Friday, April 18, 2014

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):


RankTeamRate# games
1Oregon0.962449294323
2Middlebury0.923437414213
3Ohio State0.921838465821
4Texas A&M0.892855790321
5Central Florida0.888233409627
6Cal-Poly SLO0.88076109898
7Colorado State0.87662259915
8Harvard0.856187006920
9Rice0.855667686425
10California-Santa Barbara0.852908524226
11Johns Hopkins0.84508518162
12SUNY-Binghamton0.84166666672
13Connecticut0.84038704168
14Stonehill0.83670479644
15Truman State0.822218287714
16Boston College[B]0.81696428572
17Purdue0.81481710437
18Colorado0.813799298313
19Williamette0.80552546051
20Cornell0.80404972518
21Haverford0.80202417629
22Western Washington0.801815804619
23Indiana0.798029910518
24Washington0.794929485614
25Massachusets0.7906196246
26William & Mary0.78824701855
27Northeastern0.777334162425
28Carleton College-Eclipse0.776883157713
29Michigan[B]0.776774406110
30Bowdoin0.775082831910
31Wake Forest0.770277139117
32Pacific Lutheran0.769782805811
33Stanford0.768623677612
34Clemson0.761355269717
35Auburn0.757716608821
36Texas0.756339076224
37Harding0.75495876416
38Lehigh0.75126545712
39Brigham Young0.73281740287
40Michigan0.729245184527
41Georgetown0.719698134112
42Columbia0.715093427717
43Towson0.713598937210
44Virginia0.711421389121
45Bates0.71068505376
46North Texas0.70509199074
47Dartmouth0.703559055716
48Notre Dame0.702373941219
49Tufts0.687303029412
50UCLA0.687025211721
51Alabama0.68489645624
52Chicago0.678622135120
53Rochester0.67674685039
54Brown0.672562904310
55Mount Holyoke0.67067069284
56Elon0.670211912113
57Emory0.666155493426
58Georgia Tech0.660818638127
59Claremont0.660807221110
60Missouri State0.65874628424
61Marquette0.649446511810
62Grinnell0.635074297912
63Vermont0.63294984868
64Oregon State0.62870336256
65Florida[B]0.625001315214
66Virginia Tech0.623875750520
67Hofstra0.617530863720
68Illinois State0.61640456046
69Puget Sound0.615538234110
70Florida State0.609001667230
71Smith0.608969610411
72Utah State0.60513898336
73California-San Diego0.602729058329
74North Carolina0.600988317329
75Dayton0.60052544310
76Michigan State0.597262160710
77Texas State0.590788861522
78Vanderbilt0.587401179316
79Nebraska0.583514723815
80George Washington0.580495906620
81Pennsylvania0.5796760767
82Carleton College0.57780573667
83Ithaca0.57665560286
84Appalachian State0.572943524512
85Penn State0.571922636312
86Williams0.569614071412
87San Diego State0.568290218521
88Tufts[B]0.567671757816
89West Virginia0.567635523510
90Oberlin0.565752487410
91Salisbury0.56556516512
92New Mexico0.56461193345
93Illinois0.560504623215
94Richmond0.55676188313
95Carnegie Mellon0.55657359197
96Central Michigan0.54673563556
97California-Irvine0.54593514711
98Wooster0.54374622586
99Saint Louis0.53799378495
100Northern Michigan0.536086245411
101New Hampshire0.53557285827
102Colorado College0.535001953411
103Ohio State[B]0.53360824855
104Drake0.53232946239
105Southern Illinois0.52565252548
106Davidson0.525137712910
107Utah0.52349066882
108Maryland0.5223006620
109Skidmore0.52207054876
110Goucher0.52172345442
111North Park0.51748198987
112California-Davis0.517210524530
113Delaware0.515153561212
114LSU0.513507095815
115Princeton0.51325932313
116Arizona State0.507020838121
117Wisconsin-Whitewater0.50569641656
118MIT[B]0.49851190484
119DePaul0.49565006665
120Ohio0.48848339616
121Worcester Polytech0.483468074
122Arizona0.483144753220
123Texas Christian0.481272808914
124Georgetown[B]0.47656894387
125Kansas0.47644523619
126Whitman0.475728411410
127Valparaiso0.47361883247
128MIT0.472656460114
129St Olaf0.469113447712
130Humboldt State0.468606351213
131Iowa0.468147782715
132Mississippi State0.46708695766
133Texas-Arlington0.466214630918
134St Mary's (Maryland)0.46615718226
135Wisconsin0.46445850321
136UCLA[B]0.46330540246
137Wisconsin-Milwaukee0.461954836213
138Southern California0.456165587930
139Minnesota-Duluth0.451810329310
140Wellesley0.451360979311
141South Florida0.448518781820
142Duke0.44555006611
143Boston College0.44278277267
144Colorado[B]0.441165601712
145Florida0.43806900822
146Washington University0.437958652211
147Loyola-Chicago0.43683602327
148Bentley0.43546494427
149Macalester0.43362686887
150Eastern Michigan0.433601445210
151Knox College0.4323887554
152Tennessee0.43158282067
153Arkansas0.429323836616
154Montana0.42849507374
155Lewis0.42749819256
156Messiah0.42253798815
157American0.42092947377
158Wisconsin-Eau Claire0.419001825312
159SUNY-Cortland0.41810069137
160Missouri S&T0.41729541227
161Northwestern0.417087555916
162Tulane0.416491008718
163Boston University0.412540545810
164Georgia College0.409331017918
165Mary Washington0.409229161613
166South Carolina0.408714305210
167Pittsburgh0.40629781420
168Iowa State0.399661283216
169John Brown0.397241224913
170Yale0.39547797345
171NYU0.394917745215
172California-Santa Cruz0.391375336322
173North Carolina[B]0.389949751812
174Carnegie Mellon0.3883245265
175Georgia0.387074316825
176Liberty0.38609651017
177Rutgers0.38442532287
178Santa Clara0.369560593711
179Brandeis0.36580804633
180Olin0.36458333334
181Brigham Young-Idaho0.36362519396
182Virginia Commonwealth0.36353101816
183Virginia[B]0.35884557296
184Kansas State0.35665963763
185North Carolina-Wilmington0.352796148813
186Charleston0.352589651620
187Southern California[B]0.342129938312
188Northern Iowa0.3414827058
189James Madison0.340742734714
190Catholic0.340110333613
191Swarthmore0.335994744713
192Amherst0.33293810634
193Portland State0.33283073628
194Central Florida[B]0.33238775915
195Edinboro0.33032559787
196California0.32744033529
197Miami0.326166352617
198San Diego State[B]0.32296298576
199Central Connecticut State0.31838047378
200Grinnell[B]0.317144018510
201Xavier0.31702161117
202Wisconsin-Milwaukee0.312514728110
203Winona State0.30991134787
204Franklin & Marshall0.3089561213
205Wisconsin-Stevens Point0.30820338959
206Luther0.306692694410
207North Carolina-Asheville0.305532725914
208Philadelphia0.2982941427
209Minnesota0.286271710711
210George Mason0.28418451686
211Lewis & Clark0.282176669414
212Chico State0.27246239819
213West Chester0.26892838595
214California-San Diego[B]0.268213157412
215North Carolina State0.264839130514
216Portland State0.26331019297
217Florida State[B]0.255558157718
218Delaware[B]0.25527090719
219New Hampshire[B]0.25290752098
220Miami (Ohio)0.251480526310
221Bradley0.24814979059
222Oklahoma0.246336701615
223Cincinnati0.245189322710
224College of New Jersey0.244414119310
225Redlands0.23994123756
226SUNY-Albany0.2357790866
227Sonoma State0.23502183216
228Dartmouth[B]0.22907781635
229Ohio Wesleyan0.22836182235
230Hendrix0.218823564110
231SUNY-Geneseo0.218207293811
232Cornell[B]0.204216151516
233James Madison[B]0.195830096
234Texas[B]0.18874539217
235Kennesaw State0.1829720319
236California-Davis[B]0.17896095936
237Maryland-Baltimore County0.17429652147
238Wellesley[B]0.16827196957
239Rhode Island0.16659490549
240Syracuse0.1639269065
241Northern Arizona0.16210943036
242Olivet Nazarene0.16159390487
243Northeastern[B]0.158889466217
244Occidental0.157767584411
245Illinois[B]0.147090716112
246Georgia State0.14645447518
247Southern Indiana0.12521778123
248Texas-Dallas0.12513512814
249North Carolina-Greensboro0.12344736111
250Mississippi0.11443507233
251Brown[C]0.11386858764
252Minnesota[B]0.11347634983
253St Olaf[B]0.112263298211
254Vermont[B]0.10725133364
255Brown[B]0.09716779249
256Smith[B]0.095051471855
257Portland0.089158456233
258Oberlin [B]0.083555930086
259California[B]0.0800539717213
260SUNY-Buffalo0.076719429113
261George Washington[B]0.0711211195310
262Lipscomb0.064137270796
263Washington University[B]0.060404437892
263Missouri0.060404437892
265Rowan0.058359032692
266Pennsylvania[B]0.055283653819
267Stanford[B]0.054788394559
268Ball State0.044925141844
269Idaho0.041556437124
270Arizona[B]0.029768969815
271Wisconsin-La Crosse0.028740068545
272Notre Dame[B]0.0269650255120
273Haverford[B]0.018113527485
274Southern Mississippi0.016480062979
275Bucknell0.015701187742
276Wesleyan0.0087665014042
277Dallas0.0085857350893
278Bentley[B]0.003854168494

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