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 North Carolina 100.00%,   American 0.30%,   William & Mary 0.10%,  
1 Great Lakes 1.22 Michigan 99.60%,   Notre Dame 21.90%,  
1 Metro East 0 SUNY-Binghamton 0.10%,  
2 New England 2.31 Tufts 100.00%,   Vermont 100.00%,   Northeastern 29.40%,   Brown 1.50%,  
1 North Central 1.03 Carleton College 100.00%,   Wisconsin 3.40%,  
6 Northwest 6.03 British Columbia 100.00%,   Washington 100.00%,   Oregon 100.00%,   Brigham Young 99.90%,   Victoria 99.80%,   Western Washington 98.80%,   Utah 4.50%,  
1 Ohio Valley 1.31 Pennsylvania 98.10%,   Pittsburgh 25.60%,   Ohio State 7.60%,  
2 South Central 1.91 Colorado 100.00%,   Colorado State 90.70%,  
1 Southeast 0.81 Georgia 66.80%,   Alabama-Huntsville 7.70%,   Central Florida 6.40%,  
4 Southwest 4.38 Stanford 100.00%,   California-Santa Barbara 100.00%,   California-San Diego 99.70%,   California-Santa Cruz 88.70%,   California-Davis 46.20%,   California 1.80%,   UCLA 0.80%,   Cal Poly-SLO 0.60%,  

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 1.004 1.215 0.001 2.309 1.034 6.030 1.313 1.907 0.809 4.378
Autos (all @ 1) 0.004 0.215 -0.999 1.309 0.034 5.030 0.313 0.907 -0.191 3.378
Northwest (@ 2) 0.004 0.215 -0.999 1.309 0.034 4.030 0.313 0.907 -0.191 3.378
Northwest (@ 3) 0.004 0.215 -0.999 1.309 0.034 3.030 0.313 0.907 -0.191 3.378
Southwest (@ 2) 0.004 0.215 -0.999 1.309 0.034 3.030 0.313 0.907 -0.191 2.378
Northwest (@ 4) 0.004 0.215 -0.999 1.309 0.034 2.030 0.313 0.907 -0.191 2.378
Southwest (@ 3) 0.004 0.215 -0.999 1.309 0.034 2.030 0.313 0.907 -0.191 1.378
Northwest (@ 5) 0.004 0.215 -0.999 1.309 0.034 1.030 0.313 0.907 -0.191 1.378
Southwest (@ 4) 0.004 0.215 -0.999 1.309 0.034 1.030 0.313 0.907 -0.191 0.378
New England (@ 2) 0.004 0.215 -0.999 0.309 0.034 1.030 0.313 0.907 -0.191 0.378
Northwest (@ 6) 0.004 0.215 -0.999 0.309 0.034 0.030 0.313 0.907 -0.191 0.378
South Central (@ 2) 0.004 0.215 -0.999 0.309 0.034 0.030 0.313 -0.093 -0.191 0.378
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 2770.47 53.22 1/4 24-2
2 Vermont 1 2677.17 107.88 1/11 26-1
3 Carleton College 1 2622 95.52 1/10 22-4
4 Oregon 1 2569.05 66.89 1/8 26-4
5 Stanford 1 2519.88 70.31 1/10 21-6
6 North Carolina 1 2499.4 84.4 1/11 34-3
7 Colorado 1 2426.24 74.83 2/12 20-6
8 Tufts 1 2355.7 75.26 3/17 25-5
9 California-Santa Barbara 1 2326.41 43.96 5/13 24-9
10 Washington 1 2258.08 65.7 6/20 19-13
11 Brigham Young 0.999 2256.04 87.46 5/21 13-7
12 Victoria 0.998 2153.37 61.18 8/21 14-13
13 California-San Diego 0.997 2142.18 51.87 9/23 19-13
14 Michigan 0.996 2199.69 84.8 7/24 27-6
15 Western Washington 0.988 2132.74 62.7 9/24 9-14
16 Pennsylvania 0.981 2099.13 51.63 10/24 22-9
17 Colorado State 0.907 2071.59 64.59 10/27 16-7
18 California-Santa Cruz 0.887 2078.47 79.06 8/28 14-11
19 Georgia 0.668 2028.17 107.59 6/43 18-6
20 California-Davis 0.462 1981.44 52.83 14/32 14-16
21 Northeastern 0.294 1959.88 51.63 15/34 15-12
22 Pittsburgh 0.256 1934.21 72.2 14/42 19-12
23 Notre Dame 0.219 1931.53 74.19 12/40 23-8
24 Alabama-Huntsville 0.077 1832.1 106.98 12/61 27-4
25 Ohio State 0.076 1893.87 63.09 16/43 27-10
26 Central Florida 0.064 1817.19 116.78 10/69 30-2
27 Utah 0.045 1886.02 59.41 17/41 15-16
28 Wisconsin 0.034 1877.17 55.32 17/39 13-13
29 California 0.018 1856.51 55.92 18/41 13-24
30 Brown 0.015 1869.14 50.42 18/41 20-9
31 UCLA 0.008 1853.18 47.58 18/40 19-19
32 Cal Poly-SLO 0.006 1841.91 58.73 18/45 19-19
33 American 0.003 1723.68 90.9 20/65 18-2
34 William & Mary 0.001 1759.89 73.13 18/56 13-8
35 SUNY-Binghamton 0.001 1720.35 59.43 19/57 16-8
36 Union (Tennessee) 0 1801.17 128.88 13/82 20-2
37 Washington University 0 1784.16 73.37 21/64 20-9
38 St Olaf 0 1778.48 91.71 14/62 22-4
39 Carleton College-Eclipse 0 1749.41 136.47 13/79 19-4
40 Minnesota 0 1713.8 76.29 23/63 14-7
41 South Carolina 0 1698.94 73.85 24/65 16-10
42 Texas-Dallas 0 1679.92 68.77 26/70 18-6
43 Portland 0 1661.6 68.87 27/65 15-4
44 Yale 0 1646.48 56.68 31/63 17-8
45 Macalester 0 1642.54 131.26 19/89 13-3
46 Whitman 0 1640.31 86.83 26/85 10-8
47 Southern California 0 1636.66 50.31 34/67 14-17
48 Colorado College 0 1613.36 70.29 29/74 18-7
49 Ohio 0 1606.71 82.46 28/83 17-11
50 Georgetown 0 1601.27 60.87 35/73 21-7
51 Virginia 0 1577.69 51.75 37/70 15-19
52 Haverford/Bryn Mawr 0 1569.87 72.08 35/82 21-2
53 Texas 0 1561.29 71.03 33/86 17-14
54 Georgia Tech 0 1548.96 78.2 32/89 18-7
55 North Carolina State 0 1543.77 70.59 32/84 13-10
56 Connecticut 0 1529.14 79.87 36/94 15-9
57 Cornell 0 1526.29 56.82 39/86 15-8
58 Purdue 0 1516.42 73.76 37/89 16-9
59 Utah State 0 1509.14 89.59 32/98 7-2
60 Florida 0 1493.44 86.97 35/99 17-10
61 Duke 0 1484.05 66.18 42/95 18-12
62 Tennessee 0 1478.12 77.37 41/95 19-10
63 Penn State 0 1476.98 60.92 42/97 15-15
64 James Madison 0 1462.49 76.09 38/102 11-12
65 Trinity 0 1456.11 70.57 41/96 20-6
66 Nevada-Reno 0 1439.92 79.42 39/100 11-6
67 Vermont-B 0 1437.43 71.64 41/97 19-5
68 Grand Canyon 0 1436.37 73.78 43/98 9-5
69 Northwestern 0 1419.28 72.98 46/96 15-12
70 Columbia 0 1407.82 61.8 49/100 15-16
71 Santa Clara 0 1396.79 69.75 51/105 11-9
72 Wellesley 0 1391.76 58.7 51/97 17-7
73 Lewis & Clark 0 1375.08 69.86 49/106 10-9
74 Arizona 0 1369.93 81.84 49/116 10-2
75 Missouri 0 1368.96 66.99 48/104 13-7
76 Harvard 0 1364.9 68.58 43/107 12-10
77 San Diego State 0 1360.25 52.57 56/102 15-11
78 Cincinnati 0 1354.51 102.44 42/122 14-7
79 Wesleyan 0 1353.32 76.23 47/110 15-6
80 Rochester 0 1344.48 53.86 56/103 16-6
81 Kansas 0 1343 79.3 49/114 10-8
82 California-San Diego-B 0 1339.27 54.94 52/109 14-12
83 Williams 0 1333.84 50.35 61/109 15-5
84 Bates 0 1332.33 91.79 48/122 14-6
85 California-Irvine 0 1309.28 50.67 64/112 10-11
86 Virginia Tech 0 1306.92 54.7 64/112 12-15
87 MIT 0 1306.4 73.5 52/121 10-13
88 Tennessee-Chattanooga 0 1305.72 56.98 59/110 15-11
89 Middlebury 0 1304.95 79.01 58/123 14-9
90 Rice 0 1281.27 74.02 54/119 12-6
91 Lehigh 0 1275.7 55.04 62/115 21-6
92 Iowa State 0 1253.51 57.54 63/119 14-15
93 Stanford-B 0 1235.17 126.17 51/150 3-3
94 Maryland 0 1234.7 75.73 63/129 10-12
95 Chicago 0 1219.77 56.93 71/125 11-22
96 Davenport 0 1219.44 163.02 38/155 12-5
97 Rhode Island 0 1213.69 86.16 63/130 12-11
98 Iowa 0 1212.27 70.87 68/129 11-10
99 Clemson 0 1199.73 82.9 66/131 8-13
100 Appalachian State 0 1196.7 77.74 66/133 8-13
101 Mount Holyoke 0 1188.61 75.18 70/135 13-10
102 Michigan Tech 0 1188.38 93.29 67/134 9-6
103 Florida State 0 1182.08 69.49 72/129 12-12
104 West Chester 0 1179.47 69.92 69/129 11-15
105 Brandeis 0 1165.91 58.84 80/126 12-8
106 Rutgers 0 1165.12 70.72 71/134 11-13
107 NYU 0 1141.12 77.36 75/145 11-15
108 Carnegie Mellon 0 1134.03 66.19 81/134 4-19
109 Saint Louis 0 1131.28 60.4 83/132 12-12
110 Richmond 0 1126.29 62.84 80/136 12-5
111 Denver 0 1119.61 57.06 84/133 12-20
112 Montana 0 1112.89 83.28 65/142 7-11
113 Puget Sound 0 1110.05 39.34 93/130 7-11
114 Northern Arizona 0 1087.3 73.71 86/144 3-6
115 Charleston 0 1082.15 79.43 82/153 11-12
116 Temple 0 1078.5 71.76 84/144 8-17
117 Boston College 0 1075.76 65.86 87/148 9-12
118 East Carolina 0 1073.86 75.42 88/145 11-9
119 Arkansas 0 1071.77 84.26 83/156 6-6
120 Johns Hopkins 0 1062.17 74.25 87/145 12-10
121 Massachusetts 0 1042.94 100.82 69/154 8-14
122 Wisconsin-Eau Claire 0 1041.07 76.49 91/152 12-6
123 Illinois 0 1037.5 45.96 101/140 18-13
124 Boston University 0 1020.93 110.46 85/160 5-10
125 Occidental 0 1014.86 83.08 87/159 6-5
126 Cedarville 0 1002.53 61.81 104/151 11-7
127 Truman State 0 981.98 83.04 93/155 8-11
128 Franciscan 0 981 145.51 52/171 4-2
129 Claremont 0 978.82 118.75 80/166 4-11
130 Arizona State 0 955.01 100.84 90/164 3-10
131 California-B 0 947.01 66.3 105/156 8-13
132 Liberty 0 946.76 44.91 116/152 7-20
133 Indiana 0 928.81 94.63 95/160 6-5
134 Ithaca 0 920.19 84.89 96/159 9-8
135 John Brown 0 919.46 81.36 93/157 5-10
136 Skidmore 0 912.28 73.8 107/159 11-12
137 Dartmouth 0 906.1 70.86 106/158 8-12
138 New Hampshire 0 891.89 72.14 109/160 7-13
139 Marquette 0 885.92 81.12 112/162 3-8
140 Cal Poly-SLO-B 0 881.05 57.66 118/159 3-9
141 Texas A&M 0 877.51 56.89 120/159 11-12
142 North Carolina-B 0 867.95 89.95 100/170 8-10
143 Delaware 0 865.51 62.76 120/160 5-6
144 Texas State 0 861.23 83.63 109/165 8-14
145 Oregon State 0 859.31 121.7 94/180 1-17
146 Tulane 0 848.55 63.2 122/160 10-14
147 George Washington 0 840.57 63.78 122/162 11-9
148 Case Western Reserve 0 834.5 89.13 105/165 2-16
149 Kenyon 0 825.76 65.9 120/163 7-7
150 Emory 0 816.03 62.72 128/164 9-15
151 Catholic 0 812.68 74.32 120/163 8-10
152 SUNY-Stony Brook 0 806.94 62.38 127/164 3-7
153 Swarthmore 0 777.22 59.64 130/165 10-12
154 Colorado-B 0 772.75 180.6 78/201 2-5
155 Jacksonville State 0 761.77 53.38 134/167 12-13
156 Montana State 0 754.59 107.13 106/176 1-10
157 Kentucky 0 718.59 107.74 113/187 4-6
158 Missouri State 0 682.97 57.6 142/174 3-12
159 Minnesota-B 0 627.62 163.13 117/199 1-8
160 Vermont-C 0 610.94 104.66 128/191 6-10
161 Knox 0 609.1 95.93 135/190 9-9
162 South Carolina-B 0 606.54 104.59 135/196 2-9
163 California-Davis-B 0 596.28 79.86 142/188 4-11
164 UCLA-B 0 585.49 81.85 147/188 2-8
165 Colorado Mines 0 578.65 108.43 127/193 2-6
166 Wake Forest 0 566.45 93.46 141/194 5-12
167 Michigan-B 0 553.14 78.16 146/189 8-13
168 Syracuse 0 552.54 89.5 148/193 5-11
169 Connecticut College 0 551.06 48.46 155/180 5-9
170 SUNY-Geneseo 0 538.01 56.68 156/185 4-16
171 Georgia College 0 519.2 85.63 153/196 6-10
172 Washington University-B 0 511.38 77.45 154/192 4-14
173 Texas-San Antonio 0 486.27 85.87 154/197 7-10
174 Sam Houston 0 467.35 94.07 154/202 6-8
175 Arizona-B 0 465.61 97.34 148/200 0-6
176 Columbia-B 0 442.28 101 153/200 1-9
177 Alabama 0 434.07 89.78 155/201 8-17
178 Oberlin 0 426.88 66.43 160/196 4-9
179 Elon 0 407.21 112.22 149/202 1-9
180 Texas-B 0 386.61 75.93 164/199 5-18
181 Messiah 0 377.96 105.06 159/204 2-7
182 Brown-B 0 368.51 130.36 156/208 2-7
183 Miami (Ohio) 0 349.33 26.49 177/196 1-6
184 Air Force 0 332.42 210.31 125/211 1-4
185 Vanderbilt 0 332.2 113.24 160/207 7-14
186 Auburn 0 328.01 92.36 157/204 4-13
187 Houston 0 321.58 112.77 158/208 3-11
188 Miami (Florida) 0 317.24 125.64 154/207 3-8
189 Northeastern-B 0 305.25 99.39 164/208 2-10
190 Georgetown-B 0 292.68 80.34 170/203 3-8
191 Georgia-B 0 284.36 109.17 162/207 6-17
192 William & Mary-B 0 283.01 110.77 161/206 4-7
193 Dickinson 0 273.22 118.61 159/209 1-8
194 LSU 0 256.64 92.63 168/208 7-24
195 Notre Dame-B 0 250.6 154.6 157/210 2-14
196 Colorado College-B 0 226.21 139.62 159/210 1-9
197 Butler 0 220.15 95.29 164/208 4-9
198 Carleton College-C 0 182.75 235.51 128/212 1-4
199 Virginia-B 0 159.59 167.2 159/212 1-14
200 Wisconsin-B 0 140.11 186.64 158/212 0-8
201 North Texas 0 99.18 126.8 169/211 2-13
202 Alabama-Birmingham 0 86.05 162.56 169/212 1-14
203 Florida Tech 0 61.95 182.46 163/212 1-11
204 Purdue-B 0 51.23 237.07 152/212 0-6
205 Northwestern-B 0 21.81 114.51 180/212 1-15
206 California-San Diego-C 0 17.59 182.65 162/212 0-7
207 SUNY-Albany 0 -15.01 105.5 191/212 1-12
208 American-B 0 -27.07 139.13 181/212 2-9
209 Florida-B 0 -164.95 173.74 187/212 1-17
210 Dayton 0 -194.86 275.51 138/212 0-6
211 Cornell-B 0 -282.78 171.08 196/212 1-9
212 St Olaf-B 0 -417.25 440.38 136/212 1-4

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)