be able to predict the amount of wins a team will have.

James did this by using the Pythagorean Formula, which is the formula we all learned in elementary school for calculating side lengths of a right angle triangle.

The actual formula is:

Win % = (runs scored)^2/[(runs scored)^2 +(runs allowed)^2]

The expected number of wins would then be calculated by multiplying the win percentage by the number of games (162 in baseball).

Pythagorean expectation is not complicated, but like other sabermetric analysis, the NHL has been extremely slow to adapt.  There have been other blogs out there that have looked at Pythagorean expectation for hockey, such as Nucks Misconduct, but the availability of up to date standings for the NHL is nowhere to be found.

In contrast, for Major League Baseball you can find these standings right on ESPN’s MLB page.

The NHL differs from the MLB with the fact that points, not wins, are the determining factor for getting into the playoffs.  So to generate Pythagorean Standings for the 2011-12 NHL season I first substituted goals for runs and points percentage for win percentage.  I then analyzed the past six years of NHL standings data to generate an average points-per-game number.

Since the NHL instituted the three-point game, using two points per game would not be valid.  Over the last six seasons the average points awarded per game is actually 2.23, thus generating the following formula for the NHL:

Points % = {(goals scored)^2/[(goals scored)^2 +(goals allowed)^2]} x 2.23

Using this formula for the six years of NHL data analyzed resulted in an R-squared value of 0.875, which indicates very good correlation between Pythagorean expectation and actual points.

The table below gives the NHL standings along with the Pythagorean expectation (Pyth Pts X) and the difference between the two. A negative difference indicates a team had less points than expected and a positive difference indicates a team had more points than expected.

Based on Pythagorean expectation the Maple Leafs ended the season where they should have.  They actually over performed by one point.  This doesn’t mean that the Leafs can’t improve over their performance from last year, and the first place to start would be on the defensive end.

The Maple Leafs were 10th overall in goals for, but 29th in goals against.  If the Maple Leafs would have allowed the same amount of goals that they scored (231) their Pythagorean expectation would have been 92 points. This would have put them in a tie for seventh place.

By the way, allowing 231 goals would have only put the Maple Leafs in a tie for 20th in terms of goals allowed.  You can be sure that Randy Carlyle will be focusing on the defensive end of the ice, and if the Maple Leafs can improve even a little bit while still maintaining their offensive output, they should be in the hunt for a playoff spot.

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