Probabilistic Bid Allocation

2022-23 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Bid Allocation

Bids Region Total Contributing Teams
2 Atlantic Coast 2.94 North Carolina 100.00%,   Virginia 99.90%,   North Carolina State 47.20%,   Duke 20.50%,   South Carolina 16.20%,   East Carolina 9.90%,  
1 Great Lakes 0.27 Notre Dame 21.40%,   Chicago 3.00%,   Michigan 2.70%,  
1 Metro East 0.64 Yale 55.70%,   SUNY-Binghamton 8.10%,  
3 New England 3 Vermont 100.00%,   Tufts 100.00%,   Northeastern 99.90%,   Brown 0.40%,  
1 North Central 1.25 Carleton College 100.00%,   Minnesota 24.80%,   Wisconsin 0.10%,  
5 Northwest 5.49 Washington 100.00%,   British Columbia 100.00%,   Brigham Young 100.00%,   Oregon 100.00%,   Victoria 92.50%,   Western Washington 56.50%,   Montana State 0.10%,  
1 Ohio Valley 1.02 Pittsburgh 99.90%,   Ohio State 1.90%,  
2 South Central 2.18 Colorado 100.00%,   Colorado State 74.50%,   Texas-Dallas 43.20%,  
1 Southeast 0.02 Florida State 1.20%,   Georgia 0.90%,   Florida 0.20%,   Georgia Tech 0.10%,  
3 Southwest 3.19 Stanford 100.00%,   California-Santa Barbara 100.00%,   California-San Diego 88.80%,   California-Davis 25.10%,   UCLA 3.20%,   California 1.80%,   Santa Clara 0.30%,  

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 2.937 0.271 0.638 3.003 1.249 5.491 1.018 2.177 0.024 3.192
Autos (all @ 1) 1.937 -0.729 -0.362 2.003 0.249 4.491 0.018 1.177 -0.976 2.192
Northwest (@ 2) 1.937 -0.729 -0.362 2.003 0.249 3.491 0.018 1.177 -0.976 2.192
Northwest (@ 3) 1.937 -0.729 -0.362 2.003 0.249 2.491 0.018 1.177 -0.976 2.192
Northwest (@ 4) 1.937 -0.729 -0.362 2.003 0.249 1.491 0.018 1.177 -0.976 2.192
Southwest (@ 2) 1.937 -0.729 -0.362 2.003 0.249 1.491 0.018 1.177 -0.976 1.192
New England (@ 2) 1.937 -0.729 -0.362 1.003 0.249 1.491 0.018 1.177 -0.976 1.192
Atlantic Coast (@ 2) 0.937 -0.729 -0.362 1.003 0.249 1.491 0.018 1.177 -0.976 1.192
Northwest (@ 5) 0.937 -0.729 -0.362 1.003 0.249 0.491 0.018 1.177 -0.976 1.192
Southwest (@ 3) 0.937 -0.729 -0.362 1.003 0.249 0.491 0.018 1.177 -0.976 0.192
South Central (@ 2) 0.937 -0.729 -0.362 1.003 0.249 0.491 0.018 0.177 -0.976 0.192
New England (@ 3) 0.937 -0.729 -0.362 0.003 0.249 0.491 0.018 0.177 -0.976 0.192
Total 2 1 1 3 1 5 1 2 1 3

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 North Carolina 1 2937.91 151.6 1/4 20-0
2 British Columbia 1 2548.3 97.33 1/8 9-2
3 Colorado 1 2467.86 65.32 2/7 20-1
4 Tufts 1 2426.44 126.82 1/12 11-5
5 Vermont 1 2373.3 85.45 2/10 11-3
6 Brigham Young 1 2281.72 100.28 2/13 10-4
7 Carleton College 1 2278.35 55.61 3/12 14-3
8 Stanford 1 2233.33 47.29 4/12 21-8
9 Washington 1 2183.52 86.43 3/15 5-8
10 Oregon 1 2096.82 37.32 7/15 13-8
11 California-Santa Barbara 1 2058.42 68.04 7/19 16-6
12 Northeastern 0.999 2134.33 136.57 2/23 22-0
13 Pittsburgh 0.999 1933.35 48.87 11/23 10-4
14 Virginia 0.999 1930.66 39.61 11/23 22-5
15 Victoria 0.925 1852.64 58.51 12/31 5-7
16 California-San Diego 0.888 1824.58 46.02 12/29 12-10
17 Colorado State 0.745 1811.5 64.4 11/37 8-8
18 Western Washington 0.565 1780.43 98.58 10/49 4-8
19 Yale 0.557 1786.06 110.71 10/51 9-5
20 North Carolina State 0.472 1756.31 83.45 13/44 11-6
21 Texas-Dallas 0.432 1739.5 132.01 11/63 18-1
22 California-Davis 0.251 1719.95 68.89 13/45 10-12
23 Minnesota 0.248 1685.25 113.84 12/62 11-2
24 Notre Dame 0.214 1688.33 110.12 12/56 14-5
25 Duke 0.205 1682.04 95.39 12/56 13-9
26 South Carolina 0.162 1660.8 110.23 13/68 13-6
27 East Carolina 0.099 1576.17 157.6 11/110 5-1
28 SUNY-Binghamton 0.081 1651.59 88.73 15/55 12-3
29 UCLA 0.032 1664.62 54.12 19/45 9-18
30 Chicago 0.03 1567.22 112.13 13/77 8-4
31 Michigan 0.027 1619.57 77.07 16/60 8-13
32 Ohio State 0.019 1633.9 55.69 19/48 12-7
33 California 0.018 1657.96 52.67 20/45 11-19
34 Florida State 0.012 1473.72 134.44 18/89 12-7
35 Georgia 0.009 1530.7 99.78 17/73 6-7
36 Brown 0.004 1580.07 63.79 20/56 11-9
37 Santa Clara 0.003 1539.36 77.54 16/67 12-9
38 Florida 0.002 1467.9 96.6 22/79 14-11
39 Wisconsin 0.001 1506.49 83.28 22/78 5-9
40 Montana State 0.001 1477.14 81.35 21/73 4-0
41 Georgia Tech 0.001 1352.86 116.86 22/98 13-6
42 Middlebury 0 1835.84 67.87 10/33 12-0
43 Wellesley 0 1747.49 129.78 9/70 12-1
44 Carleton College-Eclipse 0 1732.83 174.11 7/71 15-6
45 Portland 0 1632.44 99.51 13/61 13-1
46 James Madison 0 1524.02 54.27 25/59 15-2
47 Whitman 0 1499 82.69 23/80 9-1
48 Pennsylvania 0 1484.31 77.07 22/70 6-8
49 Washington University 0 1479.26 80.59 23/75 14-6
50 Texas 0 1459.95 77.46 26/83 6-14
51 Brown-B 0 1454.87 74.09 27/74 6-0
52 California-Santa Cruz 0 1437.65 80.24 28/84 15-7
53 Georgetown 0 1421.83 81.56 31/83 12-7
54 Arkansas 0 1410.94 98.81 26/88 11-2
55 Cal Poly-SLO 0 1380.02 72.14 33/78 10-13
56 Cornell 0 1345.99 69.78 35/86 9-1
57 Tennessee 0 1340.42 108.5 30/99 13-5
58 Virginia Tech 0 1337.15 62.99 38/81 10-8
59 Williams 0 1324.77 117.8 30/108 7-5
60 Penn State 0 1301.24 62.23 39/88 9-10
61 Ohio 0 1299.34 107.29 30/105 12-7
62 Vermont-B 0 1286.54 117.22 21/123 10-2
63 William & Mary 0 1277.48 116.24 23/115 6-7
64 Haverford/Bryn Mawr 0 1276.27 80.72 41/101 14-4
65 Appalachian State 0 1274.41 74.12 38/97 6-10
66 Carnegie Mellon 0 1273.97 138.74 24/136 2-3
67 Kansas 0 1268.16 57.15 49/91 7-4
68 Mount Holyoke 0 1267.7 63.03 44/95 10-4
69 Winona State 0 1266.92 80.28 32/96 15-2
70 Case Western Reserve 0 1250.46 88.45 40/104 4-9
71 Northwestern 0 1238.77 75.4 48/104 9-11
72 Massachusetts 0 1233.48 106.87 39/115 6-7
73 Iowa State 0 1230.49 68.47 50/102 15-4
74 St. Olaf 0 1226.89 74.47 50/102 16-4
75 Utah 0 1224.4 68.59 46/98 4-21
76 Boston University 0 1221.57 59.77 52/96 7-7
77 Bates 0 1181.37 84.13 49/117 7-5
78 Tennessee-Chattanooga 0 1179.39 115.6 34/129 7-3
79 Lewis & Clark 0 1178.49 86.51 44/112 7-6
80 Nevada-Reno 0 1175.72 66.78 55/106 11-7
81 American 0 1173.83 87.79 45/113 9-4
82 Oregon State 0 1173.04 107.58 47/124 4-4
83 Central Florida 0 1130.12 98.67 51/122 11-7
84 Trinity 0 1117.18 103.4 44/128 13-4
85 California-Irvine 0 1113.87 65.88 58/116 9-3
86 Catholic 0 1104.85 104.7 51/129 4-6
87 Clemson 0 1086.5 134.34 43/145 3-3
88 Southern California 0 1086.09 66.36 59/123 7-17
89 Kentucky 0 1080.73 144.7 39/145 4-3
90 Columbia 0 1078.66 75.35 65/126 6-11
91 Claremont 0 1064.06 54.83 74/117 11-7
92 Colorado College 0 1055.06 79.82 64/125 10-8
93 Seattle 0 1054.32 96.03 50/134 3-2
94 South Carolina-B 0 1047.36 160.83 38/165 3-3
95 Boston College 0 1038.5 71.04 70/128 8-3
96 Temple 0 1029.11 96.19 56/139 7-11
97 Harvard 0 1021.65 94.2 60/136 5-6
98 NYU 0 1010.21 83.95 69/137 5-6
99 Temple -B 0 1005.46 108.98 55/152 3-3
100 MIT 0 983.32 68.48 77/130 4-6
101 Alabama-Huntsville 0 982.72 118.16 58/151 2-3
102 Occidental 0 975.82 91.47 69/139 12-5
103 Dartmouth 0 973.04 189.54 42/171 3-2
104 Virginia Commonwealth 0 972.7 74.68 74/143 3-10
105 Iowa 0 966.86 56.64 85/134 12-8
106 Michigan Tech 0 959.82 54.97 87/139 7-4
107 Marquette 0 951.74 69.91 75/138 9-4
108 William & Mary-B 0 950.58 63.78 75/135 2-4
109 California-San Diego-B 0 950.19 56.59 82/137 9-10
110 Texas State 0 946.78 90.7 72/157 14-5
111 Charleston 0 918.95 184.42 55/186 6-4
112 Lehigh 0 918.2 98.07 70/152 9-9
113 Rice 0 907.62 93.04 78/154 8-6
114 Ithaca 0 905.27 61.75 88/147 6-6
115 Union (Tennessee) 0 899.39 119.05 69/162 8-9
116 Delaware 0 893.93 169.44 41/188 4-2
117 Cedarville 0 890.53 81.31 78/146 5-5
118 Arizona 0 884.59 64.23 89/144 7-4
119 Rhode Island 0 860.46 92.3 77/154 4-3
120 San Diego State 0 844.36 92.24 85/153 2-5
121 Brandeis 0 841.34 92.13 87/155 6-6
122 Texas A&M 0 830.38 64.99 97/153 8-4
123 Purdue 0 828.35 69.64 93/157 4-3
124 Denver 0 821.02 58.04 94/149 13-6
125 Saint Louis 0 819.4 64.08 97/150 6-5
126 American-B 0 818.31 100.95 91/162 3-2
127 Puget Sound 0 807.54 155.66 55/193 2-3
128 John Brown 0 795.17 88.37 90/161 2-4
129 West Chester 0 792.71 135.07 60/182 4-2
130 Maryland 0 776.19 87.6 94/167 2-7
131 Liberty 0 773.74 47.58 108/150 7-15
132 Nebraska 0 770.15 93.43 93/162 3-3
133 Emory 0 762.73 154.45 77/194 7-4
134 New Hampshire 0 748.55 69.35 106/162 6-8
135 Johns Hopkins 0 735.89 77.71 95/166 5-5
136 Mary Washington 0 726.75 71.56 107/162 5-8
137 Alabama 0 722.36 89.72 100/174 8-8
138 Cincinnati 0 716.58 45.98 115/156 4-2
139 Montana 0 711.01 95.44 97/174 0-3
140 Michigan State 0 706.15 98.5 96/182 3-3
141 Wesleyan 0 700.24 74.31 111/171 4-7
142 Rochester 0 680.32 69.22 105/173 5-2
143 Portland-B 0 675.14 201.06 47/208 2-3
144 Macalester 0 673.45 61.67 117/170 4-8
145 Connecticut 0 667.98 92.18 109/188 7-9
146 North Carolina-B 0 660.77 162.39 76/204 2-10
147 Virginia-B 0 655.94 74.54 117/174 3-9
148 SUNY-Geneseo 0 650.15 92.24 115/178 1-10
149 Sam Houston 0 623.17 64.3 125/178 5-6
150 Washington University-B 0 620.26 88.21 99/183 3-3
151 George Washington-B 0 619.66 98.71 111/190 0-5
152 SUNY-Stony Brook 0 612.96 186.52 74/215 1-2
153 Arizona State 0 606.87 70.2 125/183 8-8
154 Rutgers 0 605.51 101.68 105/190 3-8
155 Grinnell 0 595.43 57.79 127/177 2-4
156 Loyola-Chicago 0 585.59 87.15 116/187 2-8
157 Syracuse 0 582.2 98.68 116/195 5-4
158 Luther 0 555.95 80.52 112/192 1-5
159 Connecticut College 0 555.42 110.54 118/195 2-3
160 Knox 0 551.18 102.33 94/197 6-4
161 Stanford-B 0 521.55 65.82 139/183 4-11
162 Franciscan 0 513.9 108.39 113/198 2-4
163 Towson 0 509.42 127.46 100/210 3-7
164 Skidmore 0 505.55 81.8 124/195 4-5
165 UCLA-B 0 500.64 48.72 145/182 2-9
166 Washington-B 0 492.23 129.07 109/200 2-4
167 Colorado Mines 0 487.23 59.26 140/190 3-8
168 Truman State 0 482.35 78.51 134/193 4-9
169 Tulane 0 449.82 153.65 99/210 3-3
170 Jacksonville State 0 449.33 89.79 132/204 7-9
171 Grand Canyon 0 445.28 89.91 136/198 5-5
172 Wisconsin-Eau Claire 0 435.83 167.91 100/212 0-4
173 Colby 0 432.59 158.33 106/214 2-3
174 Northern Arizona 0 409.88 68.67 152/199 5-8
175 Illinois 0 408.98 51.68 145/192 8-13
176 Missouri State 0 402.17 143.54 121/213 1-5
177 Swarthmore 0 398.34 68.04 141/201 1-4
178 Michigan-B 0 392.38 161.65 107/217 3-2
179 Dayton 0 382.6 127.66 129/209 3-4
180 Bowdoin 0 378.63 124.8 137/220 0-6
181 Chico State 0 351.2 92.47 149/208 2-12
182 LSU 0 347.6 62.88 160/205 5-13
183 Wisconsin-La Crosse 0 334.74 84.87 143/207 3-7
184 St Benedict 0 317.2 217.04 94/223 1-3
185 George Washington 0 307.11 60.39 159/207 5-11
186 George Mason 0 295.3 162.14 128/219 1-2
187 Texas-San Antonio 0 275.87 64.64 167/206 5-7
188 Indiana 0 271.27 119.51 145/215 2-4
189 Georgetown-B 0 263.71 154.73 126/224 1-11
190 Messiah 0 263.48 74.88 162/214 1-11
191 Richmond 0 261.23 79.25 164/213 2-9
192 Dickinson 0 251.91 92.63 165/216 3-6
193 Wisconsin-B 0 237.78 116.95 158/216 2-9
194 Wisconsin-Milwaukee 0 230.57 130.51 138/218 2-3
195 Colorado-B 0 229.18 98.67 160/214 1-11
196 Oberlin 0 226.94 113.5 154/217 4-3
197 Pacific Lutheran 0 224.56 117.9 158/215 1-10
198 Minnesota-Duluth 0 195.81 123.51 155/220 4-7
199 Boston University-B 0 169.79 189.59 112/224 0-6
200 Georgia Tech-B 0 156.73 140.84 150/221 2-9
201 California-Davis-B 0 111.62 88.15 177/220 2-10
202 California-B 0 101.55 148.39 158/223 1-6
203 North Texas 0 88.01 130.53 162/224 4-8
204 College of New Jersey 0 87.34 133.92 159/225 2-7
205 Princeton 0 64.53 86.95 183/223 1-5
206 Wake Forest 0 62.67 116.23 167/224 2-8
207 North Carolina-Wilmington 0 45.79 240.45 132/226 3-9
208 Miami (Florida) 0 45.72 196.4 134/227 2-9
209 South Florida 0 34.44 202.7 139/226 1-5
210 Miami (Ohio) 0 30.24 153.49 165/227 1-4
211 Vanderbilt 0 21.72 181.12 156/226 1-5
212 Northwestern-B 0 10.56 114.18 185/224 2-11
213 Oklahoma 0 -11.03 266.85 123/228 0-6
214 Purdue-B 0 -33.63 176.73 164/226 1-4
215 Florida Tech 0 -87.42 222.16 153/228 3-9
216 Minnesota-B 0 -125.56 173.23 166/227 0-6
217 Houston 0 -135.03 147.61 183/226 1-5
218 SUNY-Albany 0 -152.66 254.74 131/228 1-3
219 St. Olaf-B 0 -199.73 223.77 152/228 1-4
220 Notre Dame-B 0 -204.71 114.25 197/228 2-10
221 Elon 0 -247.33 195.92 181/228 0-12
222 Florida-B 0 -263.51 225.89 186/228 3-9
223 North Park 0 -342.5 205.42 184/228 0-4
224 Texas-B 0 -418.99 314.84 167/228 0-6
225 Arizona-B 0 -488.38 169.94 203/228 0-10
226 Georgia Southern 0 -667.96 497.42 111/228 1-3
227 Emory-B 0 -694.27 261.02 196/228 1-11
228 Georgia-B 0 -906.72 436.62 141/228 0-6

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)