Probabilistic Bid Allocation

2023-24 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Bid Allocation

Bids Region Total Contributing Teams
1 Atlantic Coast 1.07 North Carolina 100.00%,   North Carolina State 6.70%,   South Carolina 0.30%,   American 0.20%,  
1 Great Lakes 1.43 Michigan 100.00%,   Notre Dame 43.20%,  
1 Metro East 0
2 New England 2.68 Tufts 100.00%,   Vermont 100.00%,   Northeastern 67.80%,  
1 North Central 1.01 Carleton College 100.00%,   Minnesota 0.40%,   Wisconsin 0.30%,  
6 Northwest 5.8 British Columbia 100.00%,   Washington 100.00%,   Oregon 100.00%,   Brigham Young 100.00%,   Western Washington 99.50%,   Victoria 79.00%,   Utah 1.90%,  
1 Ohio Valley 1.38 Pennsylvania 78.00%,   Ohio State 53.30%,   Pittsburgh 6.20%,   Ohio 0.10%,  
2 South Central 1.7 Colorado 100.00%,   Colorado State 70.20%,  
1 Southeast 0.89 Georgia 84.70%,   Central Florida 4.30%,   Georgia Tech 0.20%,  
4 Southwest 4.04 Stanford 100.00%,   California-Santa Barbara 100.00%,   California-Santa Cruz 95.10%,   California-San Diego 91.20%,   Cal Poly-SLO 10.80%,   California-Davis 6.50%,   California 0.10%,  

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 1.072 1.432 0.000 2.678 1.007 5.804 1.376 1.702 0.892 4.037
Autos (all @ 1) 0.072 0.432 -1.000 1.678 0.007 4.804 0.376 0.702 -0.108 3.037
Northwest (@ 2) 0.072 0.432 -1.000 1.678 0.007 3.804 0.376 0.702 -0.108 3.037
Northwest (@ 3) 0.072 0.432 -1.000 1.678 0.007 2.804 0.376 0.702 -0.108 3.037
Southwest (@ 2) 0.072 0.432 -1.000 1.678 0.007 2.804 0.376 0.702 -0.108 2.037
Northwest (@ 4) 0.072 0.432 -1.000 1.678 0.007 1.804 0.376 0.702 -0.108 2.037
Southwest (@ 3) 0.072 0.432 -1.000 1.678 0.007 1.804 0.376 0.702 -0.108 1.037
Northwest (@ 5) 0.072 0.432 -1.000 1.678 0.007 0.804 0.376 0.702 -0.108 1.037
New England (@ 2) 0.072 0.432 -1.000 0.678 0.007 0.804 0.376 0.702 -0.108 1.037
Southwest (@ 4) 0.072 0.432 -1.000 0.678 0.007 0.804 0.376 0.702 -0.108 0.037
Northwest (@ 6) 0.072 0.432 -1.000 0.678 0.007 -0.196 0.376 0.702 -0.108 0.037
South Central (@ 2) 0.072 0.432 -1.000 0.678 0.007 -0.196 0.376 -0.298 -0.108 0.037
Total 1 1 1 2 1 6 1 2 1 4

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 British Columbia 1 2894.15 64.25 1/4 16-1
2 Vermont 1 2789.63 72.26 1/6 19-1
3 Carleton College 1 2706.55 79.28 1/8 15-4
4 North Carolina 1 2622.41 90.56 1/12 22-3
5 Oregon 1 2605.7 70.95 1/10 18-2
6 Stanford 1 2558.63 78.15 1/11 14-6
7 Tufts 1 2520.18 75.02 2/11 18-3
8 Colorado 1 2458.07 51.77 4/12 14-6
9 California-Santa Barbara 1 2421.8 48.96 4/14 16-7
10 Washington 1 2348.78 68.26 5/17 13-7
11 Brigham Young 1 2318.86 69.12 6/19 7-5
12 Michigan 1 2311.61 60.57 6/18 14-6
13 Western Washington 0.995 2211.79 49.68 9/22 6-8
14 California-Santa Cruz 0.951 2180.23 64.58 10/27 6-8
15 California-San Diego 0.912 2162.55 66.19 8/27 10-11
16 Georgia 0.847 2154.75 83.61 9/32 7-6
17 Victoria 0.79 2121.36 60.78 11/30 8-10
18 Pennsylvania 0.78 2124.71 60.93 10/28 11-9
19 Colorado State 0.702 2113.2 78.05 10/33 10-5
20 Northeastern 0.678 2101.67 55.33 12/30 9-10
21 Ohio State 0.533 2082.16 59.45 12/32 21-6
22 Notre Dame 0.432 2055.17 90.49 11/37 12-6
23 Cal Poly-SLO 0.108 1971.29 87.75 13/43 13-11
24 North Carolina State 0.067 1928.54 94.31 12/59 7-5
25 California-Davis 0.065 1971.09 71.91 13/42 8-12
26 Pittsburgh 0.062 1962.92 79.25 15/41 10-10
27 Central Florida 0.043 1819.58 161.42 10/83 21-1
28 Utah 0.019 1921.93 74.63 17/44 10-12
29 Minnesota 0.004 1818.79 103.44 16/63 8-4
30 Wisconsin 0.003 1913.61 58.44 19/42 7-12
31 South Carolina 0.003 1763.12 111.97 20/85 7-6
32 Georgia Tech 0.002 1632.2 161.98 15/111 10-3
33 American 0.002 1584.8 166.69 15/114 9-1
34 California 0.001 1884.55 59.11 18/46 7-18
35 Ohio 0.001 1798.14 93.86 20/64 12-7
36 St Olaf 0 1921.34 104.67 11/58 19-2
37 Brown 0 1874.19 62.76 21/47 13-6
38 UCLA 0 1851.87 60.6 22/47 10-14
39 Texas-Dallas 0 1793.5 72.23 22/58 10-4
40 Washington University 0 1768.65 91.4 21/65 13-7
41 Virginia 0 1738.89 52.31 28/55 11-14
42 Union (Tennessee) 0 1718.54 141.14 18/95 18-2
43 SUNY-Binghamton 0 1703.59 50.81 32/58 6-8
44 Purdue 0 1700.79 109.41 23/77 8-4
45 Alabama-Huntsville 0 1700.69 106.88 23/85 17-3
46 Whitman 0 1692.34 93.15 22/82 6-6
47 Portland 0 1684.91 108.59 24/83 11-3
48 Texas 0 1676.99 82.73 27/71 8-11
49 Connecticut 0 1655.8 129.94 22/104 10-3
50 Carleton College-Eclipse 0 1643.69 114.92 23/98 15-3
51 Davidson 0 1613.93 94.05 30/82 4-1
52 Macalester 0 1608.92 62.03 33/75 9-3
53 Yale 0 1594.05 66.82 35/78 6-7
54 Haverford/Bryn Mawr 0 1561.45 78.59 34/89 13-1
55 Southern California 0 1556.09 45.11 43/73 6-11
56 Florida 0 1549.25 136.08 25/103 10-7
57 William & Mary 0 1544.4 109.71 33/100 4-7
58 Cornell 0 1527.53 99.65 33/93 8-4
59 Georgetown 0 1519.65 58.07 41/80 14-4
60 Colorado College 0 1518.43 66.06 41/81 12-6
61 Penn State 0 1503.49 75.57 38/93 8-10
62 Utah State 0 1501.32 116.27 31/115 6-0
63 Cincinnati 0 1497.99 140.61 30/123 10-3
64 Missouri 0 1484.36 103.78 28/105 8-4
65 Grand Canyon 0 1448.37 82.91 44/101 4-2
66 Tennessee 0 1434.85 80.09 41/101 11-6
67 Arizona 0 1433.92 109.94 37/109 8-1
68 Vermont-B 0 1423.71 149.22 34/125 11-3
69 California-San Diego-B 0 1422.37 65.05 47/96 10-8
70 James Madison 0 1419.57 86.89 37/108 7-7
71 Nevada-Reno 0 1398.78 61.92 51/103 9-3
72 Arkansas 0 1396.22 96.45 44/113 4-3
73 San Diego State 0 1388.37 90.14 41/109 10-3
74 Harvard 0 1382.6 150.64 29/132 7-6
75 Columbia 0 1374.91 60.21 54/104 8-10
76 Bates 0 1372.17 118.06 38/120 9-3
77 California-Irvine 0 1364.93 78.99 48/109 7-4
78 Kansas 0 1355.6 88.95 47/115 6-7
79 Williams 0 1343.83 65.34 50/106 9-3
80 Santa Clara 0 1335.36 71.92 54/109 8-2
81 Northwestern 0 1332.46 105.7 46/124 6-10
82 Northern Arizona 0 1330.1 48.83 61/104 3-3
83 Iowa State 0 1323.81 74.38 54/113 10-10
84 Wellesley 0 1313.8 91.34 50/116 9-6
85 Franciscan 0 1310.12 134.18 42/138 4-2
86 Indiana 0 1302.91 76.2 57/114 4-2
87 Virginia Tech 0 1297.26 57.57 55/112 8-10
88 Trinity 0 1294.64 79.95 55/117 15-5
89 Carnegie Mellon 0 1290.85 73.38 50/111 2-10
90 Lewis & Clark 0 1284.69 55.93 62/109 6-7
91 Saint Louis 0 1272.48 80.68 54/119 7-8
92 Wesleyan 0 1272.46 106.11 50/132 7-6
93 Duke 0 1267.64 82.82 60/128 10-8
94 Iowa 0 1252.41 62.57 68/115 7-5
95 Chicago 0 1251 64.51 67/118 6-16
96 Appalachian State 0 1220.34 128.83 48/150 3-7
97 Rochester 0 1217.18 74.59 70/122 10-5
98 Kenyon 0 1214.71 120.99 56/137 4-2
99 Davenport 0 1193.97 105.14 60/142 5-5
100 Tennessee-Chattanooga 0 1193.45 80.8 68/132 8-5
101 East Carolina 0 1172.52 74.9 66/124 9-4
102 Lehigh 0 1170.49 65.46 67/125 15-4
103 Massachusetts 0 1168.38 148.02 53/147 6-7
104 Rutgers 0 1156.74 100.81 63/146 7-5
105 Puget Sound 0 1151.16 74.18 69/134 5-7
106 Rice 0 1147.85 93.55 72/138 9-3
107 Middlebury 0 1146.44 165.75 38/162 6-8
108 Truman State 0 1124.52 106.39 65/142 6-8
109 Brandeis 0 1118.17 170.19 46/160 7-4
110 Rhode Island 0 1073.14 124.9 64/164 8-6
111 Maryland 0 1067.34 104.54 72/150 6-6
112 Denver 0 1064.82 67.22 92/138 9-16
113 West Chester 0 1060.72 92.29 80/148 6-8
114 Montana 0 1040.42 60.89 93/139 5-3
115 Arizona State 0 1033.73 171.12 57/181 2-4
116 Boston University 0 1026.85 107.62 74/153 5-7
117 Occidental 0 1021.24 99.53 75/152 3-4
118 Wisconsin-Eau Claire 0 1014.38 73.1 87/144 9-5
119 Johns Hopkins 0 1007.99 98.73 78/154 10-2
120 John Brown 0 1006.52 116.89 71/158 4-6
121 Illinois 0 987.6 52.62 102/141 12-8
122 Liberty 0 978.52 66.97 101/146 6-12
123 Claremont 0 969.82 141.18 76/169 3-9
124 Mount Holyoke 0 967.2 81.82 98/147 6-7
125 Colorado-B 0 949.77 110.36 87/160 2-3
126 Dartmouth 0 947.68 76.83 101/148 5-8
127 Cedarville 0 946.97 90.83 96/162 6-5
128 Richmond 0 946.74 70.18 103/150 7-4
129 Cal Poly-SLO-B 0 925.76 52.21 108/144 2-7
130 Marquette 0 918.77 99.29 87/159 1-6
131 Charleston 0 916.93 104.11 93/161 7-5
132 MIT 0 912.25 84.35 101/158 5-8
133 NYU 0 910.84 95.79 98/166 4-8
134 Florida State 0 910.04 132.42 79/168 6-6
135 Case Western Reserve 0 899.44 147.01 77/185 2-8
136 California-B 0 896.13 67.64 109/156 6-9
137 Oregon State 0 894.04 59.52 113/150 1-9
138 Boston College 0 855.31 53.9 118/153 6-6
139 Oberlin 0 850.51 89.46 108/165 3-3
140 Catholic 0 848.98 89.15 105/163 6-6
141 Kentucky 0 841.73 118.98 100/178 2-4
142 Missouri State 0 826.22 76.25 110/163 2-9
143 Emory 0 803.75 118.66 106/180 4-8
144 North Carolina-B 0 792.78 141.22 100/181 2-10
145 George Washington 0 791.23 73.4 112/163 10-7
146 Delaware 0 779.11 93.22 110/180 3-3
147 Texas A&M 0 765.22 77.59 116/169 7-6
148 Montana State 0 751.11 63.39 128/164 1-7
149 Clemson 0 722.32 194.4 89/196 3-6
150 Miami (Ohio) 0 715.4 20.19 141/161 1-6
151 Texas State 0 710.11 89.03 124/175 5-8
152 California-Davis-B 0 677.88 88.26 125/179 3-9
153 Knox 0 674.39 76.8 128/176 5-6
154 Berry 0 642.91 92.05 127/181 3-3
155 South Carolina-B 0 640.77 96.33 127/183 2-9
156 Temple 0 634.57 60.23 139/175 3-10
157 Ithaca 0 634 116.52 121/186 6-3
158 SUNY-Geneseo 0 598.3 51.9 146/182 3-9
159 Bentley 0 578.3 87.18 134/191 1-6
160 Wake Forest 0 574.52 138.72 120/195 4-7
161 Swarthmore 0 573.52 74.39 141/182 7-6
162 Colorado Mines 0 569.56 103.92 136/190 2-6
163 Butler 0 562.82 83.43 140/185 2-5
164 Stanford-B 0 560.45 218.99 87/209 1-2
165 Michigan-B 0 560.18 84.61 140/189 6-5
166 Skidmore 0 549.06 92.24 137/188 6-7
167 Georgia College 0 534.42 75.91 147/188 6-8
168 Vanderbilt 0 526.74 115.55 136/194 4-8
169 SUNY-Stony Brook 0 505.03 107.17 134/194 1-4
170 Arizona-B 0 476.56 109.42 140/196 0-6
171 Brown-B 0 468.68 147.59 135/202 1-4
172 Auburn 0 463.25 111.01 143/201 3-8
173 Virginia-B 0 461.64 155.48 122/201 1-10
174 UCLA-B 0 436.13 101.52 151/197 1-7
175 Alabama 0 426.38 106.63 148/200 5-9
176 Jacksonville State 0 422.56 122.4 133/200 5-8
177 Tulane 0 420.75 132.9 131/204 4-8
178 Texas-San Antonio 0 407.02 110.19 148/201 5-7
179 Washington University-B 0 402.54 100.96 145/199 4-9
180 Air Force 0 399.85 184.22 127/210 1-4
181 Georgia-B 0 393.46 110.25 145/203 3-9
182 Elon 0 347.39 133.34 143/203 1-5
183 Syracuse 0 309.87 79.23 165/201 5-8
184 Columbia-B 0 299.26 198.96 128/212 0-5
185 Miami (Florida) 0 296.4 74.21 168/201 1-4
186 Minnesota-B 0 270.18 236.32 118/214 0-5
187 North Carolina-Wilmington 0 266.07 138.96 154/209 2-4
188 Sam Houston 0 251.73 102.67 159/207 3-3
189 Colorado College-B 0 244.9 176.67 147/210 1-4
190 Messiah 0 236.14 48.68 177/200 2-3
191 Houston 0 217.1 154.14 144/213 2-4
192 Wisconsin-B 0 199.06 300.6 84/215 0-5
193 Dayton 0 172.26 231.99 129/213 0-6
194 Xavier 0 168.75 240.85 136/214 1-5
195 Georgia Southern 0 127.32 172.21 158/212 2-4
196 Georgetown-B 0 109.48 127.32 171/210 0-5
197 Connecticut College 0 105.54 66.99 184/207 3-7
198 Vermont-C 0 99.64 98.36 175/208 3-3
199 LSU 0 81.9 116.14 172/210 4-15
200 Dickinson 0 75.69 117.45 166/210 1-8
201 North Texas 0 53.19 171.84 159/213 2-7
202 Texas-B 0 50.33 94.36 184/209 1-12
203 California-San Diego-C 0 17.67 227.43 146/215 0-5
204 Northwestern-B 0 -26.07 137 179/212 1-11
205 Emory-B 0 -31.5 178.79 173/214 0-5
206 William & Mary-B 0 -111.77 172.56 174/214 1-4
207 Alabama-Birmingham 0 -162.69 265.15 150/215 0-10
208 Florida Tech 0 -193.33 202.32 170/215 1-11
209 Florida-B 0 -252.96 192.38 179/215 1-12
210 Northeastern-B 0 -281.54 299.32 147/215 1-6
211 SUNY-Albany 0 -360.51 72.16 206/215 1-7
212 American-B 0 -411.68 314.64 161/215 0-5
213 Notre Dame-B 0 -427.77 291.7 169/215 1-5
214 Cornell-B 0 -492.7 177.38 201/215 1-9
215 Clark 0 -881.54 565.8 126/215 1-6

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)