Probabilistic Bid Allocation

2017-18 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 1.982 0.584 0.000 2.590 1.411 4.943 3.025 2.015 0.514 2.936
Autos (all @ 1) 0.982 -0.416 -1.000 1.590 0.411 3.943 2.025 1.015 -0.486 1.936
Northwest (@ 2) 0.982 -0.416 -1.000 1.590 0.411 2.943 2.025 1.015 -0.486 1.936
Northwest (@ 3) 0.982 -0.416 -1.000 1.590 0.411 1.943 2.025 1.015 -0.486 1.936
Ohio Valley (@ 2) 0.982 -0.416 -1.000 1.590 0.411 1.943 1.025 1.015 -0.486 1.936
Northwest (@ 4) 0.982 -0.416 -1.000 1.590 0.411 0.943 1.025 1.015 -0.486 1.936
Southwest (@ 2) 0.982 -0.416 -1.000 1.590 0.411 0.943 1.025 1.015 -0.486 0.936
New England (@ 2) 0.982 -0.416 -1.000 0.590 0.411 0.943 1.025 1.015 -0.486 0.936
Ohio Valley (@ 3) 0.982 -0.416 -1.000 0.590 0.411 0.943 0.025 1.015 -0.486 0.936
South Central (@ 2) 0.982 -0.416 -1.000 0.590 0.411 0.943 0.025 0.015 -0.486 0.936
Atlantic Coast (@ 2) -0.018 -0.416 -1.000 0.590 0.411 0.943 0.025 0.015 -0.486 0.936
Northwest (@ 5) -0.018 -0.416 -1.000 0.590 0.411 -0.057 0.025 0.015 -0.486 0.936
Total 2 1 1 2 1 5 3 2 1 2

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 Dartmouth 1 2897.25 113.45 1/7 11-1
2 California-San Diego 1 2732.82 37.42 1/6 23-3
3 North Carolina 1 2730.5 71.5 1/9 16-2
4 Stanford 1 2695.52 62.98 1/13 24-3
5 Oregon 1 2610.52 59.56 1/13 22-6
6 British Columbia 1 2560.13 78.27 1/18 9-4
7 Tufts 1 2508.79 44.71 4/15 15-3
8 Colorado 1 2499.69 64.2 4/18 15-5
9 Texas 1 2471.75 48.48 5/20 14-8
10 West Chester 0.999 2505.97 85.77 2/21 8-3
11 Pittsburgh 0.998 2481.75 79.34 3/21 9-4
12 Ohio State 0.993 2404.92 59.18 5/21 17-7
13 Carleton College 0.992 2421.97 69.9 5/24 12-7
14 North Carolina State 0.939 2353.08 63.3 6/24 13-5
15 Western Washington 0.919 2344.39 69.47 7/25 11-10
16 Whitman 0.918 2386.14 99.39 3/30 6-7
17 California-Santa Barbara 0.915 2320.26 50.5 9/26 20-9
18 Brigham Young 0.686 2286.51 91.83 5/36 12-4
19 Vermont 0.583 2263.48 98.51 7/41 13-6
20 Michigan 0.463 2238.43 65.36 9/40 11-13
21 Auburn 0.432 2208.85 195.45 2/64 9-1
22 Washington 0.417 2240.23 68.09 9/39 9-12
23 Minnesota 0.415 2228.83 105.57 8/51 9-5
24 Notre Dame 0.121 2139.71 104.01 12/49 13-4
25 Kennesaw State 0.048 2017.59 137.77 12/82 11-7
26 Penn State 0.035 2086.19 87.21 15/57 11-5
27 Clemson 0.034 2019.14 131.01 14/65 12-2
28 Florida 0.033 2080.24 93.85 15/54 12-13
29 California 0.018 2133.23 52.53 18/38 11-15
30 Washington University 0.015 2113.89 65 17/44 10-8
31 Towson 0.008 1914.84 139.23 14/89 10-3
32 Harvard 0.007 1977.97 108.32 18/67 10-4
33 Wisconsin 0.004 2003.7 81.41 19/56 8-9
34 Cal Poly-SLO 0.003 2036.55 72.73 16/55 11-9
35 Victoria 0.003 2020.2 71.86 18/53 5-8
36 Georgia Tech 0.001 2009.42 66.3 20/55 9-8
37 Duke 0.001 1951.48 82.47 20/67 13-4
38 UCLA 0 2062.69 56.01 21/45 9-16
39 Colorado College 0 2033.18 57.24 21/49 9-15
40 Northwestern 0 2028.18 61.37 21/51 9-12
41 Southern California 0 1990.28 59.65 23/53 10-15
42 Colorado State 0 1981.6 68.45 22/53 10-9
43 Case Western Reserve 0 1978.58 83.88 21/64 10-3
44 North Carolina-Wilmington 0 1978.21 71.85 23/58 18-10
45 Georgia 0 1955.58 56.61 24/55 14-9
46 Florida State 0 1856.06 106.81 24/77 13-4
47 Iowa State 0 1846.46 67.73 30/70 8-13
48 Kansas 0 1836.54 89.51 24/73 13-7
49 South Carolina 0 1827.83 107.23 25/78 11-4
50 California-Davis 0 1817.92 68.34 35/69 9-16
51 Central Florida 0 1798.88 72.41 31/75 18-6
52 Arizona 0 1786.23 82.53 30/75 12-8
53 Columbia 0 1783.95 60.7 37/74 9-4
54 Utah 0 1781.92 71.4 26/74 11-7
55 Virginia 0 1771.7 54.56 41/70 9-15
56 Puget Sound 0 1768.81 72.48 34/78 12-6
57 Boise State 0 1762.64 84.71 34/78 8-3
58 San Diego State 0 1723.73 71.86 41/80 14-7
59 Massachusetts 0 1711.04 79.22 40/84 9-2
60 Pennsylvania 0 1701.53 99.38 34/92 7-4
61 Pacific Lutheran 0 1692.71 96.85 34/95 9-8
62 Brown 0 1688.92 114.09 35/103 9-3
63 Chicago 0 1653.38 69.38 47/84 5-12
64 James Madison 0 1647.06 94.32 39/94 13-6
65 Purdue 0 1636.67 92.14 42/100 7-6
66 Mississippi 0 1624.71 109.08 35/105 7-3
67 Emory 0 1616.21 119.9 40/108 10-3
68 Maryland 0 1592.3 66.86 49/92 12-6
69 California-Santa Cruz 0 1587.75 89.03 47/109 10-8
70 Georgetown 0 1578.62 71.06 48/103 8-14
71 Iowa 0 1570.48 69.26 52/93 4-8
72 Georgia College 0 1562.37 73.37 50/111 8-4
73 John Brown 0 1550.61 103.33 49/110 9-2
74 George Washington 0 1538.16 110.33 49/112 10-2
75 St Olaf 0 1526.06 88.53 52/109 5-6
76 Northern Arizona 0 1523.85 101.3 52/114 8-4
77 Princeton 0 1520.12 104.96 43/122 5-3
78 Arizona State 0 1506.24 73.8 54/104 14-6
79 Oregon State 0 1505.97 108.1 50/122 10-7
80 Claremont 0 1491.21 113.08 51/123 5-7
81 Denver 0 1481.51 62.35 63/104 13-4
82 Chico State 0 1479.34 76.39 58/113 7-13
83 St Benedict 0 1471.97 120.15 41/125 6-1
84 LSU 0 1466.19 97.87 55/116 8-5
85 Wisconsin-Eau Claire 0 1447.12 59.29 68/108 8-5
86 West Virginia 0 1433.65 99.8 50/133 9-3
87 California-Irvine 0 1433.34 68.4 65/112 6-6
88 Illinois 0 1431.05 117.47 50/132 4-5
89 Portland State 0 1430.26 89.91 61/121 8-6
90 Nebraska 0 1406.76 87.98 60/124 8-3
91 Alabama 0 1401.68 111.69 58/130 10-6
92 Lewis & Clark 0 1396.45 68.31 67/118 10-7
93 California-San Diego-B 0 1378.7 88.4 66/130 5-8
94 Dayton 0 1363.47 99.3 63/135 7-6
95 MIT 0 1359.23 99.65 63/140 3-9
96 Carleton College-Eclipse 0 1352.52 75.51 71/132 12-9
97 Ohio 0 1345.82 109.78 58/137 6-2
98 Portland 0 1313.7 80.24 72/131 8-11
99 American 0 1309.29 103.82 66/136 9-3
100 Rutgers 0 1307.83 110.14 61/139 5-4
101 Colby 0 1292.61 148.14 58/155 6-2
102 Mississippi State 0 1292.44 91.19 69/137 6-9
103 Air Force Academy 0 1285.67 91.49 76/136 7-5
104 Tennessee 0 1276.04 78.25 78/136 3-7
105 William & Mary 0 1273.75 67.58 81/129 8-9
106 Cal State-Long Beach 0 1271.41 66.23 80/131 6-6
107 Santa Clara 0 1259.54 73.17 78/137 12-8
108 Michigan State 0 1254.26 75.68 81/135 10-9
109 North Georgia 0 1242.65 67.62 83/134 4-9
110 North Park 0 1238.37 80.86 82/150 8-6
111 Truman State 0 1230.82 61.04 86/141 6-6
112 Texas-Dallas 0 1227.04 81.43 82/143 9-4
113 Liberty 0 1214.02 54.09 91/139 7-11
114 Humboldt State 0 1192.56 103.36 74/157 2-10
115 Virginia Tech 0 1189.59 84.05 84/147 6-9
116 Arkansas 0 1186.36 96.55 82/151 4-7
117 Virginia Commonwealth 0 1186.24 80.91 82/145 5-8
118 Grinnell College 0 1180.11 79.23 79/143 10-4
119 Tennessee-Chattanooga 0 1165.95 139.17 71/164 7-3
120 Colorado-B 0 1152.21 101.07 78/153 5-5
121 Minnesota-Duluth 0 1148.05 135.8 73/173 4-3
122 Missouri S&T 0 1142.48 79.69 91/155 6-8
123 Gonzaga 0 1140.09 117.33 79/160 3-2
124 Richmond 0 1129.56 90.76 90/150 6-4
125 Saint Louis 0 1127.7 116.4 84/158 4-3
126 Winona State 0 1120.25 170.51 61/179 3-4
127 Xavier 0 1109.23 62.52 101/149 7-5
128 UCLA-B 0 1106.29 190.86 60/178 2-4
129 Oklahoma 0 1069.86 96.41 89/165 5-6
130 Luther 0 1059.36 93.07 93/162 5-4
131 Wake Forest University 0 1053.39 126.77 84/169 6-3
132 North Carolina-Asheville 0 1052.04 95.18 95/160 1-5
133 Catholic 0 1046.87 84.77 98/158 6-5
134 East Carolina 0 1038.17 67.95 112/156 6-7
135 Florida-B 0 1037.55 94.99 98/166 6-7
136 Occidental 0 1010.03 71.23 117/157 5-9
137 Vermont-B 0 1007.09 118.96 96/170 5-4
138 Alabama-Birmingham 0 1004.52 101.74 96/165 5-6
139 Smith 0 1002.91 67.4 118/162 2-6
140 South Florida 0 1000.57 75.42 109/161 4-15
141 Pittsburgh-B 0 994.41 84.28 104/162 7-6
142 Western Washington-B 0 959.22 92.4 101/167 2-5
143 Maryland-Baltimore County 0 957 121.33 101/181 3-5
144 Mary Washington 0 942.86 56.7 124/160 5-6
145 Sonoma State 0 939.66 93.11 109/168 3-8
146 Wisconsin-Milwaukee 0 932.96 107.6 96/177 6-5
147 Ohio Wesleyan 0 931.92 90.06 110/172 6-6
148 Idaho 0 926.06 83.26 113/167 1-13
149 Arizona-B 0 914.92 85.9 119/176 5-8
150 Marquette 0 908.8 79.92 124/167 5-7
151 Salisbury 0 886.81 84.76 122/173 5-3
152 Nevada-Reno 0 883.18 68.16 127/169 4-8
153 SUNY-Fredonia 0 880.95 107.41 111/177 4-6
154 Shippensburg 0 880.45 97.97 119/175 2-3
155 Missouri 0 818.69 67.34 131/174 5-7
156 Miami 0 802.34 94.94 127/179 3-8
157 Missouri State 0 785.45 125.46 113/188 3-4
158 Pacific Lutheran-B 0 785.13 150.47 98/189 2-4
159 Virginia-B 0 776.36 91.29 132/180 5-13
160 Elon 0 744.95 102.08 130/184 1-10
161 Ohio State-B 0 741.16 58.23 145/178 7-12
162 Northwestern-B 0 723.7 93.29 133/186 3-4
163 Michigan-B 0 709.51 93.97 136/184 7-9
164 Drexel 0 703.13 63.5 137/182 1-6
165 Hofstra 0 696.95 115.56 130/191 3-8
166 Wisconsin-B 0 693.57 62.59 146/181 4-8
167 North Carolina-B 0 689.36 91.16 142/183 2-11
168 New Mexico 0 677.57 110.8 137/190 1-9
169 Washington-B 0 644.24 77.55 148/185 1-5
170 Tulane 0 639.41 134.85 124/192 5-9
171 Northeastern-B 0 631.32 68.04 153/190 10-4
172 Brown University-B 0 614.99 119.68 130/190 6-4
173 Kansas State 0 597.66 152.91 129/195 2-5
174 Kansas-B 0 583.69 74.7 154/188 3-9
175 Drake 0 579.42 91.95 151/191 3-9
176 Georgia Tech-B 0 574.53 184.56 116/196 3-7
177 Washington University-B 0 570.12 67.35 155/189 2-8
178 Miami (Ohio) 0 529.18 102.07 157/192 0-5
179 California-Davis-B 0 510.9 122.11 136/195 2-9
180 Georgia State 0 505.1 182.58 123/198 2-10
181 George Mason University 0 494.17 122.42 141/196 4-15
182 Georgetown-B 0 481.64 122.23 152/196 1-11
183 William & Mary-B 0 442.5 78.13 166/193 0-8
184 California-B 0 424.8 137.69 157/198 1-10
185 Davidson 0 420.47 134.81 147/197 1-8
186 Tulsa 0 418.35 81.32 169/197 3-10
187 Union 0 381.85 116.17 164/198 1-9
188 Columbia-B 0 354.71 84.87 167/196 6-2
189 Christopher Newport 0 337.52 122.8 169/198 0-10
190 Seattle 0 313.39 202.14 140/200 0-5
191 Towson-B 0 296.68 113.7 169/198 4-12
192 Oberlin-B 0 237.12 76.95 176/198 0-6
193 Maryland-B 0 138.09 137.92 176/200 1-4
194 Notre Dame-B 0 112.35 216.74 159/200 0-12
195 Hendrix 0 65.01 261.38 133/200 0-6
196 George Washington-B 0 44.08 111.82 186/200 1-8
197 Cal Poly-SLO-B 0 20.41 204.8 163/200 0-6
198 Emory-B 0 -93.94 308.04 155/200 0-7
199 Alabama-Huntsville 0 -220.56 277.4 170/200 0-7
200 American-B 0 -299.32 174.6 184/200 0-9

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)