Probabilistic Bid Allocation

2023-24 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 1.244 1.473 0.011 2.177 1.011 5.698 1.620 1.733 0.949 4.084
Autos (all @ 1) 0.244 0.473 -0.989 1.177 0.011 4.698 0.620 0.733 -0.051 3.084
Northwest (@ 2) 0.244 0.473 -0.989 1.177 0.011 3.698 0.620 0.733 -0.051 3.084
Northwest (@ 3) 0.244 0.473 -0.989 1.177 0.011 2.698 0.620 0.733 -0.051 3.084
Southwest (@ 2) 0.244 0.473 -0.989 1.177 0.011 2.698 0.620 0.733 -0.051 2.084
Northwest (@ 4) 0.244 0.473 -0.989 1.177 0.011 1.698 0.620 0.733 -0.051 2.084
Southwest (@ 3) 0.244 0.473 -0.989 1.177 0.011 1.698 0.620 0.733 -0.051 1.084
Northwest (@ 5) 0.244 0.473 -0.989 1.177 0.011 0.698 0.620 0.733 -0.051 1.084
New England (@ 2) 0.244 0.473 -0.989 0.177 0.011 0.698 0.620 0.733 -0.051 1.084
Southwest (@ 4) 0.244 0.473 -0.989 0.177 0.011 0.698 0.620 0.733 -0.051 0.084
South Central (@ 2) 0.244 0.473 -0.989 0.177 0.011 0.698 0.620 -0.267 -0.051 0.084
Northwest (@ 6) 0.244 0.473 -0.989 0.177 0.011 -0.302 0.620 -0.267 -0.051 0.084
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 2610.62 64.26 1/4 16-1
2 Vermont 1 2480.07 82.53 1/9 12-1
3 Carleton College 1 2429.62 76.93 1/7 15-4
4 North Carolina 1 2385.29 127.32 1/12 17-1
5 Oregon 1 2318.46 67.11 2/9 18-2
6 Stanford 1 2275.98 68.64 2/11 14-6
7 Tufts 1 2210.41 81.8 2/17 12-2
8 Colorado 1 2175.28 51.44 3/12 14-6
9 California-Santa Barbara 1 2144.49 46.89 4/12 16-7
10 Washington 1 2068.45 65.9 4/19 13-7
11 Michigan 1 2023.02 70.28 4/20 9-4
12 Brigham Young 0.998 2030.14 68.64 6/23 7-5
13 Western Washington 0.984 1912.56 47.84 10/22 6-8
14 California-Santa Cruz 0.937 1899.9 65.03 10/26 6-8
15 California-San Diego 0.911 1884.42 64.5 10/28 10-11
16 Georgia 0.872 1883.87 81.85 9/32 7-6
17 Pennsylvania 0.747 1847.86 78.95 10/34 8-6
18 Ohio State 0.746 1831.56 49.76 12/31 21-6
19 Colorado State 0.733 1846.67 75.75 9/35 10-5
20 Victoria 0.694 1830.95 60.99 10/32 8-10
21 Notre Dame 0.473 1797.84 86.83 10/35 12-6
22 Cal Poly-SLO 0.162 1715.91 87.25 12/55 13-11
23 Northeastern 0.147 1738.26 59.89 14/36 5-7
24 American 0.128 1598.94 182.24 9/84 9-1
25 North Carolina State 0.112 1683.38 99.15 11/51 7-5
26 Pittsburgh 0.093 1699.3 73.34 13/41 10-10
27 Central Florida 0.075 1575.43 156.19 11/79 21-1
28 California-Davis 0.071 1698.08 72.41 15/44 8-12
29 Ohio 0.034 1568.16 129.48 13/77 10-3
30 Brown 0.03 1633.04 86.77 16/56 9-4
31 Utah 0.022 1651.49 72.62 17/48 10-12
32 Cornell 0.011 1389.41 177.99 14/115 6-0
33 Minnesota 0.01 1548.65 113.83 14/73 3-3
34 South Carolina 0.004 1513.07 104.41 18/76 7-6
35 UCLA 0.003 1590.83 71.52 18/56 7-12
36 Alabama-Huntsville 0.002 1456.68 128.83 20/95 12-2
37 Wisconsin 0.001 1557.7 78.25 21/60 3-9
38 Haverford/Bryn Mawr 0 1682.91 80.94 13/47 7-0
39 California 0 1605.93 57.14 21/47 7-18
40 Union (Tennessee) 0 1516.77 139.24 11/88 12-2
41 Texas-Dallas 0 1516.29 71.74 23/63 10-4
42 Virginia 0 1489.91 63.33 26/65 9-10
43 Washington University 0 1488.91 72.92 25/63 13-7
44 Georgetown 0 1442.2 82.26 25/73 10-2
45 Yale 0 1411.17 106.92 23/94 3-4
46 Texas 0 1411.14 84.47 25/77 8-11
47 Ithaca 0 1405.02 76.16 31/81 5-0
48 Carleton College-Eclipse 0 1398.49 124.39 22/95 15-3
49 Portland 0 1394.01 97.63 28/81 11-3
50 Whitman 0 1391.96 95.43 26/83 6-6
51 Tennessee 0 1390.2 87.06 25/80 9-3
52 Purdue 0 1379.51 126.55 22/100 3-3
53 SUNY-Binghamton 0 1375.25 72.55 27/79 2-5
54 Georgia Tech 0 1332.56 152.58 23/109 10-3
55 St Olaf 0 1329.24 136.89 21/103 7-2
56 Boston University 0 1321.85 113.48 30/111 3-3
57 Penn State 0 1305.61 99.7 33/100 7-5
58 West Chester 0 1305.09 147.59 22/121 6-2
59 Florida 0 1295.65 131.13 28/116 10-7
60 Southern California 0 1289.23 42.38 44/80 6-11
61 Cincinnati 0 1287.39 135.31 26/115 10-3
62 William & Mary 0 1286.16 108.64 26/105 4-7
63 Wellesley 0 1279.76 123.1 31/109 6-2
64 Colorado College 0 1254.85 65.92 44/93 12-6
65 Columbia 0 1247.41 84.21 41/101 7-5
66 Williams 0 1245.34 114.27 29/112 5-1
67 Lehigh 0 1235.4 86.92 37/97 9-4
68 Rochester 0 1231.59 111.18 34/110 6-2
69 Davenport 0 1231.38 131.79 28/112 4-1
70 Carnegie Mellon 0 1220.33 99.16 37/115 1-5
71 James Madison 0 1186.68 69.24 47/103 7-7
72 Northwestern 0 1184.41 102.14 42/113 4-7
73 Dartmouth 0 1167.52 106.6 38/116 3-4
74 Macalester 0 1165.22 109.51 34/118 5-1
75 Connecticut College 0 1156.63 78.31 49/109 3-2
76 Grand Canyon 0 1137.65 86.32 46/111 4-2
77 Missouri 0 1134.8 97.21 45/114 8-4
78 California-San Diego-B 0 1130.15 98.25 44/117 10-8
79 Arizona 0 1117.91 110.45 46/117 8-1
80 Connecticut 0 1115.35 46.2 62/105 3-3
81 Chicago 0 1108.35 72.12 55/118 3-12
82 Utah State 0 1106.18 95.89 47/118 6-0
83 Massachusetts 0 1102.85 107.5 45/127 3-3
84 Franciscan 0 1093.41 134.62 38/124 4-2
85 Arkansas 0 1086.11 92.29 53/115 4-3
86 Harvard 0 1082.11 108.27 43/120 2-4
87 Indiana 0 1079.76 75.23 58/118 4-2
88 Trinity 0 1067.39 77.38 54/116 15-5
89 Tennessee-Chattanooga 0 1048.48 85.24 55/121 4-3
90 Richmond 0 1048.22 86.65 57/126 3-2
91 Cedarville 0 1035.69 93.03 58/125 4-2
92 Claremont 0 1034.53 88.27 54/132 3-7
93 San Diego State 0 1029.06 87.78 57/123 10-3
94 Northern Arizona 0 1019.74 51.87 70/116 3-3
95 Virginia Tech 0 999.4 69.03 64/122 5-7
96 Kenyon 0 997.6 120.38 52/139 4-2
97 Duke 0 991.12 105.9 64/132 4-8
98 Appalachian State 0 985.87 180.3 31/157 0-5
99 Santa Clara 0 963.53 74.1 61/132 8-2
100 Nevada-Reno 0 956.36 55.71 74/122 9-3
101 Iowa 0 955.65 86.08 66/130 4-2
102 California-Irvine 0 943 91.86 64/135 7-4
103 Iowa State 0 939.24 86.81 64/135 5-8
104 Saint Louis 0 939.03 57.15 82/125 7-8
105 Lewis & Clark 0 938.03 85.48 69/136 6-7
106 NYU 0 929.57 80.61 70/134 3-3
107 Rice 0 917.45 91.47 70/137 9-3
108 Liberty 0 911.21 63.23 78/130 4-8
109 Wesleyan 0 901.87 116.72 63/145 3-3
110 Case Western Reserve 0 877.08 171.67 40/169 0-5
111 Rutgers 0 876.19 105.99 73/144 1-4
112 Puget Sound 0 853.3 61.7 87/134 5-7
113 Catholic 0 849.9 92.64 81/141 6-6
114 Mount Holyoke 0 847.36 117.94 64/154 2-4
115 Emory 0 831.96 104.05 79/147 3-4
116 Maryland 0 828.79 77.62 88/141 2-5
117 Truman State 0 823.26 83.25 89/140 6-8
118 Illinois 0 822.43 58.12 91/137 6-8
119 Johns Hopkins 0 812.67 84.72 81/142 5-1
120 Denver 0 803.37 62.26 98/138 9-16
121 SUNY-Geneseo 0 792.11 64.39 92/143 0-7
122 Kansas 0 785.38 87.25 90/148 2-4
123 George Washington 0 768.94 74.76 95/151 6-5
124 SUNY-Albany 0 762.57 92.14 92/150 1-4
125 Swarthmore 0 757.69 86.92 87/147 4-3
126 Arizona State 0 726.05 160.71 63/172 2-4
127 Florida State 0 722.66 133 73/166 6-6
128 Boston College 0 704.84 70.58 109/150 3-3
129 Kentucky 0 702.73 87.42 103/161 2-4
130 John Brown 0 699.69 113.16 85/162 4-6
131 Delaware 0 689.53 74.49 100/155 3-3
132 South Carolina-B 0 679.5 133.84 86/169 1-4
133 Wisconsin-Eau Claire 0 674.26 55.91 110/150 9-5
134 MIT 0 661.42 81.13 109/161 5-8
135 Cornell-B 0 645.83 93 103/160 1-4
136 Colorado-B 0 644.97 110.48 92/170 2-3
137 Oberlin 0 630.63 88.14 111/165 3-3
138 Marquette 0 592.04 28.59 127/153 1-6
139 Oregon State 0 588.9 54.23 122/160 1-9
140 Michigan-B 0 586.44 160.45 89/178 2-2
141 Montana 0 585.77 75.35 118/159 3-3
142 Wake Forest 0 555.16 144.61 94/176 2-3
143 Texas A&M 0 536.33 78.28 113/165 7-6
144 Skidmore 0 527.01 154.05 100/181 2-4
145 North Carolina-B 0 524.87 255.65 50/195 1-5
146 Washington University-B 0 499.97 95.8 117/175 2-4
147 Miami (Ohio) 0 495.93 19.89 141/159 1-6
148 Temple 0 493.75 49.39 130/164 0-7
149 Texas State 0 486 88.48 121/171 5-8
150 Bates 0 483.27 70.99 131/169 3-2
151 Missouri State 0 483.07 72.01 127/167 2-9
152 Cal Poly-SLO-B 0 475.88 54.34 130/164 2-7
153 Occidental 0 473.1 63.08 129/168 2-4
154 California-B 0 431.94 69.43 133/176 6-9
155 Virginia-B 0 422.94 129.74 119/182 1-10
156 Montana State 0 417.68 65.14 133/170 1-5
157 Clemson 0 394.66 234.62 53/193 2-6
158 Syracuse 0 361.65 120.96 115/188 2-5
159 Elon 0 358.83 137.72 122/186 1-5
160 Brown-B 0 352.38 157.12 105/189 1-4
161 Vanderbilt 0 345.23 112.99 128/183 4-8
162 Butler 0 342.92 84.05 138/179 2-5
163 Stanford-B 0 338.84 191.47 108/192 1-2
164 Georgetown-B 0 316.03 95.25 132/185 0-5
165 Jacksonville State 0 285.34 120.22 132/185 5-7
166 Georgia College 0 267.24 77.3 145/183 6-8
167 Tulane 0 262.69 123.68 134/187 4-8
168 Miami (Florida) 0 249.52 84.87 148/185 1-4
169 Auburn 0 234.96 113.9 141/187 3-8
170 Alabama 0 232.62 101.32 142/190 5-9
171 Colorado Mines 0 223.45 100.41 146/189 2-6
172 Arizona-B 0 192.35 97.4 147/188 0-6
173 Texas-San Antonio 0 175.83 108.23 145/188 5-7
174 Knox 0 175.49 56.82 159/185 1-4
175 Georgia-B 0 171.89 110.53 146/193 3-9
176 Northwestern-B 0 139.69 141.54 134/194 1-5
177 Messiah 0 136.93 40.44 165/185 2-3
178 SUNY-Stony Brook 0 120.97 171.32 123/194 1-4
179 California-Davis-B 0 95.23 77.69 159/191 3-9
180 Air Force 0 69.17 191.41 132/196 1-4
181 Dickinson 0 55.24 186.69 139/196 1-5
182 Wisconsin-B 0 32.58 204.23 124/197 0-5
183 Sam Houston 0 24.96 102.67 152/193 3-3
184 Houston 0 -9.88 154.73 147/197 2-4
185 Dayton 0 -47.63 231.77 135/198 0-6
186 UCLA-B 0 -75.08 152.88 156/196 1-7
187 Colorado College-B 0 -95.61 186.18 143/197 1-4
188 LSU 0 -106.15 109.5 170/196 4-15
189 Texas-B 0 -170.58 92.11 177/196 1-12
190 North Texas 0 -174.59 169.64 160/198 2-7
191 William & Mary-B 0 -197.75 202.34 148/198 1-4
192 Columbia-B 0 -211.47 213.65 157/198 0-5
193 Alabama-Birmingham 0 -266.62 326.39 109/198 0-6
194 Florida Tech 0 -447.74 201.36 178/198 1-11
195 Florida-B 0 -469.73 183.36 180/198 1-12
196 American-B 0 -515.51 340.68 147/198 0-5
197 California-San Diego-C 0 -533.79 285.43 159/198 0-5
198 Notre Dame-B 0 -682.18 296.56 163/198 1-5

FAQ

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
  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
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)