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 2.96 Virginia 100.00%,   North Carolina 100.00%,   North Carolina State 49.80%,   Duke 18.30%,   South Carolina 15.70%,   East Carolina 12.20%,  
1 Great Lakes 0.29 Notre Dame 21.20%,   Chicago 5.60%,   Michigan 2.20%,  
1 Metro East 0.85 Yale 78.80%,   SUNY-Binghamton 6.60%,  
3 New England 3 Vermont 100.00%,   Tufts 100.00%,   Northeastern 99.70%,   Brown 0.20%,  
1 North Central 1.23 Carleton College 100.00%,   Minnesota 22.50%,   Wisconsin 0.10%,  
5 Northwest 5.41 Washington 100.00%,   British Columbia 100.00%,   Brigham Young 100.00%,   Oregon 100.00%,   Victoria 89.70%,   Western Washington 50.90%,  
1 Ohio Valley 1.02 Pittsburgh 100.00%,   Ohio State 2.00%,  
2 South Central 2.15 Colorado 100.00%,   Colorado State 72.70%,   Texas-Dallas 42.20%,  
1 Southeast 0.03 Florida State 2.00%,   Georgia 0.60%,   Florida 0.30%,   Georgia Tech 0.10%,  
3 Southwest 3.07 Stanford 100.00%,   California-Santa Barbara 100.00%,   California-San Diego 81.20%,   California-Davis 20.70%,   UCLA 2.70%,   California 2.00%,  

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 2.960 0.290 0.854 2.999 1.226 5.406 1.020 2.149 0.030 3.066
Autos (all @ 1) 1.960 -0.710 -0.146 1.999 0.226 4.406 0.020 1.149 -0.970 2.066
Northwest (@ 2) 1.960 -0.710 -0.146 1.999 0.226 3.406 0.020 1.149 -0.970 2.066
Northwest (@ 3) 1.960 -0.710 -0.146 1.999 0.226 2.406 0.020 1.149 -0.970 2.066
Northwest (@ 4) 1.960 -0.710 -0.146 1.999 0.226 1.406 0.020 1.149 -0.970 2.066
Southwest (@ 2) 1.960 -0.710 -0.146 1.999 0.226 1.406 0.020 1.149 -0.970 1.066
New England (@ 2) 1.960 -0.710 -0.146 0.999 0.226 1.406 0.020 1.149 -0.970 1.066
Atlantic Coast (@ 2) 0.960 -0.710 -0.146 0.999 0.226 1.406 0.020 1.149 -0.970 1.066
Northwest (@ 5) 0.960 -0.710 -0.146 0.999 0.226 0.406 0.020 1.149 -0.970 1.066
South Central (@ 2) 0.960 -0.710 -0.146 0.999 0.226 0.406 0.020 0.149 -0.970 1.066
Southwest (@ 3) 0.960 -0.710 -0.146 0.999 0.226 0.406 0.020 0.149 -0.970 0.066
New England (@ 3) 0.960 -0.710 -0.146 -0.001 0.226 0.406 0.020 0.149 -0.970 0.066
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 2812.06 169.31 1/3 17-0
2 British Columbia 1 2422.1 97.22 1/7 9-2
3 Colorado 1 2341.83 66.02 1/8 20-1
4 Tufts 1 2300.73 147.47 1/12 10-3
5 Vermont 1 2247.5 87.11 2/11 9-2
6 Brigham Young 1 2155.72 100.5 2/13 10-4
7 Carleton College 1 2152.26 53.52 4/11 14-3
8 Stanford 1 2107.31 47.69 3/12 21-8
9 Washington 1 2057.61 86.29 3/16 5-8
10 Oregon 1 1969.91 37.25 7/14 13-8
11 California-Santa Barbara 1 1933.22 68.33 7/20 16-6
12 Pittsburgh 1 1812.03 46.14 11/22 10-4
13 Virginia 1 1810.11 40 11/22 22-5
14 Northeastern 0.997 2011.29 135.81 2/28 22-0
15 Victoria 0.897 1724.36 58.62 11/32 5-7
16 California-San Diego 0.812 1697.43 46.33 13/29 12-10
17 Yale 0.788 1744.87 127.47 6/56 6-2
18 Colorado State 0.727 1687.44 64.75 12/37 8-8
19 Western Washington 0.509 1653.97 98.58 11/53 4-8
20 North Carolina State 0.498 1642.72 82.73 12/46 11-6
21 Texas-Dallas 0.422 1625.17 133.14 8/66 18-1
22 Minnesota 0.225 1565.6 112.61 11/60 11-2
23 Notre Dame 0.212 1557.49 115.17 9/68 14-5
24 California-Davis 0.207 1592.46 69.15 15/44 10-12
25 Duke 0.183 1569.18 93.46 12/52 13-9
26 South Carolina 0.157 1542.52 107.25 13/60 13-6
27 East Carolina 0.122 1462.46 154.92 11/76 5-1
28 SUNY-Binghamton 0.066 1490.56 100.32 17/64 12-3
29 Chicago 0.056 1455.93 128.68 12/81 8-4
30 UCLA 0.027 1536.29 54.19 18/43 9-18
31 Michigan 0.022 1499.43 75.42 17/54 8-13
32 California 0.02 1531.51 52.85 19/47 11-19
33 Ohio State 0.02 1516.6 56.64 18/52 12-7
34 Florida State 0.02 1360.24 144.23 16/97 12-7
35 Georgia 0.006 1414.64 98.05 18/66 6-7
36 Florida 0.003 1362.63 96.6 21/76 14-11
37 Brown 0.002 1420.21 84.66 22/73 5-9
38 Wisconsin 0.001 1375.67 82.67 19/71 5-9
39 Georgia Tech 0.001 1228.1 117.95 21/105 13-6
40 Middlebury 0 1807.95 69.53 8/28 11-0
41 Carleton College-Eclipse 0 1605.36 173.14 6/73 15-6
42 Wellesley 0 1528.75 135.72 10/80 12-1
43 Portland 0 1499.88 107.02 12/73 12-1
44 Brown-B 0 1454.87 74.09 20/59 6-0
45 James Madison 0 1407.42 53.54 26/58 15-2
46 Santa Clara 0 1405.95 77.61 22/67 12-9
47 Pennsylvania 0 1368.71 75.47 22/71 6-8
48 Washington University 0 1356.84 79.1 23/70 14-6
49 Whitman 0 1345.46 91.57 24/96 9-0
50 Texas 0 1337.76 81.03 26/72 5-14
51 Montana State 0 1336.92 80.81 28/70 4-0
52 California-Santa Cruz 0 1305.52 78.57 31/77 15-7
53 Georgetown 0 1304.65 79.3 25/75 12-7
54 Arkansas 0 1297.15 106.21 26/91 11-2
55 Haverford/Bryn Mawr 0 1271.17 99.06 23/90 10-2
56 Cal Poly-SLO 0 1249.98 72.31 30/91 10-13
57 Appalachian State 0 1233.08 70.73 38/85 6-9
58 Penn State 0 1226.18 62.21 39/80 5-8
59 Virginia Tech 0 1216.91 63.05 38/85 10-8
60 Ohio 0 1178.04 107.55 30/106 12-7
61 William & Mary 0 1160.87 114.35 33/109 6-7
62 Tennessee 0 1157.82 105.93 38/102 12-5
63 Winona State 0 1155.31 79.22 42/91 15-2
64 Williams 0 1149.81 106.5 40/110 7-5
65 Kansas 0 1149.48 59 47/93 7-4
66 Carnegie Mellon 0 1123.91 120.32 35/127 2-3
67 Case Western Reserve 0 1123.47 89.16 42/110 4-9
68 Massachusetts 0 1120.85 103.25 39/114 6-7
69 Northwestern 0 1115.6 72.57 41/106 9-11
70 Iowa State 0 1113.96 71.97 40/103 15-4
71 American 0 1107.58 84.65 34/105 9-4
72 Utah 0 1085.46 72.25 48/103 4-20
73 Tennessee-Chattanooga 0 1073.62 123.57 26/123 7-3
74 Boston University 0 1058.61 61.81 54/102 7-7
75 Lewis & Clark 0 1045.81 87.4 40/113 7-6
76 Nevada-Reno 0 1037.78 64.04 55/109 11-7
77 Oregon State 0 1035.52 106.64 43/122 4-4
78 Cornell 0 1029.45 56.41 55/102 5-1
79 Central Florida 0 1013.63 98.71 49/125 11-7
80 St. Olaf 0 1008.73 86.82 54/123 10-2
81 Temple -B 0 1005.46 108.98 48/126 3-3
82 Trinity 0 999.46 102.35 37/127 13-4
83 Dartmouth 0 998.18 183.13 25/157 3-2
84 Temple 0 978.57 130.13 41/142 3-8
85 California-Irvine 0 970.6 66.19 62/113 9-3
86 Southern California 0 957.27 67.12 66/115 7-17
87 Boston College 0 957.02 79.65 62/127 8-3
88 Kentucky 0 956.82 144.19 40/146 4-3
89 Catholic 0 954.5 107.64 51/140 3-4
90 Vermont-B 0 952.12 126.22 44/148 5-1
91 William & Mary-B 0 950.58 63.78 66/119 2-4
92 Lehigh 0 943.24 111.58 47/141 7-5
93 Clemson 0 940.48 151.34 42/159 3-3
94 South Carolina-B 0 937.38 157.79 39/154 3-3
95 Columbia 0 934.73 69.12 64/122 6-11
96 MIT 0 928.02 78.79 63/123 2-3
97 Claremont 0 924.95 54.66 70/114 11-7
98 Seattle 0 920.82 95.12 59/131 3-2
99 Colorado College 0 919.85 77.73 61/123 10-8
100 Delaware 0 865.86 148.63 45/159 4-2
101 Ithaca 0 860.97 75.37 75/139 6-6
102 Iowa 0 860.23 58.21 72/127 12-8
103 Michigan Tech 0 856.37 56.25 82/123 7-4
104 Virginia Commonwealth 0 853.4 76.35 64/131 3-10
105 Alabama-Huntsville 0 853 117.65 58/153 2-3
106 Texas State 0 840.57 90.24 66/142 14-5
107 Bates 0 832.63 104.27 63/146 2-4
108 American-B 0 818.31 100.95 66/155 3-2
109 Occidental 0 815.06 83.06 68/147 6-5
110 California-San Diego-B 0 810.12 54.56 83/134 9-10
111 Charleston 0 805.7 184.51 49/179 6-4
112 Rice 0 802.21 94.1 69/146 8-6
113 Cedarville 0 799.29 80.45 78/149 5-5
114 Marquette 0 790.78 82.82 80/149 3-3
115 Union (Tennessee) 0 756.76 116.56 65/164 8-9
116 Harvard 0 731.35 94.5 82/158 5-6
117 SUNY-Geneseo 0 725.71 162.59 55/172 1-5
118 New Hampshire 0 713.94 133.67 65/168 4-3
119 San Diego State 0 712.09 92.43 84/164 2-5
120 Texas A&M 0 711.28 63.61 99/159 8-4
121 Saint Louis 0 699.52 61.41 99/149 6-5
122 Purdue 0 691.65 83.17 90/167 4-3
123 Arizona 0 685.44 64.5 95/153 7-4
124 Syracuse 0 678.79 120.57 70/167 4-2
125 John Brown 0 676.32 90.81 85/161 2-4
126 Johns Hopkins 0 674.07 96.28 81/167 3-4
127 Puget Sound 0 673.5 155.61 63/183 2-3
128 Rochester 0 666.88 76.37 95/159 5-2
129 Emory 0 636.55 152.35 64/196 7-4
130 Liberty 0 631.48 60.95 106/158 4-13
131 Nebraska 0 623.64 97.05 84/175 3-3
132 George Washington-B 0 619.66 98.71 91/174 0-5
133 Mary Washington 0 618.32 71.05 101/164 5-8
134 Brandeis 0 614.14 95.73 99/168 6-6
135 NYU 0 612.75 111.24 93/175 2-3
136 Rhode Island 0 605.87 92.34 97/174 4-3
137 Michigan State 0 597.22 97.9 100/178 3-3
138 Cincinnati 0 595.28 45.98 119/159 4-2
139 Towson 0 595.2 130.55 81/186 3-4
140 Alabama 0 592.88 87.51 103/174 8-8
141 West Chester 0 575.75 108.42 89/177 4-2
142 Montana 0 572.26 91.78 96/173 0-3
143 North Carolina-B 0 569.51 158.47 81/200 2-10
144 Denver 0 562.08 61.2 116/166 9-3
145 Virginia-B 0 551.38 77.56 105/170 3-9
146 Macalester 0 549.74 62.28 113/167 4-8
147 Portland-B 0 541.8 201.02 71/207 2-3
148 Connecticut College 0 529.41 92.18 100/180 2-3
149 Knox 0 524.1 82.11 110/173 3-2
150 Skidmore 0 509.12 93.07 115/188 2-3
151 Maryland 0 508.14 65.14 119/172 0-5
152 Washington University-B 0 501.52 92.02 111/183 3-3
153 Sam Houston 0 501.44 61.86 123/171 5-6
154 Loyola-Chicago 0 483.53 83.95 115/180 2-8
155 Grinnell 0 468.49 45.24 131/170 2-4
156 Luther 0 447.55 81.51 124/180 1-5
157 Franciscan 0 446.17 102.86 118/192 2-4
158 Arizona State 0 445.42 65.08 127/179 8-8
159 Stanford-B 0 390.4 67.46 131/192 4-11
160 Illinois 0 372.41 47.67 145/180 7-7
161 Swarthmore 0 372.09 66.53 137/183 1-4
162 Washington-B 0 359.18 129.07 110/205 2-4
163 UCLA-B 0 358.7 50.08 142/181 2-9
164 Truman State 0 351.63 112.87 111/203 2-4
165 Connecticut 0 342.95 118.85 118/205 4-8
166 George Washington 0 332.04 67.97 141/193 5-7
167 Michigan-B 0 331.35 172.77 95/213 3-2
168 Colorado Mines 0 326.07 65.61 145/193 3-8
169 Wisconsin-Eau Claire 0 314.63 164.44 108/212 0-4
170 Jacksonville State 0 294.35 85.64 143/203 7-9
171 Wesleyan 0 286.92 97.98 137/207 2-3
172 SUNY-Stony Brook 0 268.19 194.49 107/221 1-2
173 Rutgers 0 263.33 113.91 128/211 1-4
174 Dayton 0 261.3 127.66 129/208 3-4
175 Colby 0 259.51 160.09 117/214 2-3
176 Missouri State 0 248.45 152.52 103/215 1-5
177 LSU 0 231.02 58.45 157/201 5-13
178 Chico State 0 222.34 92.01 149/207 2-12
179 Wisconsin-La Crosse 0 220.11 84.87 143/204 3-7
180 Northern Arizona 0 208.72 72.86 155/203 3-5
181 St Benedict 0 206.85 215.2 104/220 1-3
182 Tulane 0 197.65 176.86 127/218 3-3
183 Dickinson 0 180.96 82.06 157/209 3-6
184 Richmond 0 176.02 68.99 160/204 2-9
185 Georgetown-B 0 172.85 148.86 118/214 1-11
186 Texas-San Antonio 0 159.73 64.24 158/208 5-7
187 Indiana 0 156.05 117.09 151/213 2-4
188 Wisconsin-Milwaukee 0 147.71 125.53 148/213 2-3
189 Grand Canyon 0 141.06 100.62 152/213 3-4
190 Wisconsin-B 0 124.63 116.47 152/216 2-9
191 Bowdoin 0 118.31 142.7 140/216 0-6
192 Oberlin 0 105.64 113.5 156/217 4-3
193 Colorado-B 0 102.82 92.19 162/213 1-11
194 Pacific Lutheran 0 93.38 117.06 155/213 1-10
195 California-Davis-B 0 73.33 103.8 164/214 1-7
196 Princeton 0 44.64 86.4 166/213 1-5
197 College of New Jersey 0 30.13 93.83 165/214 2-7
198 Wake Forest 0 1.21 96.48 174/216 2-8
199 California-B 0 -14.67 141.6 154/220 1-6
200 Minnesota-Duluth 0 -21.29 138.85 163/220 4-7
201 North Texas 0 -24.46 130.3 161/220 4-8
202 North Carolina-Wilmington 0 -71.37 239.89 101/224 3-9
203 Miami (Florida) 0 -77.74 198.57 140/223 2-9
204 Georgia Tech-B 0 -80.5 155.52 158/221 2-9
205 Miami (Ohio) 0 -91.06 153.49 152/222 1-4
206 Northwestern-B 0 -94.42 109.94 182/222 2-11
207 Boston University-B 0 -117.98 199.54 146/224 0-6
208 Purdue-B 0 -119.67 168.48 165/223 1-4
209 Vanderbilt 0 -136.44 181.49 162/223 1-5
210 Columbia-B 0 -161.96 331.41 88/225 0-4
211 Oklahoma 0 -164.82 277.83 116/225 0-6
212 Florida Tech 0 -184.5 217.36 146/224 3-9
213 SUNY-Albany 0 -191.65 196.07 152/224 1-3
214 Minnesota-B 0 -237.6 173.49 162/224 0-6
215 Houston 0 -249.4 146.44 181/224 1-5
216 St. Olaf-B 0 -291.5 217.38 173/225 1-4
217 South Florida 0 -296.97 234.61 141/225 1-5
218 Elon 0 -311.04 186.59 170/224 0-12
219 Florida-B 0 -380.67 225.89 166/225 3-9
220 Arizona-B 0 -458.94 100.98 209/225 0-6
221 Texas-B 0 -533.39 315.95 158/225 0-6
222 Notre Dame-B 0 -592.63 228.33 190/225 0-6
223 Georgia Southern 0 -785.12 494.14 124/225 1-3
224 Emory-B 0 -811.43 257.66 202/225 1-11
225 Georgia-B 0 -1023.88 434.98 101/225 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)