Frozen Assets: A Fresh (Pythagorean) Perspective on Team Rankings

Posted by Ari in Columns,Frozen Assets on December 18, 2009 — 3 Comments

From Wikipedia:

Pythagorean expectation is a formula invented by Bill James to estimate how many games a baseball team “should” have won based on the number of runs they scored and allowed. Comparing a team’s actual and Pythagorean winning percentage can be used to evaluate how lucky (or alternatively how “clutch”) that team was (by examining the variation between the two winning percentages). The term is derived from the formula’s resemblance to the Pythagorean theorem.

The basic formula is:

\mathrm{Win\%} = \frac{\text{runs scored}^2}{\text{runs scored}^2 + \text{runs allowed}^2} = \frac{1}{1+(\text{runs allowed}/\text{runs scored})^2}.

where Win% is the winning percentage generated by the formula. The expected number of wins would be the expected winning percentage multiplied by the number of games played.

Applied to hockey, the formula looks like this:

Win% = (Goals For^2)/((Goals For^2) + (Goals Against^2))

 

EAST                  
                   
ATLANTIC GP W L OTL PTS GF GA EXP WIN % PROJ PTS
                   
New Jersey 32 23 8 1 47 93 69 0.645 111
Pittsburgh 35 24 10 1 49 114 90 0.616 107
Philadelphia 33 15 16 2 32 93 97 0.479 79
NY Rangers 34 15 16 3 33 94 100 0.469 78
NY Islanders 35 13 15 7 33 88 113 0.378 68
                   
NORTHEAST GP W L OTL PTS GF GA EXP WIN % PROJ PTS
                   
Buffalo 32 20 10 2 42 85 70 0.596 102
Boston 32 16 10 6 38 84 80 0.524 90
Ottawa 33 17 12 4 38 94 96 0.489 86
Montreal 36 15 18 3 33 90 104 0.428 72
Toronto 34 12 15 7 31 100 122 0.402 70
                   
SOUTHEAST GP W L OTL PTS GF GA EXP WIN % PROJ PTS
                   
Washington 34 21 7 6 48 124 95 0.630 108
Atlanta 33 18 12 3 39 108 99 0.543 92
Florida 35 14 14 7 35 99 115 0.426 75
Tampa Bay 34 11 14 9 31 81 104 0.378 67
Carolina 33 8 19 6 22 82 120 0.318 53
                   
WEST                  
                   
CENTRAL GP W L OTL PTS GF GA EXP WIN % PROJ PTS
                   
Chicago 32 21 8 3 45 95 67 0.668 112
Nashville 35 21 11 3 45 101 98 0.515 93
Detroit 34 18 11 5 41 95 89 0.533 92
St. Louis 32 14 13 5 33 78 88 0.440 77
Columbus 35 14 14 7 35 101 121 0.411 74
                   
NORTHWEST GP W L OTL PTS GF GA EXP WIN % PROJ PTS
                   
Calgary 34 20 10 4 44 98 82 0.588 100
Vancouver 34 19 15 0 38 106 88 0.592 95
Colorado 36 19 11 6 44 104 105 0.495 90
Minnesota 34 17 14 3 37 89 95 0.467 82
Edmonton 34 15 15 4 34 103 109 0.472 79
                   
PACIFIC GP W L OTL PTS GF GA EXP WIN % PROJ PTS
                   
San Jose 35 20 8 7 47 115 93 0.605 104
Phoenix 35 21 12 2 44 89 79 0.559 97
Los Angeles 37 22 12 3 47 111 108 0.514 93
Dallas 34 14 9 11 39 101 105 0.481 85
Anaheim 34 13 14 7 33 95 109 0.432 74

*Note actual points should be higher because the formula does not factor in overtime losses.

Any surprises?  Comments? There are certainly flaws with a) the theorem itself (that has been refined numerous times), and b) its application to hockey (doesn’t factor in the overtime loss).  But I am not a statistician and this was done for fun not to make any worthwhile predictions.  Please feel free to criticize/correct my work.  Also, the formula only applies to a team’s remaining games.

Dedicated to Michael Remis

  • http://ontheforecheck.com Dirk Hoag

    This is fun stuff to dig into, and I’d offer a couple suggestions if you want to take this a step further. One’s easy, the other involves a little more heavy lifting:

    1) The GF/GA numbers from the standings include a bogus goal given to teams that win the shootout. You’d want to remove those from your totals before running the numbers, and you could also justify removing Empty Netters. The reason being that you’re getting to GF/GA as a cause of teams winning or losing games. With Empty Netters, they’re more a result of winning a game rather than a cause.

    2) Head over to HockeyAnalytics.com and read up on a couple of the thick papers in there, to calculate a more accurate exponent than 2. The last time I did this, it was closer to 2.2.

    Either way, this makes for a good check on teams that might trend up or down in the standings as the season goes on.

  • http://www.illegalcurve.com Drew

    The best part is the dedication at the end.

  • http://ndgoon.blogspot.com goon

    I still see Boston being higher than a 6 seed. Just saying. Hum, math to explain hockey…