Probabilistic Bid Allocation

2016-2017 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 2.850 1.814 0.137 2.674 1.349 2.568 1.861 2.265 0.765 3.717
Autos (all @ 1) 1.850 0.814 -0.863 1.674 0.349 1.568 0.861 1.265 -0.235 2.717
Southwest (@ 2) 1.850 0.814 -0.863 1.674 0.349 1.568 0.861 1.265 -0.235 1.717
Atlantic Coast (@ 2) 0.850 0.814 -0.863 1.674 0.349 1.568 0.861 1.265 -0.235 1.717
Southwest (@ 3) 0.850 0.814 -0.863 1.674 0.349 1.568 0.861 1.265 -0.235 0.717
New England (@ 2) 0.850 0.814 -0.863 0.674 0.349 1.568 0.861 1.265 -0.235 0.717
Northwest (@ 2) 0.850 0.814 -0.863 0.674 0.349 0.568 0.861 1.265 -0.235 0.717
South Central (@ 2) 0.850 0.814 -0.863 0.674 0.349 0.568 0.861 0.265 -0.235 0.717
Ohio Valley (@ 2) 0.850 0.814 -0.863 0.674 0.349 0.568 -0.139 0.265 -0.235 0.717
Atlantic Coast (@ 3) -0.150 0.814 -0.863 0.674 0.349 0.568 -0.139 0.265 -0.235 0.717
Great Lakes (@ 2) -0.150 -0.186 -0.863 0.674 0.349 0.568 -0.139 0.265 -0.235 0.717
Southwest (@ 4) -0.150 -0.186 -0.863 0.674 0.349 0.568 -0.139 0.265 -0.235 -0.283
Total 3 2 1 2 1 2 2 2 1 4

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 Stanford 1 2308.97 84.35 1/10 19-3
2 Texas 1 2223.13 57.98 1/10 16-3
3 Virginia 1 2197.2 89.61 1/17 22-2
4 Dartmouth 1 2153.57 85.19 1/16 16-3
5 Tufts 1 2132.44 64.7 1/14 17-3
6 British Columbia 1 2119.23 80.9 1/18 9-4
7 UCLA 1 2109.21 67.19 1/15 18-4
8 California 1 2065.04 73.49 1/19 16-9
9 Pittsburgh 0.996 2007.39 64.03 2/22 15-5
10 Oregon 0.996 1958.12 64.42 5/27 17-10
11 Notre Dame 0.982 2102.1 137.91 1/35 16-4
12 Colorado 0.962 1939.33 70.68 4/28 7-10
13 North Carolina 0.939 1921.53 69.65 6/30 13-6
14 Ohio State 0.837 1869.14 56.66 9/36 16-10
15 Michigan 0.832 1884.25 72.11 7/32 9-11
16 Carleton College 0.812 1868.95 62.33 8/38 11-8
17 Southern California 0.661 1838.84 59.41 9/37 14-9
18 Whitman 0.522 1816.38 50.42 11/33 9-10
19 Florida 0.509 1822.24 61.49 9/36 18-10
20 Georgetown 0.494 1818.38 98.94 5/56 22-4
21 Vermont 0.397 1790.18 97.16 6/51 13-6
22 Iowa State 0.342 1783.89 93.59 5/59 14-5
23 Boston College 0.277 1734.29 161.66 3/72 12-2
24 Kennesaw State 0.254 1745.85 113.15 7/54 16-4
25 Minnesota 0.195 1751.8 80.83 9/49 6-7
26 Delaware 0.177 1743.34 75.03 11/47 7-6
27 Kansas 0.161 1735.59 78.85 11/53 22-6
28 Colorado State 0.141 1725.75 84.75 10/53 16-4
29 North Carolina-Wilmington 0.138 1727.59 72.5 11/49 15-10
30 Cornell 0.085 1705.13 81.87 13/52 26-2
31 California-San Diego 0.056 1703.71 69.35 13/56 14-10
32 Western Washington 0.05 1650 99.67 10/64 4-8
33 North Carolina State 0.047 1634.71 112.19 10/76 12-6
34 Columbia 0.046 1637.14 101.13 12/73 9-3
35 Duke 0.029 1663.19 78.7 10/62 12-2
36 Liberty 0.026 1659.15 79.87 15/58 17-7
37 West Chester 0.019 1587.82 92.96 11/76 15-4
38 Case Western Reserve 0.008 1582.56 100.04 12/76 12-2
39 Connecticut 0.006 1556.52 102.37 13/87 12-2
40 Auburn 0.002 1509.24 119.4 19/100 16-4
41 Colorado College 0.001 1576.66 62.89 19/58 6-12
42 Penn State 0.001 1531.59 98.35 19/79 8-10
43 Williams 0 1733.78 87.53 11/49 17-1
44 California-Davis 0 1639.59 50.08 21/48 16-10
45 Washington 0 1604.68 52.11 22/54 6-13
46 Bowdoin 0 1577.5 118.01 12/81 8-2
47 Florida State 0 1538.4 69.77 23/63 14-12
48 Wisconsin 0 1531.23 59.57 30/63 7-13
49 Georgia 0 1481.27 92.41 25/87 10-11
50 Illinois 0 1458.29 71.7 30/90 6-7
51 Georgia Tech 0 1425.4 104.87 22/98 12-12
52 Cincinnati 0 1424.42 110.56 22/103 9-4
53 South Carolina 0 1414.25 99.68 26/105 11-7
54 Akron 0 1409.77 104.58 22/104 8-5
55 Clemson 0 1405.09 75.17 35/90 9-10
56 Northwestern 0 1398.33 66.15 39/86 9-10
57 Amherst 0 1388.38 99.48 33/100 7-4
58 Harvard 0 1380.77 86.93 32/100 13-5
59 Bates 0 1375.38 107.15 25/112 8-3
60 Pennsylvania 0 1360.53 71.48 44/99 11-7
61 Carnegie Mellon 0 1349.1 63.99 43/89 15-6
62 Brigham Young 0 1339.71 73.98 41/95 8-7
63 Indiana 0 1334.63 72.96 42/93 16-5
64 Princeton 0 1323 63.18 44/92 14-5
65 Central Florida 0 1321.32 91.15 38/104 10-8
66 Victoria 0 1320.02 93.24 40/113 6-8
67 George Mason 0 1308.22 77.35 42/96 15-5
68 California-Santa Barbara 0 1302.12 49.54 51/94 10-11
69 Northeastern 0 1302.04 70.14 42/96 6-14
70 Cal Poly-SLO 0 1284.76 68.68 49/101 11-6
71 Missouri State 0 1281.04 109.84 41/115 9-3
72 West Virginia 0 1276.38 103.77 41/116 12-1
73 Brown 0 1272.18 72.57 47/105 9-11
74 St Olaf 0 1264.46 106.25 40/114 6-7
75 Skidmore 0 1261.04 119.75 40/130 10-2
76 James Madison 0 1259.66 76.18 50/117 13-6
77 Washington University 0 1256.78 72.21 50/101 6-13
78 Carleton College-Eclipse 0 1251.94 56.78 51/97 14-5
79 Valparaiso 0 1231.08 74.29 51/109 9-3
80 Mount Holyoke 0 1229.06 144.54 36/153 5-5
81 Portland 0 1227.33 58.59 56/100 15-3
82 Chicago 0 1225.31 76.12 50/109 11-7
83 Winona State 0 1224.08 119.97 39/126 8-4
84 Denver 0 1220.72 75.79 46/113 14-5
85 Iowa 0 1208.64 57.37 57/105 12-8
86 Maryland 0 1197.56 50.4 61/103 13-11
87 Boston University 0 1181.46 86.44 51/126 10-4
88 SUNY-Binghamton 0 1169.33 87.61 49/136 9-5
89 Emory 0 1127.97 90.93 55/133 9-9
90 San Diego State 0 1116.28 88.04 57/130 6-8
91 Truman State 0 1115.61 76.04 60/130 14-6
92 Towson 0 1107.96 85.32 58/128 15-6
93 Tennessee 0 1093.68 84.81 63/136 9-10
94 Chico State 0 1087.75 61.09 69/125 14-4
95 SUNY-Stony Brook 0 1087.13 43.91 78/116 9-4
96 South Florida 0 1082.06 102.84 49/144 6-8
97 Santa Clara 0 1074.1 78.55 67/134 5-6
98 MIT 0 1067.35 95.23 59/140 5-8
99 Vanderbilt 0 1065.35 146.89 48/170 8-4
100 LSU 0 1062.81 66.61 69/131 10-7
101 Michigan State 0 1059.57 85.08 66/136 12-3
102 American 0 1049.58 68.66 72/133 11-8
103 Saint Louis 0 1034.68 100.14 61/160 8-5
104 Haverford 0 1027.32 64.31 74/136 5-9
105 Rochester 0 1026.2 69.03 78/136 10-4
106 Wooster 0 1009.68 92.39 67/151 10-2
107 Arkansas 0 1004.42 84.99 73/148 8-5
108 Puget Sound 0 997.47 74.48 78/151 9-7
109 Massachusetts 0 993.03 60.06 86/139 6-12
110 Rutgers 0 980.91 80.56 72/158 11-9
111 Catholic 0 970.98 62.52 86/146 10-10
112 John Brown 0 960.4 70.53 78/157 15-4
113 Virginia Tech 0 957.26 63.86 87/144 6-11
114 Wellesley 0 953.22 63.37 88/142 10-9
115 Oberlin 0 940.75 56.97 91/140 8-5
116 Texas Christian 0 935.6 83.38 82/154 10-7
117 College of New Jersey 0 932.81 76.11 78/163 6-7
118 Oregon State 0 930.6 79.04 83/158 10-4
119 Idaho 0 916.83 63.81 94/150 9-9
120 Arizona 0 909.81 98.37 80/172 10-8
121 Purdue 0 906.08 102.63 79/173 7-5
122 Delaware-B 0 898.76 87.58 76/161 10-3
123 Lehigh 0 893.58 71.97 92/155 9-11
124 Alabama 0 892.66 61.8 98/154 16-9
125 Georgia College 0 874.14 44.73 105/148 7-4
126 Rice 0 867.81 72.84 94/159 9-7
127 Missouri S&T 0 865.7 70.28 95/162 7-6
128 Richmond 0 864.59 93.16 84/167 8-5
129 NYU 0 862.69 63.68 99/169 11-10
130 Wisconsin-La Crosse 0 853.77 116.67 76/196 5-5
131 Elon 0 846.3 50.42 104/158 6-8
132 North Carolina-B 0 835.44 64.65 101/166 8-11
133 Utah 0 826.32 57.76 105/163 10-7
134 Mississippi 0 824.29 54.4 105/162 8-10
135 St Benedict 0 815.85 100.88 92/181 6-5
136 Grinnell 0 808.68 68.88 99/168 7-7
137 DePaul 0 805.89 93.02 98/175 6-4
138 Arizona State 0 804.64 88.4 97/177 6-10
139 Boise State 0 800.9 93.8 96/183 7-8
140 Texas State 0 797.37 71.2 104/170 4-8
141 Maryland-B 0 795.43 105.91 95/179 10-3
142 Tulane 0 788.23 128.79 76/191 5-8
143 Rensselaer Polytech 0 787.79 88.6 92/175 9-4
144 Ohio 0 786.31 63.51 111/175 9-5
145 Luther 0 776.88 68.59 107/174 6-6
146 Temple 0 762.74 74.44 111/174 8-11
147 Colorado-B 0 761.63 134.35 85/200 6-4
148 Pacific Lutheran 0 760.61 71.08 113/175 10-3
149 Allegheny 0 752.47 76.8 107/176 8-6
150 George Washington 0 717.01 63.44 121/178 7-14
151 California-Santa Cruz 0 716.23 85.72 100/183 6-11
152 Sonoma State 0 711.21 64.43 122/175 6-11
153 Nebraska 0 693.84 55.36 123/176 8-11
154 Brandeis 0 687 70.79 125/180 10-5
155 Oklahoma 0 683.68 66.66 123/179 9-8
156 Loyola-Chicago 0 672.67 62.5 129/188 8-5
157 William & Mary 0 667.57 89.45 114/187 5-12
158 Mary Washington 0 656.93 72.57 120/188 5-9
159 Virginia Commonwealth 0 650.79 65.17 129/187 8-12
160 Montana 0 649.06 70.37 127/184 2-8
161 Swarthmore 0 635.22 93.76 114/195 3-13
162 Dickinson 0 634.79 115.82 112/208 5-6
163 North Carolina-Asheville 0 632.96 81.55 113/188 5-8
164 Claremont 0 630.43 131.93 104/205 3-7
165 North Georgia 0 630.04 71.04 134/194 6-13
166 Kansas State 0 617.64 78.28 118/191 6-7
167 Wisconsin-Milwaukee 0 615.54 82.99 130/199 3-7
168 Illinois State 0 602.87 43.39 146/180 4-7
169 Mississippi State 0 598.27 67.41 139/197 7-13
170 Lewis & Clark 0 581.25 70.04 142/190 4-13
171 Wisconsin-Eau Claire 0 571.98 60.71 139/187 5-6
172 Texas-San Antonio 0 557.14 67.79 138/191 11-9
173 Pittsburgh-B 0 542.3 78.15 136/198 4-7
174 Wake Forest 0 538.1 94.79 135/206 5-13
175 Alabama-Birmingham 0 521.88 111.73 104/210 4-11
176 Messiah 0 520.04 65.43 147/196 6-9
177 SUNY-Buffalo 0 518.67 67.35 146/197 6-7
178 Texas-Dallas 0 517.69 84.8 138/202 10-5
179 Nevada-Reno 0 507.79 76.66 143/204 3-9
180 Salisbury 0 454.71 77.34 151/206 8-14
181 Edinboro 0 443.83 76.43 151/206 4-5
182 California-Irvine 0 435.56 120.49 142/214 2-8
183 Tennessee-Chattanooga 0 431.04 116.7 139/212 3-8
184 North Park 0 425.68 41.9 172/201 10-5
185 Ohio Wesleyan 0 424.83 78.06 153/207 5-8
186 Texas-B 0 416.78 67.47 160/206 11-9
187 Ithaca 0 413.91 66.35 165/206 4-11
188 Minnesota-Duluth 0 400.26 66.25 166/209 6-9
189 Northeastern-B 0 399.39 57.93 169/208 10-11
190 Appalachian State 0 387.85 137.84 112/226 0-10
191 Miami (Ohio) 0 375.19 109.05 152/216 4-8
192 Georgia State 0 362.45 142.27 140/223 3-7
193 California-San Diego-B 0 341.41 76.58 169/211 3-9
194 Wheaton (Illinois) 0 337.66 62.39 173/211 8-5
195 Miami 0 323.73 98.18 154/215 3-9
196 Vermont-B 0 309.95 66.4 176/214 6-7
197 Virginia-B 0 301.56 107.36 152/220 3-21
198 Wisconsin-B 0 297.68 54.26 181/210 5-13
199 Michigan-B 0 296.81 77.8 168/216 5-13
200 Occidental 0 292.07 69.68 176/215 5-7
201 Georgetown-B 0 273.62 78.63 173/214 6-7
202 Harding 0 255.7 71.09 177/217 2-10
203 Washington University-B 0 241.01 69.17 178/215 3-9
204 Texas A&M 0 196.89 76.93 183/219 6-12
205 Florida State-B 0 188.67 163.41 151/228 3-8
206 Syracuse 0 164.91 88.53 184/222 2-8
207 Georgia Southern 0 163.81 134.56 168/228 3-9
208 Marquette 0 162.86 124.69 175/225 2-9
209 Davidson 0 150.18 117.25 174/227 2-9
210 Drexel 0 144.55 103.84 183/225 4-10
211 Cornell-B 0 130.61 102.23 187/224 3-17
212 California-B 0 118.23 83.05 183/224 2-10
213 Grinnell-B 0 115.54 114.78 182/225 2-10
214 Kansas-B 0 74.21 113.4 176/228 1-11
215 Missouri 0 71.72 96.41 192/228 4-14
216 Goucher 0 67.96 85.9 193/228 4-7
217 Wooster-B 0 -15.1 123.31 194/230 1-11
218 Philadelphia 0 -73.46 133.54 197/230 4-7
219 Towson-B 0 -78.02 104.75 203/230 5-13
220 SUNY Cortland 0 -84.51 95.26 203/230 0-15
221 Notre Dame-B 0 -110.05 141.8 192/230 3-10
222 Northwestern-B 0 -136.38 82.46 210/230 3-8
223 Trinity 0 -137.67 67.09 212/230 1-21
224 Florida-B 0 -167.18 154.03 196/230 0-23
225 Columbia-B 0 -183.26 157.58 198/230 2-9
226 Emory-B 0 -234.9 191.8 193/230 2-10
227 Southern Indiana 0 -263.16 139.97 208/230 2-10
228 American-B 0 -263.36 94.13 215/230 1-16
229 George Washington-B 0 -316.95 118.33 215/230 1-9
230 Princeton-B 0 -356.93 182.5 200/230 0-10

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 20
  4. Sum the fractions for each region for how often each of it's teams appeared in the top 20
  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)