Bracket Math for the MDS Model

I finally finished my own MDS Model for college basketball, and got it done just in time to predict the bracket. Since it wasn't in action for any of the regular season, I have no baseline to measure its performance against. Here goes nothing!


Here's the predicted bracket (based on my Pyth rating):

Not many major differences, and we end up with the same Final Four. All the ratings love Louisville though. Here are the full round-by-round probabilities:

Seed	Team	1st Round	2nd Round	Sweet 16	Elite 8	Final Four	Championship	Champion
1	Florida	100.00%	98.49%	75.34%	51.40%	31.58%	20.52%	9.89%
16*	Albany	56.41%	0.95%	0.06%	0.00%	0.00%	0.00%	0.00%
16*	Mount St. Mary's	43.59%	0.57%	0.03%	0.00%	0.00%	0.00%	0.00%
8	Colorado	100.00%	28.06%	3.96%	1.01%	0.21%	0.05%	0.01%
9	Pittsburgh	100.00%	71.94%	20.61%	9.41%	3.66%	1.54%	0.42%
5	VCU	100.00%	86.12%	45.85%	17.84%	7.87%	3.73%	1.19%
12	Stephen F. Austin	100.00%	13.88%	2.40%	0.25%	0.03%	0.00%	0.00%
4	UCLA	100.00%	79.44%	45.91%	19.11%	8.97%	4.51%	1.55%
13	Tulsa	100.00%	20.56%	5.84%	0.98%	0.19%	0.04%	0.01%
6	Ohio St.	100.00%	76.35%	54.16%	27.53%	13.47%	7.42%	2.86%
11	Dayton	100.00%	23.65%	10.58%	2.74%	0.65%	0.18%	0.03%
3	Syracuse	100.00%	84.38%	33.42%	11.64%	3.81%	1.45%	0.35%
14	Western Michigan	100.00%	15.62%	1.83%	0.18%	0.02%	0.00%	0.00%
7	New Mexico	100.00%	54.64%	14.18%	5.39%	1.54%	0.52%	0.11%
10	Stanford	100.00%	45.36%	10.35%	3.51%	0.88%	0.26%	0.05%
2	Kansas	100.00%	96.10%	74.98%	48.96%	27.12%	16.67%	7.45%
15	Eastern Kentucky	100.00%	3.90%	0.49%	0.04%	0.00%	0.00%	0.00%
1	Virginia	100.00%	97.92%	76.23%	46.15%	27.77%	13.68%	5.45%
16	Coastal Carolina	100.00%	2.08%	0.15%	0.01%	0.00%	0.00%	0.00%
8	Memphis	100.00%	55.72%	14.12%	4.72%	1.56%	0.38%	0.07%
9	George Washington	100.00%	44.28%	9.50%	2.73%	0.77%	0.16%	0.02%
5	Cincinnati	100.00%	59.78%	24.24%	9.72%	4.18%	1.37%	0.35%
12	Harvard	100.00%	40.22%	12.95%	4.10%	1.40%	0.35%	0.07%
4	Michigan St.	100.00%	92.54%	61.75%	32.49%	18.23%	8.23%	2.97%
13	Delaware	100.00%	7.46%	1.06%	0.10%	0.01%	0.00%	0.00%
6	North Carolina	100.00%	70.47%	34.24%	13.84%	5.31%	1.70%	0.42%
11	Providence	100.00%	29.53%	8.84%	2.02%	0.43%	0.07%	0.01%
3	Iowa St.	100.00%	89.84%	55.26%	25.35%	11.10%	4.12%	1.19%
14	North Carolina Central	100.00%	10.16%	1.66%	0.16%	0.01%	0.00%	0.00%
7	Connecticut	100.00%	64.95%	22.35%	10.69%	3.96%	1.22%	0.29%
10	Saint Joseph's	100.00%	35.05%	7.99%	2.68%	0.66%	0.13%	0.02%
2	Villanova	100.00%	96.73%	69.39%	45.24%	24.62%	11.69%	4.46%
15	Milwaukee	100.00%	3.27%	0.27%	0.02%	0.00%	0.00%	0.00%
1	Arizona	100.00%	98.46%	77.46%	67.36%	51.39%	33.19%	23.63%
16	Weber St.	100.00%	1.54%	0.09%	0.01%	0.00%	0.00%	0.00%
8	Gonzaga	100.00%	42.00%	8.15%	4.93%	2.11%	0.66%	0.24%
9	Oklahoma St.	100.00%	58.00%	14.30%	9.68%	4.89%	1.86%	0.82%
5	Oklahoma	100.00%	69.94%	39.35%	7.86%	2.87%	0.75%	0.23%
12	North Dakota St.	100.00%	30.06%	11.04%	1.12%	0.23%	0.03%	0.01%
4	San Diego St.	100.00%	76.51%	42.81%	8.54%	3.12%	0.81%	0.25%
13	New Mexico St.	100.00%	23.49%	6.80%	0.51%	0.08%	0.01%	0.00%
6	Baylor	100.00%	68.17%	24.12%	9.64%	2.43%	0.64%	0.20%
11	Nebraska	100.00%	31.83%	6.90%	1.68%	0.25%	0.04%	0.01%
3	Creighton	100.00%	92.68%	67.62%	39.55%	15.75%	6.73%	3.31%
14	Louisiana Lafayette	100.00%	7.32%	1.36%	0.15%	0.01%	0.00%	0.00%
7	Oregon	100.00%	59.36%	23.62%	9.90%	2.70%	0.78%	0.26%
10	BYU	100.00%	40.64%	12.95%	4.36%	0.92%	0.20%	0.05%
2	Wisconsin	100.00%	92.26%	62.27%	34.59%	13.24%	5.43%	2.57%
15	American	100.00%	7.74%	1.17%	0.13%	0.01%	0.00%	0.00%
1	Wichita St.	100.00%	96.64%	55.11%	19.87%	10.89%	4.42%	2.12%
16*	Cal Poly	77.11%	3.08%	0.18%	0.01%	0.00%	0.00%	0.00%
16*	Texas Southern	22.89%	0.28%	0.01%	0.00%	0.00%	0.00%	0.00%
8	Kentucky	100.00%	73.31%	37.19%	13.16%	7.11%	2.83%	1.33%
9	Kansas St.	100.00%	26.69%	7.52%	1.41%	0.43%	0.09%	0.02%
5	Saint Louis	100.00%	67.32%	12.29%	4.09%	1.47%	0.37%	0.11%
12*	North Carolina St.	37.93%	9.92%	0.83%	0.13%	0.02%	0.00%	0.00%
12*	Xavier	62.07%	22.77%	2.78%	0.63%	0.16%	0.03%	0.01%
4	Louisville	100.00%	94.72%	82.58%	60.51%	45.33%	27.80%	19.32%
13	Manhattan	100.00%	5.28%	1.52%	0.21%	0.03%	0.00%	0.00%
6	Massachusetts	100.00%	33.02%	9.13%	3.56%	0.68%	0.14%	0.04%
11*	Iowa	51.23%	34.59%	14.70%	8.26%	2.62%	0.89%	0.36%
11*	Tennessee	48.77%	32.39%	13.41%	7.38%	2.27%	0.75%	0.29%
3	Duke	100.00%	89.36%	60.54%	40.91%	17.43%	7.80%	4.09%
14	Mercer	100.00%	10.64%	2.22%	0.48%	0.04%	0.00%	0.00%
7	Texas	100.00%	46.04%	13.21%	3.18%	0.49%	0.08%	0.02%
10	Arizona St.	100.00%	53.96%	17.17%	4.62%	0.81%	0.16%	0.04%
2	Michigan	100.00%	96.43%	69.31%	31.60%	10.19%	3.51%	1.44%
15	Wofford	100.00%	3.57%	0.31%	0.01%	0.00%	0.00%	0.00%

And here are the final ratings as well, for all 351 teams:

Rank	Team	Rate
1	Arizona	0.976
2	Louisville	0.974
3	Florida	0.960
4	Kansas	0.953
5	Duke	0.946
6	Virginia	0.943
7	Ohio St.	0.940
8	Creighton	0.939
9	Villanova	0.938
10	Wichita St.	0.936
11	Wisconsin	0.934
12	Kentucky	0.933
13	Michigan St.	0.933
14	UCLA	0.927
15	Oklahoma St.	0.925
16	VCU	0.919
17	Michigan	0.916
18	Iowa	0.914
19	Tennessee	0.910
20	Iowa St.	0.907
21	Pittsburgh	0.901
22	Gonzaga	0.900
23	Cincinnati	0.889
24	Oregon	0.888
25	North Carolina	0.886
26	Syracuse	0.884
27	Connecticut	0.880
28	Baylor	0.875
29	Oklahoma	0.872
30	San Diego St.	0.872
31	Saint Louis	0.867
32	New Mexico	0.862
33	Arkansas	0.846
34	BYU	0.845
35	Harvard	0.844
36	Stanford	0.838
37	Memphis	0.838
38	Kansas St.	0.836
39	Massachusetts	0.836
40	Minnesota	0.831
41	St. John's	0.831
42	Dayton	0.828
43	Louisiana Tech	0.826
44	Southern Methodist	0.825
45	Georgetown	0.820
46	Arizona St.	0.820
47	Florida State	0.805
48	George Washington	0.804
49	Saint Joseph's	0.798
50	Texas	0.796
51	Maryland	0.794
52	Saint Mary's	0.791
53	Xavier	0.791
54	Clemson	0.789
55	Indiana	0.789
56	Utah	0.786
57	West Virginia	0.782
58	Colorado	0.779
59	LSU	0.774
60	Tulsa	0.768
61	Nebraska	0.766
62	Providence	0.764
63	Boise State	0.760
64	Alabama	0.754
65	Missouri	0.754
66	California	0.750
67	Illinois	0.749
68	North Dakota St.	0.746
69	Southern Miss	0.741
70	Green Bay	0.725
71	Georgia	0.721
72	Marquette	0.712
73	St. Bonaventure	0.710
74	UNLV	0.702
75	North Carolina St.	0.698
76	Richmond	0.696
77	Penn State	0.695
78	La Salle	0.695
79	Ole Miss	0.686
80	Northern Iowa	0.682
81	San Francisco	0.680
82	Iona	0.680
83	Middle Tennessee	0.677
84	New Mexico St.	0.677
85	Mercer	0.676
86	Miami (FL)	0.676
87	Notre Dame	0.676
88	Manhattan	0.673
89	Georgia State	0.671
90	Texas Tech	0.670
91	Seton Hall	0.665
92	UTEP	0.662
93	Ohio	0.658
94	Vermont	0.656
95	Stephen F. Austin	0.646
96	Oregon State	0.641
97	Buffalo	0.638
98	Purdue	0.634
99	Cleveland State	0.634
100	Washington	0.618
101	Eastern Michigan	0.617
102	Wyoming	0.617
103	Columbia	0.616
104	George Mason	0.613
105	Toledo	0.610
106	Vanderbilt	0.606
107	Butler	0.601
108	Texas A&M	0.595
109	Belmont	0.593
110	South Carolina	0.591
111	Western Michigan	0.585
112	Portland	0.583
113	UC Irvine	0.581
114	UC Santa Barbara	0.581
115	Boston University	0.576
116	Princeton	0.565
117	Temple	0.559
118	Rhode Island	0.558
119	Indiana State	0.558
120	Utah State	0.551
121	Fresno State	0.549
122	Louisiana Lafayette	0.547
123	Denver	0.545
124	American	0.544
125	Wake Forest	0.540
126	Akron	0.537
127	Auburn	0.537
128	Colorado State	0.535
129	UAB	0.528
130	Delaware	0.527
131	North Carolina Central	0.525
132	Hawaii	0.525
133	Nevada	0.523
134	Canisius	0.516
135	Drexel	0.511
136	San Diego	0.502
137	Illinois State	0.500
138	USC	0.492
139	Pacific	0.490
140	Missouri State	0.485
141	Davidson	0.483
142	Boston College	0.481
143	Northwestern	0.467
144	Georgia Tech	0.459
145	Quinnipiac	0.454
146	Eastern Kentucky	0.453
147	Southern Illinois	0.444
148	Towson	0.443
149	Bucknell	0.441
150	DePaul	0.440
151	Northeastern	0.432
152	Pepperdine	0.431
153	Virginia Tech	0.428
154	Bowling Green	0.427
155	Charlotte	0.425
156	Santa Clara	0.422
157	South Dakota State	0.416
158	Oakland	0.408
159	Rutgers	0.407
160	Loyola Marymount	0.407
161	William & Mary	0.402
162	Wright State	0.402
163	Holy Cross	0.401
164	Long Beach State	0.399
165	Drake	0.398
166	Valparaiso	0.391
167	Duquesne	0.386
168	Weber St.	0.385
169	Houston	0.383
170	Yale	0.382
171	Florida Gulf Coast	0.381
172	Murray State	0.381
173	Morehead State	0.380
174	USC Upstate	0.379
175	Kent State	0.378
176	Cal Poly	0.376
177	Washington State	0.372
178	Old Dominion	0.372
179	Siena	0.370
180	Colgate	0.370
181	Charleston	0.368
182	UCF	0.367
183	Oral Roberts	0.365
184	Western Kentucky	0.364
185	Brown	0.354
186	IPFW	0.349
187	Milwaukee	0.340
188	Elon	0.339
189	Detroit	0.333
190	Youngstown State	0.332
191	Southern University	0.331
192	East Carolina	0.330
193	Miami (OH)	0.327
194	Fordham	0.322
195	Arkansas State	0.321
196	North Texas	0.319
197	Evansville	0.318
198	Stony Brook	0.316
199	Northwestern State	0.316
200	Rider	0.314
201	Nebraska-Omaha	0.313
202	Bryant University	0.306
203	Montana	0.303
204	Niagara	0.297
205	Bradley	0.297
206	Northern Illinois	0.294
207	Marist	0.294
208	Marshall	0.293
209	Charleston Southern	0.292
210	Mississippi State	0.289
211	Albany	0.288
212	Robert Morris	0.288
213	Wofford	0.287
214	Florida Atlantic	0.282
215	Texas-Arlington	0.281
216	Loyola (IL)	0.281
217	East Tennessee State	0.276
218	Sam Houston State	0.272
219	Arkansas-Little Rock	0.272
220	Dartmouth	0.270
221	Lafayette	0.265
222	TCU	0.264
223	South Florida	0.264
224	St. Francis (NY)	0.263
225	Coastal Carolina	0.259
226	Hofstra	0.259
227	Seattle	0.257
228	North Dakota	0.257
229	Northern Colorado	0.255
230	UNC Asheville	0.254
231	Eastern Washington	0.253
232	Louisiana-Monroe	0.253
233	Cal State Bakersfield	0.252
234	South Alabama	0.251
235	Wagner	0.250
236	Idaho State	0.249
237	Troy	0.248
238	Air Force	0.245
239	Utah Valley	0.244
240	Fairfield	0.243
241	Mount St. Mary's	0.238
242	Lehigh	0.235
243	Idaho	0.235
244	Winthrop	0.234
245	St. Peter's	0.232
246	Hampton	0.231
247	Morgan State	0.230
248	James Madison	0.229
249	Tennessee State	0.225
250	Army	0.224
251	South Dakota	0.220
252	Illinois-Chicago	0.217
253	Florida International	0.216
254	Grand Canyon	0.209
255	Texas A&M-CC	0.207
256	Monmouth	0.202
257	North Florida	0.202
258	Ball State	0.200
259	Western Illinois	0.198
260	High Point	0.196
261	Cal State Fullerton	0.195
262	Western Carolina	0.195
263	Texas State	0.194
264	Cal State Northridge	0.193
265	Northern Arizona	0.189
266	Central Michigan	0.186
267	Pennsylvania	0.186
268	Tennessee Tech	0.184
269	UMKC	0.182
270	Lipscomb	0.176
271	Liberty	0.174
272	Virginia Military	0.172
273	Portland State	0.167
274	North Carolina-Wilmington	0.165
275	Norfolk State	0.161
276	Gardner-Webb	0.157
277	Southeast Missouri State	0.156
278	Hartford	0.155
279	Sacramento State	0.155
280	Tulane	0.152
281	Texas Southern	0.152
282	San Jose State	0.149
283	Incarnate Word	0.144
284	Northern Kentucky	0.138
285	Rice	0.138
286	UTSA	0.136
287	Coppin State	0.135
288	Texas-Pan American	0.133
289	Chicago State	0.129
290	Austin Peay	0.126
291	Fairleigh Dickinson	0.125
292	UC Riverside	0.123
293	Jackson State	0.120
294	Jacksonville	0.118
295	Loyola (MD)	0.114
296	IUPUI	0.112
297	SIU-Edwardsville	0.112
298	Sacred Heart	0.110
299	Montana State	0.105
300	Chattanooga	0.102
301	LIU Brooklyn	0.101
302	Radford	0.098
303	Jacksonville State	0.097
304	Eastern Illinois	0.094
305	Central Connecticut State	0.094
306	Cornell	0.092
307	Savannah State	0.092
308	McNeese State	0.088
309	Georgia Southern	0.085
310	Alabama A&M	0.083
311	Alabama State	0.083
312	Kennesaw State	0.083
313	UC Davis	0.079
314	UNC Greensboro	0.077
315	Tennessee-Martin	0.077
316	Southeastern Louisiana	0.077
317	Navy	0.077
318	St. Francis U	0.075
319	Appalachian State	0.074
320	Lamar	0.073
321	Samford	0.072
322	Florida A&M	0.072
323	Campbell	0.068
324	Maine	0.067
325	New Hampshire	0.067
326	N.J.I.T.	0.067
327	Prairie View A&M	0.066
328	New Orleans	0.065
329	Arkansas-Pine Bluff	0.064
330	UMBC	0.064
331	Nicholls State	0.064
332	Massachusetts Lowell	0.063
333	Delaware State	0.061
334	Alcorn State	0.059
335	Stetson	0.056
336	Central Arkansas	0.056
337	Citadel	0.047
338	Houston Baptist	0.046
339	Binghamton	0.045
340	North Carolina A&T	0.040
341	Howard	0.039
342	Maryland-Eastern Shore	0.037
343	South Carolina State	0.035
344	Bethune-Cookman	0.035
345	Southern Utah	0.033
346	Longwood	0.032
347	Abilene Christian	0.029
348	Mississippi Valley State	0.027
349	Furman	0.026
350	Presbyterian	0.024
351	Grambling State	0.019