Applying the MDS Model to Ultimate Frisbee

I've applied the Matrix portion of the MDS Model to that of Ultimate Frisbee with the goal of obtaining a retrodictive model that improves on the limitations of the official ranking algorithm. (Why include sin and pi? Why not use e? Why not just use the Elo system?) 
Plus it gives me the opportunity to use the name The Ultimate Matrix.

The Ultimate Matrix does the following things:
• It takes into account all official matches between College division teams in the United States
• It omits games that were forfeits
• It does not take into account final score: only wins/losses (the official algorithm takes into account score)
• It emphasizes the strength of each team's opponent (much more so than the official algorithm)
• It fully updates the model after each game (and is thus Bayesian) instead of adding a rating differential to the teams' previous ratings

I plan on following up this post with an in-depth explanation of my original idea for a retrodictive model that I ended up scrapping.

Here are the resulting rankings ("# games" refers to the number included in the model):

Rank	Team	Rate	# games
1	Oregon	0.9624492943	23
2	Middlebury	0.9234374142	13
3	Ohio State	0.9218384658	21
4	Texas A&M	0.8928557903	21
5	Central Florida	0.8882334096	27
6	Cal-Poly SLO	0.8807610989	8
7	Colorado State	0.876622599	15
8	Harvard	0.8561870069	20
9	Rice	0.8556676864	25
10	California-Santa Barbara	0.8529085242	26
11	Johns Hopkins	0.8450851816	2
12	SUNY-Binghamton	0.8416666667	2
13	Connecticut	0.8403870416	8
14	Stonehill	0.8367047964	4
15	Truman State	0.8222182877	14
16	Boston College[B]	0.8169642857	2
17	Purdue	0.8148171043	7
18	Colorado	0.8137992983	13
19	Williamette	0.8055254605	1
20	Cornell	0.804049725	18
21	Haverford	0.8020241762	9
22	Western Washington	0.8018158046	19
23	Indiana	0.7980299105	18
24	Washington	0.7949294856	14
25	Massachusets	0.790619624	6
26	William & Mary	0.7882470185	5
27	Northeastern	0.7773341624	25
28	Carleton College-Eclipse	0.7768831577	13
29	Michigan[B]	0.7767744061	10
30	Bowdoin	0.7750828319	10
31	Wake Forest	0.7702771391	17
32	Pacific Lutheran	0.7697828058	11
33	Stanford	0.7686236776	12
34	Clemson	0.7613552697	17
35	Auburn	0.7577166088	21
36	Texas	0.7563390762	24
37	Harding	0.754958764	16
38	Lehigh	0.751265457	12
39	Brigham Young	0.7328174028	7
40	Michigan	0.7292451845	27
41	Georgetown	0.7196981341	12
42	Columbia	0.7150934277	17
43	Towson	0.7135989372	10
44	Virginia	0.7114213891	21
45	Bates	0.7106850537	6
46	North Texas	0.7050919907	4
47	Dartmouth	0.7035590557	16
48	Notre Dame	0.7023739412	19
49	Tufts	0.6873030294	12
50	UCLA	0.6870252117	21
51	Alabama	0.684896456	24
52	Chicago	0.6786221351	20
53	Rochester	0.6767468503	9
54	Brown	0.6725629043	10
55	Mount Holyoke	0.6706706928	4
56	Elon	0.6702119121	13
57	Emory	0.6661554934	26
58	Georgia Tech	0.6608186381	27
59	Claremont	0.6608072211	10
60	Missouri State	0.6587462842	4
61	Marquette	0.6494465118	10
62	Grinnell	0.6350742979	12
63	Vermont	0.6329498486	8
64	Oregon State	0.6287033625	6
65	Florida[B]	0.6250013152	14
66	Virginia Tech	0.6238757505	20
67	Hofstra	0.6175308637	20
68	Illinois State	0.6164045604	6
69	Puget Sound	0.6155382341	10
70	Florida State	0.6090016672	30
71	Smith	0.6089696104	11
72	Utah State	0.6051389833	6
73	California-San Diego	0.6027290583	29
74	North Carolina	0.6009883173	29
75	Dayton	0.600525443	10
76	Michigan State	0.5972621607	10
77	Texas State	0.5907888615	22
78	Vanderbilt	0.5874011793	16
79	Nebraska	0.5835147238	15
80	George Washington	0.5804959066	20
81	Pennsylvania	0.579676076	7
82	Carleton College	0.5778057366	7
83	Ithaca	0.5766556028	6
84	Appalachian State	0.5729435245	12
85	Penn State	0.5719226363	12
86	Williams	0.5696140714	12
87	San Diego State	0.5682902185	21
88	Tufts[B]	0.5676717578	16
89	West Virginia	0.5676355235	10
90	Oberlin	0.5657524874	10
91	Salisbury	0.565565165	12
92	New Mexico	0.5646119334	5
93	Illinois	0.5605046232	15
94	Richmond	0.556761883	13
95	Carnegie Mellon	0.5565735919	7
96	Central Michigan	0.5467356355	6
97	California-Irvine	0.545935147	11
98	Wooster	0.5437462258	6
99	Saint Louis	0.5379937849	5
100	Northern Michigan	0.5360862454	11
101	New Hampshire	0.5355728582	7
102	Colorado College	0.5350019534	11
103	Ohio State[B]	0.5336082485	5
104	Drake	0.5323294623	9
105	Southern Illinois	0.5256525254	8
106	Davidson	0.5251377129	10
107	Utah	0.5234906688	2
108	Maryland	0.52230066	20
109	Skidmore	0.5220705487	6
110	Goucher	0.5217234544	2
111	North Park	0.5174819898	7
112	California-Davis	0.5172105245	30
113	Delaware	0.5151535612	12
114	LSU	0.5135070958	15
115	Princeton	0.513259323	13
116	Arizona State	0.5070208381	21
117	Wisconsin-Whitewater	0.5056964165	6
118	MIT[B]	0.4985119048	4
119	DePaul	0.4956500666	5
120	Ohio	0.4884833961	6
121	Worcester Polytech	0.48346807	4
122	Arizona	0.4831447532	20
123	Texas Christian	0.4812728089	14
124	Georgetown[B]	0.4765689438	7
125	Kansas	0.476445236	19
126	Whitman	0.4757284114	10
127	Valparaiso	0.4736188324	7
128	MIT	0.4726564601	14
129	St Olaf	0.4691134477	12
130	Humboldt State	0.4686063512	13
131	Iowa	0.4681477827	15
132	Mississippi State	0.4670869576	6
133	Texas-Arlington	0.4662146309	18
134	St Mary's (Maryland)	0.4661571822	6
135	Wisconsin	0.464458503	21
136	UCLA[B]	0.4633054024	6
137	Wisconsin-Milwaukee	0.4619548362	13
138	Southern California	0.4561655879	30
139	Minnesota-Duluth	0.4518103293	10
140	Wellesley	0.4513609793	11
141	South Florida	0.4485187818	20
142	Duke	0.445550066	11
143	Boston College	0.4427827726	7
144	Colorado[B]	0.4411656017	12
145	Florida	0.438069008	22
146	Washington University	0.4379586522	11
147	Loyola-Chicago	0.4368360232	7
148	Bentley	0.4354649442	7
149	Macalester	0.4336268688	7
150	Eastern Michigan	0.4336014452	10
151	Knox College	0.432388755	4
152	Tennessee	0.4315828206	7
153	Arkansas	0.4293238366	16
154	Montana	0.4284950737	4
155	Lewis	0.4274981925	6
156	Messiah	0.4225379881	5
157	American	0.4209294737	7
158	Wisconsin-Eau Claire	0.4190018253	12
159	SUNY-Cortland	0.4181006913	7
160	Missouri S&T	0.4172954122	7
161	Northwestern	0.4170875559	16
162	Tulane	0.4164910087	18
163	Boston University	0.4125405458	10
164	Georgia College	0.4093310179	18
165	Mary Washington	0.4092291616	13
166	South Carolina	0.4087143052	10
167	Pittsburgh	0.406297814	20
168	Iowa State	0.3996612832	16
169	John Brown	0.3972412249	13
170	Yale	0.3954779734	5
171	NYU	0.3949177452	15
172	California-Santa Cruz	0.3913753363	22
173	North Carolina[B]	0.3899497518	12
174	Carnegie Mellon	0.388324526	5
175	Georgia	0.3870743168	25
176	Liberty	0.3860965101	7
177	Rutgers	0.3844253228	7
178	Santa Clara	0.3695605937	11
179	Brandeis	0.3658080463	3
180	Olin	0.3645833333	4
181	Brigham Young-Idaho	0.3636251939	6
182	Virginia Commonwealth	0.3635310181	6
183	Virginia[B]	0.3588455729	6
184	Kansas State	0.3566596376	3
185	North Carolina-Wilmington	0.3527961488	13
186	Charleston	0.3525896516	20
187	Southern California[B]	0.3421299383	12
188	Northern Iowa	0.341482705	8
189	James Madison	0.3407427347	14
190	Catholic	0.3401103336	13
191	Swarthmore	0.3359947447	13
192	Amherst	0.3329381063	4
193	Portland State	0.3328307362	8
194	Central Florida[B]	0.3323877591	5
195	Edinboro	0.3303255978	7
196	California	0.327440335	29
197	Miami	0.3261663526	17
198	San Diego State[B]	0.3229629857	6
199	Central Connecticut State	0.3183804737	8
200	Grinnell[B]	0.3171440185	10
201	Xavier	0.3170216111	7
202	Wisconsin-Milwaukee	0.3125147281	10
203	Winona State	0.3099113478	7
204	Franklin & Marshall	0.308956121	3
205	Wisconsin-Stevens Point	0.3082033895	9
206	Luther	0.3066926944	10
207	North Carolina-Asheville	0.3055327259	14
208	Philadelphia	0.298294142	7
209	Minnesota	0.2862717107	11
210	George Mason	0.2841845168	6
211	Lewis & Clark	0.2821766694	14
212	Chico State	0.2724623981	9
213	West Chester	0.2689283859	5
214	California-San Diego[B]	0.2682131574	12
215	North Carolina State	0.2648391305	14
216	Portland State	0.2633101929	7
217	Florida State[B]	0.2555581577	18
218	Delaware[B]	0.2552709071	9
219	New Hampshire[B]	0.2529075209	8
220	Miami (Ohio)	0.2514805263	10
221	Bradley	0.2481497905	9
222	Oklahoma	0.2463367016	15
223	Cincinnati	0.2451893227	10
224	College of New Jersey	0.2444141193	10
225	Redlands	0.2399412375	6
226	SUNY-Albany	0.235779086	6
227	Sonoma State	0.235021832	16
228	Dartmouth[B]	0.2290778163	5
229	Ohio Wesleyan	0.2283618223	5
230	Hendrix	0.2188235641	10
231	SUNY-Geneseo	0.2182072938	11
232	Cornell[B]	0.2042161515	16
233	James Madison[B]	0.19583009	6
234	Texas[B]	0.188745392	17
235	Kennesaw State	0.18297203	19
236	California-Davis[B]	0.1789609593	6
237	Maryland-Baltimore County	0.1742965214	7
238	Wellesley[B]	0.1682719695	7
239	Rhode Island	0.1665949054	9
240	Syracuse	0.163926906	5
241	Northern Arizona	0.1621094303	6
242	Olivet Nazarene	0.1615939048	7
243	Northeastern[B]	0.1588894662	17
244	Occidental	0.1577675844	11
245	Illinois[B]	0.1470907161	12
246	Georgia State	0.146454475	18
247	Southern Indiana	0.1252177812	3
248	Texas-Dallas	0.1251351281	4
249	North Carolina-Greensboro	0.123447361	11
250	Mississippi	0.1144350723	3
251	Brown[C]	0.1138685876	4
252	Minnesota[B]	0.1134763498	3
253	St Olaf[B]	0.1122632982	11
254	Vermont[B]	0.1072513336	4
255	Brown[B]	0.0971677924	9
256	Smith[B]	0.09505147185	5
257	Portland	0.08915845623	3
258	Oberlin [B]	0.08355593008	6
259	California[B]	0.08005397172	13
260	SUNY-Buffalo	0.07671942911	3
261	George Washington[B]	0.07112111953	10
262	Lipscomb	0.06413727079	6
263	Washington University[B]	0.06040443789	2
263	Missouri	0.06040443789	2
265	Rowan	0.05835903269	2
266	Pennsylvania[B]	0.05528365381	9
267	Stanford[B]	0.05478839455	9
268	Ball State	0.04492514184	4
269	Idaho	0.04155643712	4
270	Arizona[B]	0.02976896981	5
271	Wisconsin-La Crosse	0.02874006854	5
272	Notre Dame[B]	0.02696502551	20
273	Haverford[B]	0.01811352748	5
274	Southern Mississippi	0.01648006297	9
275	Bucknell	0.01570118774	2
276	Wesleyan	0.008766501404	2
277	Dallas	0.008585735089	3
278	Bentley[B]	0.00385416849	4