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 1.34 North Carolina 91.70%,   Virginia 41.00%,   William & Mary 1.00%,   American 0.50%,   Georgetown 0.10%,  
1 Great Lakes 0.87 Michigan 86.80%,   Notre Dame 0.20%,  
1 Metro East 0.02 Cornell 2.30%,  
2 New England 2.9 Tufts 100.00%,   Vermont 99.90%,   Northeastern 90.00%,  
1 North Central 1 Carleton College 100.00%,  
6 Northwest 6.26 Oregon 100.00%,   Washington 100.00%,   British Columbia 100.00%,   Utah 99.80%,   Brigham Young 99.40%,   Victoria 74.70%,   Western Washington 52.20%,  
1 Ohio Valley 0.39 Ohio State 20.80%,   Pennsylvania 17.80%,   Pittsburgh 0.20%,   Ohio 0.10%,  
1 South Central 1.11 Colorado 100.00%,   Texas 8.10%,   Missouri 1.50%,   Colorado State 1.10%,   Texas-Dallas 0.40%,  
1 Southeast 0.01 Georgia Tech 0.80%,  
5 Southwest 6.1 California-Santa Cruz 100.00%,   Stanford 100.00%,   California-San Diego 100.00%,   Cal Poly-SLO 99.50%,   California-Davis 98.40%,   California-Santa Barbara 93.30%,   UCLA 17.80%,   California 0.60%,  

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 1.343 0.870 0.023 2.899 1.000 6.261 0.389 1.111 0.008 6.096
Autos (all @ 1) 0.343 -0.130 -0.977 1.899 0.000 5.261 -0.611 0.111 -0.992 5.096
Northwest (@ 2) 0.343 -0.130 -0.977 1.899 0.000 4.261 -0.611 0.111 -0.992 5.096
Southwest (@ 2) 0.343 -0.130 -0.977 1.899 0.000 4.261 -0.611 0.111 -0.992 4.096
Northwest (@ 3) 0.343 -0.130 -0.977 1.899 0.000 3.261 -0.611 0.111 -0.992 4.096
Southwest (@ 3) 0.343 -0.130 -0.977 1.899 0.000 3.261 -0.611 0.111 -0.992 3.096
Northwest (@ 4) 0.343 -0.130 -0.977 1.899 0.000 2.261 -0.611 0.111 -0.992 3.096
Southwest (@ 4) 0.343 -0.130 -0.977 1.899 0.000 2.261 -0.611 0.111 -0.992 2.096
Northwest (@ 5) 0.343 -0.130 -0.977 1.899 0.000 1.261 -0.611 0.111 -0.992 2.096
Southwest (@ 5) 0.343 -0.130 -0.977 1.899 0.000 1.261 -0.611 0.111 -0.992 1.096
New England (@ 2) 0.343 -0.130 -0.977 0.899 0.000 1.261 -0.611 0.111 -0.992 1.096
Northwest (@ 6) 0.343 -0.130 -0.977 0.899 0.000 0.261 -0.611 0.111 -0.992 1.096
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 2901.21 99.61 1/4 13-0
2 Tufts 1 2737.84 97.15 1/7 11-0
3 Carleton College 1 2708.16 115.63 1/9 8-2
4 Oregon 1 2564.31 47.57 2/7 11-3
5 Colorado 1 2482.06 57.59 3/12 10-3
6 Stanford 1 2373.21 62.09 4/17 11-7
7 California-San Diego 1 2356.58 41.64 5/14 12-8
8 California-Santa Cruz 1 2345.27 41.26 5/16 12-8
9 Washington 1 2344.56 69.83 4/17 7-4
10 Vermont 0.999 2366.61 98.23 2/23 9-2
11 Utah 0.998 2330.78 89.52 3/22 7-7
12 Cal Poly-SLO 0.995 2270.8 100.05 3/22 14-6
13 Brigham Young 0.994 2210.64 62.9 6/22 9-6
14 California-Davis 0.984 2155.33 50.81 10/23 9-11
15 California-Santa Barbara 0.933 2161.32 75.51 7/27 11-8
16 North Carolina 0.917 2332.8 205.37 1/62 10-1
17 Northeastern 0.9 2122.77 74.24 7/27 6-5
18 Michigan 0.868 2156.96 110.35 6/29 5-0
19 Victoria 0.747 2078.42 60.61 12/28 4-10
20 Western Washington 0.522 2035.16 72.33 13/37 3-5
21 Virginia 0.41 2009.1 101.66 8/44 13-4
22 Ohio State 0.208 1926.9 122.69 11/53 8-4
23 Pennsylvania 0.178 1964.07 82.58 13/49 4-6
24 UCLA 0.178 1959.3 79.16 15/45 9-15
25 Texas 0.081 1878.54 111.58 12/61 1-6
26 Cornell 0.023 1781.93 124.15 15/64 6-1
27 Missouri 0.015 1809.93 103.03 19/60 11-1
28 Colorado State 0.011 1759.29 106.63 19/68 0-7
29 William & Mary 0.01 1790.38 101.03 18/63 3-2
30 Georgia Tech 0.008 1728.38 126.4 17/72 8-5
31 California 0.006 1752.36 105.51 17/66 6-7
32 American 0.005 1721.43 112.97 19/71 10-4
33 Texas-Dallas 0.004 1683.6 114.14 18/72 1-4
34 Pittsburgh 0.002 1804.85 67.67 20/52 5-5
35 Notre Dame 0.002 1797.85 68.7 20/52 4-3
36 Ohio 0.001 1846.76 63.91 21/48 5-2
37 Georgetown 0.001 1757.19 59.11 20/53 8-4
38 Carleton College-Eclipse 0 1919.26 93.46 13/49 10-3
39 Whitman 0 1791.77 97.12 19/64 12-2
40 Wisconsin 0 1766.57 59.58 23/54 4-7
41 Georgia 0 1725.96 68.18 22/58 3-2
42 Kenyon 0 1725.41 138.18 17/88 12-0
43 Minnesota 0 1718.24 36.63 29/52 2-3
44 Oregon State 0 1709.67 70.93 25/59 10-4
45 Southern California 0 1703.39 73.88 25/61 5-8
46 British Columbia-B 0 1695.84 107.31 17/79 4-3
47 Wesleyan 0 1678 81.53 22/71 7-0
48 California-Irvine 0 1676.72 86.42 26/68 13-4
49 Washington University 0 1670.87 111.77 21/73 10-3
50 Duke 0 1648.48 87.17 26/70 11-2
51 Portland 0 1639.15 89.11 24/71 8-5
52 Colorado College 0 1601.63 119.52 22/83 8-4
53 Santa Clara 0 1586.14 66.6 32/68 10-6
54 Liberty 0 1563.42 112.64 25/89 7-4
55 Haverford/Bryn Mawr 0 1512.61 105.85 27/84 9-4
56 Lewis & Clark 0 1510.13 110.04 28/87 4-3
57 South Carolina 0 1505.46 151.12 24/112 2-3
58 Connecticut 0 1503.35 70.44 41/79 4-2
59 Utah State 0 1480 114.44 32/89 3-1
60 St Olaf 0 1477.21 133.69 25/112 7-5
61 Davenport 0 1456.9 80.19 33/84 8-1
62 Rochester 0 1449.92 74.63 44/83 5-1
63 San Diego State 0 1449.58 123.2 32/107 6-0
64 North Carolina State 0 1442.6 78.71 44/88 5-6
65 MIT 0 1433.86 57.9 51/82 4-2
66 Wellesley 0 1407.97 96.59 32/92 5-1
67 Maryland 0 1385.89 84 47/105 8-5
68 James Madison 0 1381 87.53 46/94 7-5
69 Macalester 0 1378.37 151.98 29/118 5-2
70 Florida 0 1377.42 142.97 27/113 6-5
71 Columbia 0 1357.4 89.75 48/105 3-3
72 Montana 0 1357.38 76.27 51/97 4-3
73 Brown 0 1338.48 63.24 55/92 0-11
74 Union (Tennessee) 0 1328.02 52.59 57/93 4-0
75 Appalachian State 0 1319.8 108.21 45/112 4-6
76 Denver 0 1301.13 87.97 51/108 9-3
77 Grand Canyon 0 1292.78 96.21 53/110 5-1
78 NYU 0 1253.65 67.89 58/106 5-1
79 Tennessee 0 1249.86 74.04 62/109 3-2
80 Case Western Reserve 0 1247.55 142.72 45/130 1-4
81 Penn State 0 1240.15 97.76 57/111 7-5
82 California-San Diego-B 0 1231.17 103.93 56/125 7-6
83 Central Florida 0 1218.43 102.8 56/122 5-5
84 Occidental 0 1161.9 58.44 71/112 4-2
85 Chicago 0 1157.69 75.85 65/124 4-4
86 Butler 0 1155.45 75.23 67/117 5-2
87 Brown-B 0 1150.43 167.68 39/141 5-2
88 Cal Poly-SLO-B 0 1149.14 69.41 72/117 3-7
89 SUNY-Binghamton 0 1144.57 122.01 59/133 4-3
90 West Chester 0 1138.05 40.52 78/110 1-3
91 Ithaca 0 1135.73 117.4 56/131 3-3
92 Arizona State 0 1135.58 67.72 71/116 12-7
93 Northwestern 0 1133.03 95.63 62/126 3-8
94 Rice 0 1127.65 93.11 67/129 5-0
95 Northern Arizona 0 1126.01 132.26 57/134 2-4
96 Alabama-Huntsville 0 1125.53 225.82 22/153 1-3
97 Cedarville 0 1106.14 91.91 65/128 5-1
98 Vermont-B 0 1104.25 104.85 65/130 2-1
99 California-B 0 1098.48 83.35 70/128 5-6
100 Stanford-B 0 1082.07 113.17 61/131 1-5
101 Richmond 0 1077.04 89.51 60/129 2-3
102 Yale 0 1073.52 76.05 76/125 3-3
103 Cincinnati 0 1065.31 75.6 68/133 4-2
104 Purdue 0 1062.39 123.1 68/141 1-4
105 Lehigh 0 1059.31 90.25 72/128 8-6
106 Iowa 0 1047.56 63.81 83/125 5-1
107 Iowa State 0 1040.09 53.74 83/122 8-4
108 Claremont 0 1036.24 107.4 64/139 3-8
109 Michigan-B 0 1012.03 55.21 86/128 2-2
110 Trinity 0 977.01 62.62 82/130 6-4
111 George Washington 0 969.97 76.68 81/140 7-5
112 Massachusetts 0 955.82 59.34 85/130 3-3
113 Puget Sound 0 941.74 49.61 97/130 5-7
114 Temple 0 938.82 114.33 72/144 1-4
115 Wisconsin-Eau Claire 0 927.44 105.66 83/140 4-3
116 Kansas 0 919.54 95.2 81/141 3-3
117 Nevada-Reno 0 917.23 88.5 82/141 3-7
118 Montana State 0 916.8 75.07 85/140 2-5
119 Illinois 0 916.34 55.32 97/139 4-3
120 California-Davis-B 0 905.64 94.61 82/144 1-5
121 Virginia Tech 0 900.39 135.21 74/149 1-4
122 Emory 0 893.06 153.5 66/150 2-4
123 Arkansas 0 890.23 79.39 86/143 3-3
124 Swarthmore 0 879.79 79.99 87/141 5-2
125 Syracuse 0 838.41 53.93 108/138 3-4
126 Catholic 0 835.52 101.05 92/147 3-8
127 Wake Forest 0 822.17 93.86 91/150 3-3
128 Delaware 0 816.9 81.91 102/147 3-3
129 North Carolina-B 0 792.88 98.89 97/149 3-9
130 Marquette 0 791.07 32.92 117/139 0-2
131 Tulane 0 783.25 101.98 101/153 3-2
132 Arizona 0 759.35 59.79 116/148 6-12
133 SUNY-Geneseo 0 732.04 116.79 95/157 1-6
134 Indiana 0 724.87 116.41 99/157 4-2
135 Jacksonville State 0 714.25 66.48 113/149 0-3
136 Colorado-B 0 705.34 57.71 119/148 3-9
137 Saint Louis 0 701.23 55.54 120/149 3-3
138 Carnegie Mellon 0 696.85 123.84 101/157 1-5
139 Florida State 0 695.72 64 116/148 4-5
140 Miami (Florida) 0 653.24 47.17 127/151 8-7
141 Harvard 0 612.7 143.51 91/165 1-4
142 Colorado Mines 0 601.14 83.69 119/159 5-5
143 Boston College 0 581.18 146.78 99/171 1-5
144 Utah-B 0 566.11 144.8 110/171 0-7
145 Oberlin 0 542.95 88.98 123/165 1-4
146 UCLA-B 0 534.3 94.86 118/164 4-7
147 St Olaf-B 0 533.22 124.73 115/166 1-7
148 Texas A&M 0 507.5 75.39 132/163 2-4
149 Missouri State 0 499.2 188.44 85/176 1-4
150 Dayton 0 490.66 152.59 106/175 2-5
151 Knox 0 430.47 150.77 120/174 1-5
152 Texas State 0 409 17.01 147/160 0-2
153 Georgetown-B 0 405.9 135.59 117/173 1-5
154 Truman State 0 401.41 118.69 127/172 5-7
155 Johns Hopkins 0 396.94 68.65 142/171 1-4
156 Cornell-B 0 375.68 127.37 130/175 1-5
157 William & Mary-B 0 355.2 70.27 144/170 0-6
158 Vanderbilt 0 347.45 58.38 147/171 5-4
159 Florida Tech 0 325.1 0 154/165 1-1
160 Skidmore 0 298.63 111.73 139/176 1-5
161 Arizona-B 0 260.45 151.16 130/178 0-6
162 Emory-B 0 242.97 310.04 102/182 0-6
163 Alabama 0 211.47 71.06 153/174 4-4
164 Texas-B 0 202.01 118.26 144/177 0-4
165 Miami (Ohio) 0 190.66 73.97 152/175 2-4
166 Dickinson 0 177.84 116.47 146/178 1-5
167 Washington University-B 0 168.61 67.93 154/176 2-4
168 Washington-B 0 158.42 112.22 150/179 1-3
169 American-B 0 150.61 153.44 141/179 1-6
170 Pennsylvania-B 0 131.65 210.27 132/181 0-7
171 Florida-B 0 111.08 203.55 137/181 1-5
172 Wisconsin-B 0 101.47 90.88 149/178 0-5
173 John Brown 0 51.67 226.17 129/182 0-4
174 Georgia-B 0 45.46 218.51 135/182 0-6
175 California-San Diego-C 0 37.15 218.91 131/182 1-10
176 Georgia Tech-B 0 -96.6 209.82 145/182 1-5
177 Northwestern-B 0 -104.47 215.93 148/182 0-5
178 Purdue-B 0 -201.32 108.77 167/182 0-6
179 LSU 0 -248.15 105.35 172/182 3-1
180 Auburn 0 -409.48 43.23 177/182 2-2
181 Southern California-B 0 -562.85 346.6 146/182 0-3
182 Alabama-Birmingham 0 -566.1 88.1 178/182 1-3

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)