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goblue78
03-21-2016, 09:07 PM
Shirtless Guy has a thread in which he wants to augment the Pairwise somehow. It got me to resurrect my old idea to rank teams via Poisson Regression. (Since Poisson is French for fish I call them the Fish rankings.) These are in one sense more accurate than other college rankings and in another sense less accurate. They are more accurate in that they use more information: goals scored and given up, which is obviously a lot more information than who won a game. On the other hand, they don't know anything about who won a game, so if knowing how to win is a skill, these rankings ignore them. In fact, I don't even use overtime goals at all.
For the mathematically inclined, the Poisson model assumes goals by a team in regulation time are Poisson-distributed with a mean that is the exponential sum of an offense rating for a team and a defense rating for their opponents, plus adjustments for home and neutral ice. Once you have the scores of all the games in a statistical package, it is a single line in the statistical package Stata to estimate the model. Herewith, the Fish ratings for 2015:16:
offense -defense total
St. Cloud State 0.5877 0.2376 0.8253
North Dakota 0.3730 0.4398 0.8127
Providence 0.3316 0.4383 0.7699
Boston College 0.5289 0.2391 0.7681
Quinnipiac 0.4398 0.2362 0.6760
Minnesota Duluth 0.2588 0.4014 0.6602
Michigan 0.6581 -0.0348 0.6232
UMass Lowell 0.1779 0.4350 0.6129
Denver 0.3033 0.3059 0.6092
Harvard 0.4258 0.1519 0.5777
Notre Dame 0.3264 0.2445 0.5709
Northeastern 0.3577 0.1607 0.5184
Yale 0.0637 0.4327 0.4964
Boston University 0.3599 0.1344 0.4943
Minnesota 0.3194 0.1309 0.4503
Michigan Tech 0.2387 0.1378 0.3765
St. Lawrence 0.1698 0.1736 0.3434
Minnesota State 0.0402 0.2183 0.2585
Ohio State 0.3698 -0.1188 0.2510
Omaha 0.2668 -0.0285 0.2383
Bowling Green 0.1202 0.1151 0.2353
Miami 0.0940 0.1301 0.2241
Penn State 0.3445 -0.1345 0.2101
Robert Morris 0.3603 -0.1637 0.1965
Cornell -0.0547 0.1523 0.0976
New Hampshire 0.2640 -0.1841 0.0799
Union 0.0561 0.0225 0.0786
Ferris State 0.0827 -0.0094 0.0732
Vermont -0.0576 0.1138 0.0562
Clarkson 0.0298 0.0141 0.0440
Michigan State 0.0340 -0.0023 0.0316
Dartmouth 0.0910 -0.0740 0.0170
Rensselaer -0.0343 0.0493 0.0149
Air Force 0.0000 0.0000 0.0000
Bemidji State -0.0086 -0.0253 -0.0339
Merrimack -0.0011 -0.0372 -0.0384
Wisconsin 0.0891 -0.1653 -0.0762
Northern Michigan -0.0840 -0.0149 -0.0989
Holy Cross 0.0120 -0.1353 -0.1233
Colgate 0.1024 -0.2783 -0.1759
Connecticut -0.0273 -0.1599 -0.1872
Western Michigan 0.0630 -0.2519 -0.1889
Brown 0.0812 -0.2766 -0.1954
RIT 0.0261 -0.2453 -0.2193
Maine -0.1293 -0.1483 -0.2775
Army West Point -0.3021 0.0114 -0.2907
Mercyhurst 0.0233 -0.3268 -0.3035
Colorado College -0.0140 -0.2923 -0.3063
Massachusetts 0.0376 -0.3457 -0.3081
Alaska -0.0571 -0.2588 -0.3159
Bentley -0.0344 -0.2850 -0.3194
Alabama Huntsville -0.1061 -0.2369 -0.3430
Princeton -0.1981 -0.1791 -0.3771
Alaska Anchorage -0.0203 -0.3684 -0.3887
Sacred Heart -0.1942 -0.2454 -0.4396
Lake Superior State -0.3670 -0.0779 -0.4449
Canisius -0.2360 -0.3121 -0.5481
Niagara -0.4178 -0.3559 -0.7737
American International -0.3702 -0.6043 -0.9745
Arizona State -0.9316 -0.4919 -1.4236

By coming first in alphabetical order, Air Force gets ratings of 0 and 0 and everyone else is defined relative to them. The most interesting thing off the top of the bat is Quinnipiac falling to 5th in these rankings. That can be taken as a "they know how to win" indicator in the same way that divergence between Pythagorean expectation and wins in baseball (for Bill James fans) is a recognition of intangibles, or luck.

Enjoy.

mookie1995
03-21-2016, 09:11 PM
maine is too high. this is flawed....

LordofBrewtown
03-21-2016, 09:13 PM
Interesting Stuff. Thanks for posting. Though the one thing I always like to see accounted for that Pairwise, KRACH, and this don't account for is home/road, since some teams have to travel more.

Patman
03-21-2016, 09:14 PM
Robin Locke beat you to it by at least 17 years... CHODR.

http://it.stlawu.edu/~chodr/

I've run this model in the past, I usually adjust for overtime.

goblue78
03-21-2016, 09:17 PM
Robin Locke beat you to it by at least 17 years... CHODR.

http://it.stlawu.edu/~chodr/

I've run this model in the past, I usually adjust for overtime.

I didn't say it was original, but you're right, and I have a number of variants that adjust for overtime. This is the simple model that just takes regulation time.

And I had forgotten Robin's website. Thanks for posting that Patman...

joecct
03-22-2016, 09:51 AM
I prefer the Poisson mort tables.