# 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:

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

### 3 responses to “Frozen Assets: A Fresh (Pythagorean) Perspective on Team Rankings”

1. Dirk Hoag says:

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.

2. Drew says:

The best part is the dedication at the end.

3. goon says:

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