Probabilistic Bid Allocation

2024-25 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Bid Allocation

Bids Region Total Contributing Teams
1 Atlantic Coast 1.5 North Carolina 96.00%,   Virginia 54.10%,  
1 Great Lakes 1.65 Michigan 100.00%,   Notre Dame 64.80%,  
1 Metro East 0
2 New England 2.02 Tufts 100.00%,   Vermont 100.00%,   Northeastern 1.50%,  
1 North Central 1.03 Carleton College 100.00%,   Minnesota 2.70%,   Wisconsin 0.10%,  
6 Northwest 6.11 Oregon 100.00%,   British Columbia 100.00%,   Washington 100.00%,   Utah 99.70%,   Victoria 93.70%,   Brigham Young 70.10%,   Western Washington 47.40%,  
1 Ohio Valley 0.97 Ohio State 54.60%,   Pennsylvania 41.30%,   Ohio 0.70%,  
1 South Central 1.09 Colorado 100.00%,   Texas 8.70%,  
1 Southeast 0.04 Georgia Tech 4.00%,   Georgia 0.10%,  
5 Southwest 5.6 California-Santa Cruz 100.00%,   California-San Diego 100.00%,   Stanford 99.90%,   Cal Poly-SLO 98.90%,   California-Davis 80.40%,   California-Santa Barbara 74.40%,   UCLA 6.90%,  

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 1.501 1.648 0.000 2.015 1.028 6.109 0.966 1.087 0.041 5.605
Autos (all @ 1) 0.501 0.648 -1.000 1.015 0.028 5.109 -0.034 0.087 -0.959 4.605
Northwest (@ 2) 0.501 0.648 -1.000 1.015 0.028 4.109 -0.034 0.087 -0.959 4.605
Southwest (@ 2) 0.501 0.648 -1.000 1.015 0.028 4.109 -0.034 0.087 -0.959 3.605
Northwest (@ 3) 0.501 0.648 -1.000 1.015 0.028 3.109 -0.034 0.087 -0.959 3.605
Southwest (@ 3) 0.501 0.648 -1.000 1.015 0.028 3.109 -0.034 0.087 -0.959 2.605
Northwest (@ 4) 0.501 0.648 -1.000 1.015 0.028 2.109 -0.034 0.087 -0.959 2.605
Southwest (@ 4) 0.501 0.648 -1.000 1.015 0.028 2.109 -0.034 0.087 -0.959 1.605
Northwest (@ 5) 0.501 0.648 -1.000 1.015 0.028 1.109 -0.034 0.087 -0.959 1.605
Southwest (@ 5) 0.501 0.648 -1.000 1.015 0.028 1.109 -0.034 0.087 -0.959 0.605
Northwest (@ 6) 0.501 0.648 -1.000 1.015 0.028 0.109 -0.034 0.087 -0.959 0.605
New England (@ 2) 0.501 0.648 -1.000 0.015 0.028 0.109 -0.034 0.087 -0.959 0.605
Total 1 1 1 2 1 6 1 1 1 5

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 British Columbia 1 3030.03 91.14 1/5 18-1
2 Carleton College 1 3026.32 99.67 1/6 14-2
3 Tufts 1 2867.99 56.26 1/7 18-0
4 Colorado 1 2777.36 67.87 2/9 15-4
5 Oregon 1 2772.08 44.21 3/8 14-6
6 Vermont 1 2699 87.51 1/14 14-4
7 Michigan 1 2596.43 98.94 2/20 9-3
8 Washington 1 2555.43 62.04 5/19 11-8
9 California-San Diego 1 2523.72 41.72 6/16 14-12
10 California-Santa Cruz 1 2504.92 44.59 7/17 12-8
11 Stanford 0.999 2502.86 58.36 5/21 13-11
12 Utah 0.997 2506.53 79.23 4/21 12-7
13 Cal Poly-SLO 0.989 2470.9 79.95 6/25 17-9
14 North Carolina 0.96 2550.36 153.35 2/29 13-5
15 Victoria 0.937 2398.9 71.14 7/26 7-13
16 California-Davis 0.804 2334.48 53.72 11/27 9-11
17 California-Santa Barbara 0.744 2331.63 73.52 9/29 11-8
18 Brigham Young 0.701 2321.04 61.33 11/30 9-10
19 Notre Dame 0.648 2314.22 72.09 8/33 10-4
20 Ohio State 0.546 2294.56 101.07 6/37 13-6
21 Virginia 0.541 2297.05 93.25 8/32 18-6
22 Western Washington 0.474 2278.52 119.42 6/41 11-8
23 Pennsylvania 0.413 2274.09 58.39 12/29 9-8
24 Texas 0.087 2156.74 98.77 11/47 6-7
25 UCLA 0.069 2161.19 82.28 13/40 14-16
26 Georgia Tech 0.04 2084.8 112.27 14/54 14-5
27 Minnesota 0.027 2162.37 62.82 16/42 7-5
28 Northeastern 0.015 2120.17 75.7 16/43 8-9
29 Ohio 0.007 1983.44 121.01 13/65 11-2
30 Georgia 0.001 2089.77 63.48 20/44 7-5
31 Wisconsin 0.001 2051.18 72.69 18/46 8-10
32 Pittsburgh 0 2042.07 63.52 22/45 9-7
33 Georgetown 0 2035.36 50.39 23/42 12-7
34 Cornell 0 1996.41 78.48 22/54 10-3
35 Carleton College-Eclipse 0 1980.12 91.4 23/61 10-3
36 MIT 0 1927.38 66.65 26/56 7-6
37 American 0 1925.82 88.24 24/62 13-8
38 Duke 0 1917.91 84.16 24/66 15-5
39 California 0 1895.25 70.4 27/60 11-9
40 Haverford/Bryn Mawr 0 1872.17 89.92 25/69 13-7
41 Southern California 0 1870.03 75.88 27/69 6-12
42 Kenyon 0 1863.86 123.07 20/80 12-0
43 Colorado State 0 1863.6 88.11 27/74 0-12
44 Whitman 0 1859.21 99 26/73 12-2
45 Missouri 0 1854.92 91.77 25/73 16-2
46 Wesleyan 0 1849.92 78.5 25/71 11-3
47 Texas-Dallas 0 1849.86 84.35 27/73 5-7
48 Liberty 0 1849.32 122.11 23/82 13-4
49 William & Mary 0 1842.25 88.17 25/73 6-6
50 British Columbia-B 0 1772.15 109.94 27/89 4-3
51 Washington University 0 1765.36 75.79 33/74 14-5
52 Oregon State 0 1743.82 78.38 34/76 14-6
53 Appalachian State 0 1727.48 125.25 27/98 10-7
54 Middlebury 0 1727.44 82.35 36/79 10-1
55 Maryland 0 1727.01 76.21 31/80 12-8
56 James Madison 0 1709.36 108.73 27/93 7-5
57 Brown 0 1699.5 47.18 42/77 6-11
58 Davenport 0 1687.54 75.19 37/80 14-1
59 Purdue 0 1684.97 116.15 30/111 7-4
60 Lewis & Clark 0 1684.85 102.29 34/102 9-4
61 North Carolina State 0 1679.27 124.36 29/114 5-6
62 California-Irvine 0 1672.89 66.23 40/83 18-5
63 South Carolina 0 1661.93 101.69 35/98 5-7
64 Portland 0 1655.33 77.45 39/94 11-8
65 St Olaf 0 1651.33 81.38 40/95 9-10
66 Rochester 0 1624.78 71.87 45/89 9-2
67 Florida 0 1622.31 109.47 33/108 9-5
68 Santa Clara 0 1616.41 73.13 41/99 10-6
69 Connecticut 0 1595.33 65.82 50/95 6-7
70 Colorado College 0 1583.24 98.65 44/108 12-6
71 Central Florida 0 1568.58 84.83 45/102 7-6
72 Utah State 0 1547.22 114.47 38/123 3-1
73 Chicago 0 1545.69 112.45 27/120 8-6
74 Union (Tennessee) 0 1543.08 78.47 51/104 9-1
75 Columbia 0 1534.9 77.69 47/106 5-7
76 Penn State 0 1526.54 79.97 52/118 8-10
77 Mount Holyoke 0 1520.17 85.27 49/106 2-4
78 Tennessee 0 1507.33 82.66 53/118 12-4
79 Carnegie Mellon 0 1503.68 97.3 49/113 5-8
80 Case Western Reserve 0 1473.1 94.09 51/117 6-6
81 Illinois 0 1464.97 57.34 60/103 13-6
82 Wellesley 0 1461.59 50.91 65/102 11-5
83 Macalester 0 1459.63 94.58 53/129 9-5
84 Michigan State 0 1435.08 69.55 62/115 8-4
85 Montana 0 1424.67 76.28 61/121 4-3
86 San Diego State 0 1423.59 73.01 58/120 13-4
87 Vermont-B 0 1404.78 93.59 59/140 4-3
88 Ithaca 0 1403.02 78.47 56/120 7-5
89 Brown-B 0 1395.63 160.24 43/155 5-2
90 Richmond 0 1388.03 74.48 67/122 6-5
91 Williams 0 1371.09 66.31 67/121 13-5
92 Wisconsin-Eau Claire 0 1370.48 99.54 61/132 9-4
93 Rice 0 1370.01 94.24 63/132 7-5
94 Michigan Tech 0 1363.12 85.57 60/130 8-5
95 Grand Canyon 0 1360.24 98.85 60/147 5-1
96 Iowa State 0 1356.25 64.63 74/122 13-6
97 Denver 0 1350.14 73.12 66/128 14-3
98 Emory 0 1349.9 105.01 53/147 7-6
99 SUNY-Buffalo 0 1339.51 83.06 65/140 11-4
100 Butler 0 1338.57 82.46 70/143 5-2
101 Lehigh 0 1310.66 76.53 76/132 9-11
102 California-San Diego-B 0 1296.08 90.86 66/157 10-9
103 Loyola-Chicago 0 1294.21 123.04 65/163 8-3
104 Temple 0 1290.71 83.24 71/138 3-8
105 Virginia Tech 0 1283.14 82.64 75/144 4-7
106 Alabama-Huntsville 0 1278.24 225.7 40/189 1-3
107 Dartmouth 0 1273.03 175.59 40/187 3-1
108 Arkansas 0 1265.23 116.55 60/171 3-3
109 George Washington 0 1257.53 78.16 76/144 7-5
110 Swarthmore 0 1247.58 71.94 82/138 8-5
111 SUNY-Binghamton 0 1247.41 95.06 73/157 5-6
112 West Chester 0 1240.75 69.25 81/139 1-9
113 Cedarville 0 1238.87 46.84 91/139 8-4
114 Arizona State 0 1237.04 69.02 84/143 12-7
115 Clemson 0 1221.87 56.34 91/134 7-4
116 Cincinnati 0 1221.32 77.37 85/147 9-4
117 Yale 0 1207.96 82.08 82/152 4-8
118 Puget Sound 0 1200.16 49.03 95/146 5-7
119 Kansas 0 1199.69 101.82 76/174 3-3
120 Claremont 0 1181.91 59.03 98/144 9-10
121 Northwestern 0 1169.46 92.96 81/156 5-13
122 Xavier 0 1159.6 66.7 95/152 8-5
123 Northern Arizona 0 1154.55 137.41 69/178 2-4
124 Claremont-B 0 1144.85 170.24 57/186 1-2
125 Saint Louis 0 1137.59 77.47 97/159 6-7
126 NYU 0 1135.98 66.67 96/157 8-4
127 Winona State 0 1125.5 61.68 102/156 12-7
128 Harvard 0 1097.52 63.82 104/166 6-8
129 Grand Valley 0 1091.37 61.09 97/156 5-7
130 Catholic 0 1090.13 93.36 92/170 3-8
131 Cal Poly-SLO-B 0 1089.96 81.83 97/170 3-7
132 Stanford-B 0 1076.73 111.6 81/189 1-5
133 SUNY-Geneseo 0 1071.2 71.43 106/168 6-8
134 California-B 0 1060.63 87.23 97/179 5-6
135 Trinity 0 1056.98 66.21 105/166 7-9
136 Rutgers 0 1041.04 95.19 96/178 9-5
137 Georgia College 0 1040.81 62.58 109/167 6-7
138 North Carolina-Wilmington 0 1040.8 81.23 102/172 8-15
139 RIT 0 1036.87 151.98 75/199 1-4
140 Berry 0 1027.74 88.96 102/180 8-7
141 Jacksonville State 0 1027.64 82.39 104/174 1-5
142 Boston College 0 1023.94 81.42 108/175 3-10
143 Delaware 0 1007.06 84.23 105/185 6-3
144 Wisconsin-La Crosse 0 1004.42 63.93 114/172 4-7
145 North Carolina-B 0 1002.64 112.99 94/184 3-9
146 Tulane 0 999.54 86.68 105/180 5-3
147 Davidson 0 999 78.78 104/182 7-6
148 Boston University 0 997.82 104.92 95/181 4-8
149 Iowa 0 991.52 105.7 93/182 7-5
150 Montana State 0 983.93 75.1 115/181 2-5
151 Occidental 0 981.52 76.52 111/179 5-4
152 Wake Forest 0 974.93 121.1 101/195 3-3
153 Syracuse 0 974.32 79.57 113/177 5-6
154 Alabama 0 963.65 85.11 101/182 7-7
155 Knox 0 961.36 65.17 114/178 5-8
156 Vermont-C 0 920.37 36.28 139/172 2-2
157 Massachusetts 0 913.62 86.67 112/194 3-7
158 East Carolina 0 894.2 91.19 118/192 3-2
159 Arizona 0 878.21 67.44 131/189 6-12
160 UCLA-B 0 870.58 77.88 124/193 7-10
161 Florida State 0 868.85 73.45 128/190 6-7
162 Indiana 0 867.86 73.63 125/191 6-5
163 Oberlin 0 863.56 113.31 117/206 1-8
164 Colby 0 856.39 86.48 131/198 3-7
165 Miami (Florida) 0 843.32 61.15 139/193 9-9
166 George Mason 0 841.5 49.58 144/187 6-6
167 California-Davis-B 0 836.59 107.06 126/198 1-5
168 Nevada-Reno 0 833.31 79.76 132/191 4-9
169 Pacific Lutheran 0 822 85.87 130/200 4-7
170 Michigan-B 0 817.62 78.04 136/199 4-6
171 Charleston 0 802.08 81.04 137/204 5-8
172 Colorado-B 0 800.95 55.64 145/193 3-9
173 Colorado Mines 0 789.65 92.72 127/205 5-5
174 Bates 0 781.86 67.93 147/198 3-6
175 New Hampshire 0 780.06 73.01 140/194 5-13
176 Skidmore 0 779.17 91.9 135/207 4-6
177 Missouri State 0 773.84 166.13 99/215 1-4
178 Truman State 0 766.39 70.49 147/197 7-12
179 Harding 0 754.36 144.31 115/217 3-4
180 Georgia Southern 0 719.14 111.52 133/208 3-8
181 St Olaf-B 0 694.71 88.71 153/209 2-12
182 Vanderbilt 0 680.74 74.05 161/206 6-9
183 LSU 0 679.37 97.91 148/213 7-6
184 Tennessee-Chattanooga 0 637.27 68.38 165/207 2-8
185 Cal State-Long Beach 0 636.05 84.75 152/209 5-12
186 Utah-B 0 633.23 144.87 135/222 0-7
187 Towson 0 632.21 137.11 136/220 3-4
188 Dayton 0 619.71 104.92 150/214 4-8
189 Texas A&M 0 615.78 84.54 161/213 3-8
190 California-Santa Barbara-B 0 603.12 112.9 151/217 1-5
191 William & Mary-B 0 566.24 85.28 163/214 0-6
192 Florida Tech 0 559.91 86.78 159/219 4-8
193 Dickinson 0 546.39 111.75 152/219 3-9
194 Cal Poly-Humboldt 0 545.68 143.9 142/222 1-10
195 Washington-B 0 539.07 161.99 140/223 2-7
196 Georgetown-B 0 536.62 155.23 152/223 1-5
197 Johns Hopkins 0 530.95 89.62 168/218 2-6
198 Miami (Ohio) 0 527.3 92.8 171/220 2-4
199 Connecticut College 0 526.03 128.46 157/221 0-4
200 Washington University-B 0 520.04 37.3 185/212 4-7
201 Georgia-B 0 504.83 94.05 176/222 2-10
202 Texas State 0 501.39 6.92 193/207 0-2
203 South Carolina-B 0 476.88 191 116/224 1-5
204 SUNY-Stony Brook 0 462.6 73.19 182/220 2-4
205 Cornell-B 0 461.77 111.48 172/222 1-5
206 Wisconsin-B 0 441.14 86.04 181/220 0-5
207 California-San Diego-C 0 414.58 126.85 159/224 2-15
208 Notre Dame-B 0 408.27 115.83 171/222 1-5
209 Auburn 0 392.65 119.58 176/223 2-8
210 Arizona-B 0 368.85 124.59 179/224 0-6
211 Pennsylvania-B 0 363.09 225.03 136/224 0-7
212 John Brown 0 329.56 200.02 148/224 0-4
213 Georgia Tech-B 0 294.54 199.03 153/224 1-5
214 Purdue-B 0 288.95 76.2 199/223 1-11
215 Northeastern-B 0 272.69 102.28 190/224 1-10
216 Alabama-Birmingham 0 270.13 61.8 203/223 1-3
217 Florida-B 0 265.45 143.47 167/224 1-10
218 American-B 0 259.38 132.62 182/224 1-12
219 Lewis & Clark -B 0 259.28 311.14 103/224 0-6
220 Northwestern-B 0 237.85 189.99 164/224 0-5
221 Elon 0 231.25 123.24 187/224 1-5
222 Texas-B 0 103.95 213.11 163/224 0-9
223 Columbia-B 0 96 185.38 186/224 0-5
224 Emory-B 0 -127.2 305.65 173/224 0-12

FAQ

What is the uncertainty of the mean?
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
What's the algorithm again?
  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
Is there a longer explanation of all this?
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)