Power Ratings Explanation

Just thought I'd make a comment on how my algorithm differs from Laxpower.com's. Basically, I am solving a least squares problem in linear algebra for those who know what that is. Essentially, I use a similar strategy to Laxpower, in that I am attempting to make

P(i) - P(j) = D(i,j)

where P(i) and P(j) are the power ratings for teams i and j, and D(i,j) is the goal differential for those two teams for when they played each other head to head. I have not implemented a home field advantage, but it would be reasonably easy to do.

I implement this by setting up and solving the equation

M*A*P=D

where P is the list of power rankings for all the teams (which is unknown), and D is the list of goal differentials for all the games. A is simply a matrix which maps the correct power ranking with the correct goal differential. M is a masking matrix which simply eliminates the entries of A that represent games that haven't happened or never will. Then I use a linear equation solver to find P in a least squares sense (I use MATLAB's \ operator).

MCLA D1 Power Rankings

I delved into the world of power rankings today. Here are my MCLA D1 power rankings early in the season. I'll update periodically. Compare to laxpower.com:

1	'Indiana'	28.75
2	'Simon Fraser'	28.07059
3	'Georgia'	27.32143
4	'Georgia Tech'	24.32143
5	'Florida State'	24
6	'Minnesota - Duluth'	24
7	'Vanderbilt'	23.32143
8	'Mississippi'	23.32143
9	'Oregon'	22.97059
10	'SMU'	21.75
11	'Lindenwood'	21
12	'Colorado State'	21
13	'Chico State'	21
14	'Central Michigan'	21
15	'Florida'	21
16	'Cal Poly - SLO'	20.41176
17	'Arizona State'	20.35294
18	'California'	19.77059
19	'Chapman'	19.11765
20	'Baylor'	18.75
21	'Brigham Young'	18.52941
22	'Texas State'	18.25
23	'Western Washington'	18.07059
24	'Miami (FL)'	18
25	'Central Florida'	18
26	'Alabama'	17.89286
27	'Texas'	17.5
28	'UC Santa Barbara'	17.47059
29	'Minnesota St. Mankato'	17
30	'Arizona'	16.25
31	'St. John''s (MN)'	16
32	'Hendrix (D-III)'	16
33	'Rice'	14.5
34	'Reinhardt'	14.32143
35	'Middle Tennessee'	14.17857
36	'South Florida'	14
37	'Palm Beach Atlantic'	14
38	'Loyola Marymount'	13.64706
39	'Stanford'	13.17059
40	'Washington'	13.07059
41	'North Florida'	13
42	'Missouri'	13
43	'North Carolina State'	12
44	'Grove City'	12
45	'USC'	11.97059
46	'Oregon State'	11.87059
47	'Texas Tech'	11.75
48	'Washington - St. Louis'	11
49	'UC San Diego'	11
50	'Toledo'	11
51	'Texas A&M'	11
52	'Tennessee'	11
53	'St. Cloud State'	11
54	'South Carolina'	11
55	'San Diego State'	11
56	'Portland State'	11
57	'Pittsburgh'	11
58	'Oklahoma'	11
59	'Northern Colorado'	11
60	'Nevada'	11
61	'Nebraska'	11
62	'Louisiana State'	11
63	'Iowa'	11
64	'Gonzaga'	11
65	'Georgia Southern'	11
66	'Ferris State'	11
67	'Auburn'	11
68	'Memphis'	10.60714
69	'UCLA'	10.35294
70	'Claremont'	10.23529
71	'TCU'	10
72	'Eastern Michigan'	10
73	'Creighton'	10
74	'Central Washington'	10
75	'Santa Clara'	9.823529
76	'San Diego'	9.176471
77	'Southern Maine (D-III)'	9.117647
78	'UC Davis'	9
79	'Grand Canyon'	8.294118
80	'UC Santa Cruz'	8
81	'Clemson'	7.666667
82	'UNLV'	7.294118
83	'Southern Oregon'	7
84	'Southwestern (D-III)'	6.25
85	'Northern Arizona'	6.25
86	'Cal State Fullerton'	5.352941
87	'Kentucky'	4.333333
88	'Carleton'	4
89	'Willamette'	1
90	'Stephen F. Austin'	1
91	'Pacific Lutheran'	1
92	'Marymount Coll. (CA)'	1
93	'John Carroll'	1
94	'Cornell College'	1
95	'C. of Charleston'	1
96	'Biola'	0.235294
97	'Centenary (LA)'	0