## Pythagorean theorem and playoff success

Recently, there's been a lot of discussion around finding a Pythagorean-based formula to predict regular season point values. However, as any Sharks fan will tell you, winning the President's Cup doesn't always guarantee post-season success. Using post-lockout data, I attempted to find a link between goal differential, PK%/PP% and the last teams standing in the Stanley Cup playoffs. I am admittedly a relatively new fan of hockey, so I would appreciate any insight you all can provide into the numbers below.

Methodology

Using Microsoft Excel's RANK function, I calculated every team's ranking in the three categories I mentioned above. I used Goal Differential as a standalone metric, but calculated a composite "Special Teams" rank as an average of the PP% and PK% ranks. As an example, the 2010 Caps are 1st in goal differential and PP Conversion %, and 19th in PK%, so GD = 1 while Special Teams = 10. Using the formula SQRT(GD² + Special Teams²), I derived a total score for each team. Bear in mind with this methodology, the lower the score the better.

Note: Stats as of January 31, 2010; Source: ESPN

Results

Listed below are the top 5 teams each season based on this formula, starting in the 2005-2006 season.

2005-2006

 GD PP% PK% ST Total 1 Detroit 2 1 3 2 2.8 2 Ottawa 1 4 4 4 4.1 3 Buffalo 4 3 2 2.5 4.7 4 NY Rangers 4 7 10 8.5 9.4 5 Nashville 7 10 5 7.5 10.3

Final Four: Buffalo, Carolina, Anaheim, Edmonton (ranked 3, 11, 9, 12, respectively). Bold highlight denotes Stanley Cup Final match-up.

2006-2007

 GD PP% PK% ST Total 1 Anaheim 6 3 5 4 7.2 2 Minnesota 7 6 2 4 8.1 3 San Jose 4 2 14 8 8.9 4 Nashville 3 17 3 10 10.4 5 Ottawa 1 14 9 11.5 11.5

Final Four: Anaheim, Ottawa, Detroit, Buffalo (ranked 1, 5, 8, 14, respectively).

2007-2008

 GD PP% PK% ST Total 1 Detroit 1 3 8 5.5 5.6 2 San Jose 5 10 1 5.5 7.4 3 Dallas 3 13 2 7.5 8.1 4 Montreal 2 1 15 8 8.2 5 Philadelphia 6 2 10 6 8.5

Final Four: Detroit, Dallas, Philadelphia, Pittsburgh (ranked 1, 3, 5, 6, respectively)

2008-2009

 GD PP% PK% ST Total 1 San Jose 2 3 5 4 4.5 2 Boston 1 4 11 7.5 7.6 3 Philadelphia 7 6 6 6 9.2 4 Washington 6 2 17 9.5 11.2 5 Minnesota 10 9 2 5.5 11.4

Final Four: Detroit, Pittsburgh, Carolina, Chicago (ranked 6, 9, 16, 7, respectively)

The results are somewhat mixed. It is interesting to me that in the past four years, the top regular season team as predicted by this formula has won the Stanley Cup twice. The other two years? Two Presidents Cup winners that were eliminated in the first round ('06 Detroit, '09 San Jose).

I also went back and looked at the playoff tree for these four seasons to see if this formula could predict winners more accurately than comparing regular season point totals. I viewed a match-up of teams that were directly adjacent in Pythagorean rank as a toss-up, which I treated as a tie. Similarly, a match-up of two teams that finished with identical point totals was also treated as a tie.

Pythagorean formula: 34-17-9; point % = 64.1%

Picking based on regular season point totals: 35-23-2; point % = 60.0%

It appears the Pythagorean formula is slightly better at picking winners, but again, the sample size is probably too small to make a definitive conclusion.

For those of you wondering, this is what the current 2010 rankings look like:

 GD PP% PK% ST Total 1 San Jose 2 3 1 2 2.8 2 Chicago 3 6 4 5 5.8 3 Buffalo 6 13 2 7.5 9.6 4 Washington 1 1 19 10 10.0 5 Vancouver 4 5 14 9.5 10.3

Clearly, the Sharks are either going to flame out in the 1st round (again) or win it all this year.

If this FanPost is written by someone other than one of the blog's editors, the opinions expressed in it do not necessarily reflect those of this blog or SB Nation.

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