Probabilistic Bid Allocation

2018-19 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 2.429 0.018 0.002 3.078 2.866 3.031 2.013 1.921 0.078 4.564
Autos (all @ 1) 1.429 -0.982 -0.998 2.078 1.866 2.031 1.013 0.921 -0.922 3.564
Southwest (@ 2) 1.429 -0.982 -0.998 2.078 1.866 2.031 1.013 0.921 -0.922 2.564
Southwest (@ 3) 1.429 -0.982 -0.998 2.078 1.866 2.031 1.013 0.921 -0.922 1.564
New England (@ 2) 1.429 -0.982 -0.998 1.078 1.866 2.031 1.013 0.921 -0.922 1.564
Northwest (@ 2) 1.429 -0.982 -0.998 1.078 1.866 1.031 1.013 0.921 -0.922 1.564
North Central (@ 2) 1.429 -0.982 -0.998 1.078 0.866 1.031 1.013 0.921 -0.922 1.564
Southwest (@ 4) 1.429 -0.982 -0.998 1.078 0.866 1.031 1.013 0.921 -0.922 0.564
Atlantic Coast (@ 2) 0.429 -0.982 -0.998 1.078 0.866 1.031 1.013 0.921 -0.922 0.564
New England (@ 3) 0.429 -0.982 -0.998 0.078 0.866 1.031 1.013 0.921 -0.922 0.564
Northwest (@ 3) 0.429 -0.982 -0.998 0.078 0.866 0.031 1.013 0.921 -0.922 0.564
Ohio Valley (@ 2) 0.429 -0.982 -0.998 0.078 0.866 0.031 0.013 0.921 -0.922 0.564
Total 2 1 1 3 2 3 2 1 1 4

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 North Carolina 1 2530.07 72.35 1/5 18-2
2 California-San Diego 1 2419.06 54.58 1/6 23-3
3 Ohio State 1 2373 66.61 1/10 23-3
4 California-Santa Barbara 1 2280.49 66.86 2/14 16-4
5 Carleton College-Syzygy 1 2265.5 63.82 1/15 15-5
6 Western Washington 1 2199.67 77.05 2/18 8-6
7 Dartmouth 1 2158.85 53.73 4/19 14-5
8 Texas 1 2144 63.11 3/20 12-7
9 British Columbia 0.999 2231.77 92.96 1/22 8-5
10 Pittsburgh 0.998 2083.27 45.63 6/22 14-6
11 Northeastern 0.992 2107.95 68.95 4/22 7-5
12 Minnesota 0.976 2069.71 61.06 5/23 7-5
13 Stanford 0.975 2055.63 55.38 5/24 13-15
14 Colorado 0.92 2046.85 73.88 5/28 12-8
15 Wisconsin 0.89 2021.96 67.14 6/28 8-5
16 Oregon 0.851 2017.73 74.74 6/30 9-11
17 UCLA 0.69 1965.86 48.63 8/28 14-13
18 Vermont 0.626 2013.2 209.39 1/95 7-4
19 South Carolina 0.578 1971.42 142.27 3/50 16-0
20 North Carolina-Wilmington 0.556 1960.18 65.03 6/31 17-9
21 Cal Poly-SLO 0.519 1943.59 89 6/42 17-8
22 Tufts 0.46 1934.61 61.89 9/38 10-9
23 California 0.38 1917.92 74.93 9/39 22-10
24 Clemson 0.232 1872.28 100.75 7/55 23-4
25 Washington 0.156 1872.59 66.11 11/37 8-11
26 Georgia 0.073 1848.3 62.54 11/38 12-8
27 Delaware 0.063 1814.9 85.05 12/46 14-2
28 Utah 0.025 1758.87 87.13 12/58 11-7
29 Northwestern 0.018 1767.62 85.41 14/52 5-6
30 West Chester 0.015 1714.02 110.46 10/62 15-3
31 Vanderbilt 0.005 1673.28 93.63 18/67 12-3
32 Ottawa 0.002 1440.6 194.57 20/176 5-3
33 Colorado College 0.001 1703.78 68.53 20/53 7-6
34 North Carolina State 0 1773.66 50.47 21/39 13-8
35 Brigham Young 0 1710.48 47.07 23/48 6-14
36 Bates 0 1706.49 120.01 14/65 17-0
37 Truman State 0 1684.45 135.01 8/88 11-0
38 Washington University 0 1670.56 60.37 23/53 10-6
39 Florida 0 1611.11 66.52 27/65 11-16
40 California-Davis 0 1593.28 86.35 24/70 13-9
41 Michigan 0 1569.43 69.25 25/71 11-12
42 Harvard 0 1567.65 64.91 30/69 13-7
43 Chicago 0 1564.5 102.08 23/87 2-9
44 Georgia Tech 0 1555.59 54.7 31/67 8-14
45 Brown 0 1554.41 81.59 27/74 12-4
46 Virginia 0 1545.7 56.48 33/67 15-10
47 Middlebury 0 1538.47 92.92 25/82 8-3
48 Williams 0 1526.41 75.85 29/78 10-2
49 California-Santa Cruz 0 1520.82 86.26 30/83 4-5
50 Emory 0 1518.42 97.16 28/87 13-4
51 Whitman 0 1508.9 94.44 26/93 1-10
52 Florida State 0 1508.35 50.3 34/70 15-12
53 Columbia 0 1503.27 74.58 30/83 14-6
54 Puget Sound 0 1492.13 111.77 26/108 13-4
55 Portland 0 1487.97 93.7 30/87 11-6
56 Pennsylvania 0 1487.36 64.62 33/74 9-8
57 Cornell 0 1460.62 63.51 38/79 7-10
58 Penn State 0 1451.04 57.95 39/78 9-9
59 Duke 0 1445.96 84.99 33/94 12-8
60 James Madison 0 1435.16 72.36 34/89 15-8
61 Oberlin 0 1417.04 122.4 18/120 7-3
62 New Hampshire 0 1414.87 121.92 28/123 17-3
63 Carleton College-Eclipse 0 1405.19 114.12 20/110 6-3
64 Massachusetts 0 1396.29 67.07 42/93 7-7
65 Yale 0 1383.49 85.35 32/100 8-5
66 Lewis & Clark 0 1330.23 90.46 38/110 10-6
67 Notre Dame 0 1328.85 72.52 41/103 11-10
68 Maryland 0 1328.26 89.59 37/115 10-7
69 William & Mary 0 1326.62 94.61 36/113 16-4
70 Texas-Dallas 0 1326.4 54.52 50/94 11-6
71 Northern Arizona 0 1324.82 104.5 36/121 14-4
72 Denver 0 1321.88 95.96 40/119 14-3
73 Purdue 0 1288.08 118.21 38/146 6-4
74 Rensselaer Polytech 0 1285.87 110.91 40/138 8-5
75 Cal State-Long Beach 0 1281.81 102.61 38/136 12-5
76 Winona State 0 1278.15 76.18 45/112 8-2
77 Ball State 0 1273.29 89.22 44/120 4-2
78 St Olaf 0 1271.04 132.88 33/142 7-4
79 Ohio 0 1268.3 99.83 35/139 12-5
80 Georgetown 0 1266.46 67.22 57/111 9-9
81 Colby 0 1257.61 122.86 38/157 6-5
82 Victoria 0 1245.36 128.54 36/145 6-7
83 Dayton 0 1243.31 120.71 34/147 11-9
84 San Diego State 0 1242.2 114.2 35/140 10-7
85 Auburn 0 1235.26 74.07 53/116 10-6
86 John Brown 0 1226.55 60.46 62/126 9-1
87 Iowa State 0 1223.1 78.5 56/125 11-7
88 Colorado State 0 1217.13 83.57 55/136 9-9
89 Case Western Reserve 0 1202.67 65.68 61/124 6-13
90 Skidmore 0 1188.27 67.84 58/141 8-5
91 Kennesaw State 0 1188.04 55.13 67/124 13-9
92 Carnegie Mellon 0 1184.72 81.32 53/131 14-5
93 Missouri S&T 0 1177.58 109.62 40/152 4-5
94 Swarthmore 0 1152.85 158.34 32/166 10-2
95 Mississippi State 0 1128.15 66.44 63/134 17-5
96 MIT 0 1127.48 64.61 68/139 13-8
97 Wellesley 0 1126.35 106.48 56/165 12-4
98 Trinity 0 1125.74 136.94 50/168 12-2
99 LSU 0 1119.43 75.55 64/144 16-8
100 Michigan Tech 0 1107.39 75.52 68/150 2-3
101 Boston College 0 1094.98 83.76 59/151 7-7
102 Liberty 0 1087.19 84.75 68/155 9-8
103 Lehigh 0 1079.64 86.43 68/156 5-7
104 Chico State 0 1076.39 101.23 56/170 12-6
105 Southern California 0 1072.45 72.18 67/142 8-13
106 Texas State 0 1064.56 128.14 59/170 7-7
107 Dallas 0 1061.85 143.33 50/181 4-2
108 Michigan State 0 1058.24 65.49 80/148 14-6
109 Central Florida 0 1054.26 84.43 69/157 4-9
110 Oklahoma 0 1052.65 65.74 75/152 9-8
111 Minnesota-Duluth 0 1052.38 65.8 69/155 11-2
112 South Florida 0 1050.61 59.27 84/142 7-10
113 Air Force 0 1047.21 80.38 74/164 6-7
114 Catholic 0 1043.8 81.1 67/159 14-5
115 Arizona 0 1039.72 98.96 66/171 8-6
116 UCLA-B 0 1036.67 106.5 68/164 9-4
117 Arizona State 0 1027.17 61.07 86/161 15-10
118 Towson 0 1024.96 95.12 70/166 7-6
119 Georgia College 0 1023.21 119.63 62/178 7-4
120 Boise State 0 1019.37 92.23 71/168 5-8
121 Brandeis 0 1015.92 87.01 68/170 5-7
122 St Benedict 0 1012.69 110.99 67/172 7-4
123 North Park 0 1012.13 117.06 63/186 10-3
124 SUNY-Stony Brook 0 1007.41 125.13 65/180 8-4
125 North Georgia 0 1005.34 58.54 88/156 9-8
126 Pacific Lutheran 0 999.54 95.72 73/172 7-10
127 Connecticut 0 992.45 89.28 79/169 7-4
128 Rutgers 0 990.5 99.07 74/170 8-6
129 Boston University 0 979.62 129.5 62/181 8-6
130 Haverford 0 978.63 122.54 53/178 7-4
131 Syracuse 0 969.92 102.25 78/178 4-6
132 Princeton 0 942.48 70.14 89/172 5-7
133 Occidental 0 938.15 125.62 71/186 5-5
134 Illinois 0 936.64 60.69 100/163 12-6
135 Oregon State 0 934.17 68.19 96/170 6-6
136 Tennessee-Chattanooga 0 931.07 110.13 76/178 6-6
137 Cincinnati 0 912.84 97.02 92/182 12-8
138 Iowa 0 906.31 92.84 85/176 10-8
139 Amherst 0 898.03 68.58 103/180 6-4
140 Alabama 0 897.51 68.97 100/170 15-9
141 Tennessee 0 896.06 83.52 85/180 5-12
142 American 0 891.77 107.16 80/182 11-4
143 Belmont 0 888.6 105.74 86/190 4-3
144 George Washington 0 881.09 80.15 94/181 13-7
145 Marquette 0 880.94 77.28 99/179 10-8
146 Luther 0 869.27 79.47 98/182 7-6
147 Bowdoin 0 867.72 67.77 104/175 8-7
148 Kentucky 0 862.08 84.31 102/192 7-6
149 Montana State 0 861.75 72.92 101/176 1-5
150 Virginia Tech 0 860.33 94.99 88/187 6-3
151 Smith 0 857.04 85.8 108/184 6-4
152 Appalachian State 0 850.07 66.36 108/176 8-5
153 Wisconsin-Milwaukee 0 845.02 66.55 107/174 9-8
154 Virginia Commonwealth 0 841.9 59.33 109/178 5-13
155 Claremont 0 826.85 82.82 112/200 3-9
156 SUNY-Albany 0 824.44 70.22 105/185 5-6
157 DePaul 0 814.05 53.82 120/176 7-4
158 Drexel 0 810.99 67.31 117/186 6-7
159 SUNY-Binghamton 0 782.43 76.5 115/193 9-8
160 Pittsburgh-B 0 779.09 78.5 118/192 12-3
161 Temple 0 777.8 89.75 103/194 6-8
162 Richmond 0 770.47 63.54 128/183 4-9
163 Knox 0 769.94 83.29 116/192 9-6
164 Rice 0 766.54 80.07 120/187 11-9
165 Rochester 0 754.37 48.99 134/181 6-6
166 Vermont-B 0 735.6 73.59 128/193 10-7
167 NYU 0 735.1 94.24 117/204 5-7
168 Baylor 0 722.32 73.73 134/202 6-6
169 Tulsa 0 720.8 85.38 122/207 4-7
170 Santa Clara 0 678.03 68.39 137/202 5-4
171 Wisconsin-La Crosse 0 669 68.45 143/203 5-10
172 Wheaton College IL 0 655.76 125.8 111/221 5-4
173 Georgia State 0 630.73 83.62 135/216 6-9
174 Arkansas 0 629.19 106.58 120/217 3-5
175 George Mason 0 628.31 64.46 146/207 3-15
176 Marist 0 626.16 86.99 138/210 1-5
177 Northeastern-B 0 620.36 69.8 149/208 10-8
178 Kenyon 0 612.2 127.09 85/230 4-2
179 Western Washington-B 0 611.14 68.71 146/208 2-5
180 California-San Diego-B 0 598.15 74.36 145/212 7-6
181 Tulane 0 593.98 86.73 138/216 5-14
182 Texas Christian 0 578.39 71.24 156/214 10-10
183 William & Mary-B 0 577.01 96.16 137/214 6-7
184 Utah State 0 573.27 53.43 164/208 3-3
185 Texas A&M 0 568.44 83.31 151/216 9-11
186 Seattle 0 566.91 65.43 161/213 4-1
187 Christopher Newport 0 565.13 89.31 147/219 3-9
188 Miami 0 553.62 81.69 155/218 4-9
189 Indiana 0 538.64 101.13 142/228 3-11
190 Colorado School of Mines 0 531.74 67.91 166/215 4-10
191 Wake Forest 0 508.51 58.38 169/215 6-4
192 Georgia Southern 0 506.6 76.33 149/225 7-10
193 Portland State 0 502.95 107.24 142/236 2-4
194 Texas-San Antonio 0 502.39 114.27 144/236 4-8
195 Wisconsin-Eau Claire 0 498.84 49.62 175/215 2-11
196 North Carolina-B 0 486.44 58.73 175/217 7-11
197 Cedarville 0 484.08 95.93 159/229 6-5
198 Alabama-Huntsville 0 482.58 86.71 151/235 5-7
199 SUNY-Fredonia 0 478.81 215.12 102/249 1-4
200 Mary Washington 0 476.29 88.8 160/229 5-5
201 Mississippi 0 445.64 90.65 161/233 5-8
202 Olivet Nazarene 0 433.06 61.16 179/220 7-5
203 Montana 0 432.17 127.23 153/239 0-6
204 Minnesota-B 0 427.03 75.37 169/229 2-5
205 Loyola-Chicago 0 423.24 112.81 165/241 3-9
206 Florida Tech 0 392.07 131.57 157/240 3-8
207 Bentley 0 386.51 118.67 152/243 2-6
208 Valparaiso 0 384.15 100.58 166/238 2-10
209 Elon 0 383.22 88.72 173/238 4-12
210 Sonoma State 0 363.71 118.36 157/240 3-10
211 Florida-B 0 362.25 114.86 167/243 1-15
212 Brown-B 0 356.97 118.06 171/245 3-2
213 Delaware-B 0 356.49 107.65 170/244 0-11
214 Xavier 0 333.49 106.66 172/243 6-7
215 New Mexico 0 320.67 73.12 189/236 2-8
216 Pennsylvania-B 0 317.18 73.31 187/238 8-12
217 California-Irvine 0 286.61 142.49 159/249 1-10
218 SUNY Cortland 0 278.81 162.97 165/250 0-6
219 Nevada-Reno 0 271.07 148.9 163/250 2-8
220 Ithaca 0 267.06 123.45 173/247 2-7
221 North Texas 0 259.68 65.13 198/241 5-12
222 Worcester Polytechnic 0 238.69 119.21 176/248 3-7
223 Columbia-B 0 234.82 103.04 176/247 5-6
224 Georgetown-B 0 232.56 72.98 201/243 7-5
225 Cornell-B 0 228.44 59.92 207/240 4-15
226 Colorado-B 0 190.79 94.99 197/248 2-8
227 Ohio State-B 0 185.83 103.74 193/246 6-7
228 California-B 0 180.65 104.84 192/249 3-8
229 Southern Indiana 0 162.58 136.04 182/249 2-7
230 Johns Hopkins University 0 162.52 69.36 206/245 3-7
231 Alabama-Birmingham 0 152.77 85.13 205/248 1-6
232 California-Davis-B 0 147.51 115.27 199/249 5-8
233 Washington-B 0 144.32 102.43 199/248 2-3
234 Wellesley-B 0 119.54 84.64 209/248 4-8
235 Georgia Tech-B 0 115.46 128.98 192/252 2-14
236 Wisconsin-Stevens Point 0 115.29 204.56 166/256 1-5
237 College of New Jersey 0 109.93 72.92 211/249 5-6
238 Maryland-Baltimore County 0 75.92 83.62 213/251 2-9
239 East Carolina 0 73.16 119.57 205/251 1-10
240 Hendrix 0 70.91 80.53 216/249 0-7
241 Emory-B 0 57.5 126.87 198/252 2-21
242 Michigan-B 0 34.6 100.17 211/252 3-13
243 George Washington-B 0 22.34 137.98 204/254 3-7
244 Northwestern-B 0 -3.52 70.36 222/250 2-8
245 Notre Dame-B 0 -4.4 98.52 211/251 2-10
246 Illinois-Chicago 0 -113.83 131.39 219/256 0-7
247 Virginia-B 0 -183.46 144.58 221/256 1-17
248 Boston College -B 0 -196.09 178.76 202/257 0-6
249 Wooster 0 -214.18 120.38 227/257 0-11
250 Cal Poly SLO-B 0 -269.21 184.56 213/258 0-10
251 Arizona-B 0 -328.55 229.32 208/258 0-11
252 Texas-B 0 -340.65 138.73 237/257 3-10
253 Towson-B 0 -411.7 122.62 243/257 1-10
254 Rhode Island 0 -467.75 247.77 213/258 1-10
255 Miami (Ohio) 0 -592.75 252.26 207/258 1-10
256 Eastern Michigan 0 -603.52 160.62 244/258 0-6
257 Oberlin-B 0 -741.57 326.21 210/258 1-5
258 Houston 0 -940.65 272.7 249/258 0-13

FAQ

The uncertainty of the mean is equal to the standard deviation of the set of game ratings, divided by the square root of the number of games. We treated a team’s ranking as a normally distributed random variable, with the USAU ranking as the mean and the uncertainty of the ranking as the standard deviation
  1. Calculate uncertainy for USAU ranking averge
  2. Model ranking as a normal distribution around USAU averge with standard deviation equal to uncertainty
  3. Simulate seasons by drawing a rank for each team from their distribution. Note the teams in the top 16 (club) or top 20 (college)
  4. Sum the fractions for each region for how often each of its teams appeared in the top 16 (club) or top 20 (college)
  5. Subtract one from each fraction for "autobids"
  6. Award remainings bids to the regions with the highest remaining fraction, subtracting one from the fraction each time a bid is awarded
There is an article on Ulitworld written by Scott Dunham and I that gives a little more context (though it probably was the thing that linked you here)