Probabilistic Bid Allocation

2018-19 Season

Bid Distribution    Step by Step Allocation    Team Statistics    FAQ

Allocation Breakdown

Region AC GL ME NE NC NW OV SC SE SW
Initial 2.622 0.154 0.000 3.643 1.760 2.585 2.414 0.828 1.913 4.081
Autos (all @ 1) 1.622 -0.846 -1.000 2.643 0.760 1.585 1.414 -0.172 0.913 3.081
Southwest (@ 2) 1.622 -0.846 -1.000 2.643 0.760 1.585 1.414 -0.172 0.913 2.081
New England (@ 2) 1.622 -0.846 -1.000 1.643 0.760 1.585 1.414 -0.172 0.913 2.081
Southwest (@ 3) 1.622 -0.846 -1.000 1.643 0.760 1.585 1.414 -0.172 0.913 1.081
New England (@ 3) 1.622 -0.846 -1.000 0.643 0.760 1.585 1.414 -0.172 0.913 1.081
Atlantic Coast (@ 2) 0.622 -0.846 -1.000 0.643 0.760 1.585 1.414 -0.172 0.913 1.081
Northwest (@ 2) 0.622 -0.846 -1.000 0.643 0.760 0.585 1.414 -0.172 0.913 1.081
Ohio Valley (@ 2) 0.622 -0.846 -1.000 0.643 0.760 0.585 0.414 -0.172 0.913 1.081
Southwest (@ 4) 0.622 -0.846 -1.000 0.643 0.760 0.585 0.414 -0.172 0.913 0.081
Southeast (@ 2) 0.622 -0.846 -1.000 0.643 0.760 0.585 0.414 -0.172 -0.087 0.081
North Central (@ 2) 0.622 -0.846 -1.000 0.643 -0.240 0.585 0.414 -0.172 -0.087 0.081
Total 2 1 1 3 2 2 2 1 2 4

Teams Ranked By Bid Fraction

Rank Team Bid Frac Rating Uncertainty High/Low Sim Record
1 Carleton College 1 2514.9 86.22 1/6 12-0
2 North Carolina 1 2486.51 98.13 1/7 12-1
3 Tufts 1 2268.54 88.15 1/14 9-2
4 California-San Diego 1 2237.65 59.81 2/12 17-5
5 Washington 0.999 2145.52 64.51 3/21 10-3
6 Ohio State 0.999 2106.77 60.32 3/21 15-5
7 Northeastern 0.998 2106.64 78.94 3/22 9-4
8 Stanford 0.998 2105.14 67.84 3/21 15-6
9 California-Santa Barbara 0.993 2041.89 58.86 4/23 16-7
10 Dartmouth 0.982 2035.62 64.02 4/23 6-1
11 Georgia Tech 0.981 2132.31 118.66 1/29 10-1
12 UCLA 0.962 1988.29 59.47 5/25 16-8
13 Virginia 0.939 2035.27 101.77 3/30 16-2
14 Pittsburgh 0.93 1994.81 78.93 3/27 10-8
15 Florida 0.882 1978.2 77.61 5/32 9-3
16 Western Washington 0.822 1962.17 77.7 6/30 6-3
17 Colorado 0.786 1936.04 60.29 8/31 9-7
18 British Columbia 0.764 1954.58 105.44 2/36 3-3
19 Wisconsin 0.685 1934.47 103.39 3/36 3-3
20 South Carolina 0.665 1944.86 126.17 3/40 3-2
21 Vermont 0.663 1925.53 98.98 4/36 9-6
22 Ohio 0.414 1783.41 336.26 1/159 12-1
23 Northwestern 0.136 1789.74 90.47 12/45 12-9
24 California-Davis 0.128 1745.47 120.96 11/53 8-4
25 Minnesota 0.075 1783.65 65.87 11/43 3-3
26 Case Western Reserve 0.066 1457.21 284.3 3/165 8-5
27 Texas 0.042 1763.42 68.32 15/41 7-8
28 Georgia 0.034 1775.26 59.72 11/39 8-10
29 Michigan 0.018 1730.66 69.86 18/46 5-5
30 Florida State 0.011 1663.97 91.97 15/59 10-4
31 James Madison 0.011 1632.11 119.33 8/76 9-3
32 Vanderbilt 0.005 1678.14 74.97 17/51 7-5
33 West Chester 0.005 1542.56 127.28 17/95 5-1
34 Towson 0.004 1324.09 196.14 18/153 14-1
35 William & Mary 0.002 1640.57 82.73 20/60 6-5
36 North Carolina State 0.001 1638.31 65.09 18/52 5-6
37 California 0 1680.52 53.4 21/43 8-14
38 Utah 0 1574.56 71.92 23/67 6-8
39 Brigham Young 0 1567.15 80.93 23/62 9-4
40 Boston University 0 1558.66 74.71 23/66 5-1
41 Duke 0 1557.66 84.47 21/72 6-5
42 Cal Poly-SLO 0 1556.98 58.57 26/63 9-13
43 Colorado College 0 1553.68 93.19 21/75 6-5
44 Skidmore 0 1544.52 101.42 19/86 5-1
45 George Washington 0 1542.77 83.58 24/71 11-3
46 Whitman 0 1526.67 70.27 27/66 7-7
47 Chicago 0 1517.53 90.21 23/81 10-8
48 Pennsylvania 0 1470.4 71.91 28/75 5-6
49 Alabama 0 1459.81 81.39 31/86 16-3
50 Puget Sound 0 1447.51 106.87 26/93 10-1
51 Mount Holyoke 0 1440.73 60.03 29/73 11-0
52 Texas-Dallas 0 1429.97 90.78 30/95 14-2
53 Victoria 0 1408.07 70.23 33/91 0-5
54 Kennesaw State 0 1400.36 86.26 31/96 11-3
55 New Mexico 0 1397.01 135.63 25/118 7-0
56 Columbia 0 1390.42 58.93 37/84 8-5
57 North Carolina-Wilmington 0 1384.72 93.21 33/95 5-13
58 Kansas 0 1370.45 96.45 31/94 13-2
59 California-Santa Cruz 0 1366.65 57.73 42/89 11-12
60 Washington University 0 1361.69 78.88 36/92 7-7
61 Oregon 0 1346.76 55.4 42/90 6-13
62 Massachusetts 0 1330.06 89.23 36/105 2-7
63 Penn State 0 1324.65 85.03 38/103 1-4
64 Mississippi 0 1319.43 160.65 22/131 5-2
65 Liberty 0 1314.23 74.83 41/99 12-8
66 Bates 0 1310.2 72.82 41/100 7-3
67 Carleton College 0 1299.76 78.92 43/114 12-6
68 Virginia Tech 0 1293.35 129.89 29/133 9-4
69 New Hampshire 0 1291.81 64.66 44/99 10-2
70 Ball State 0 1282.07 113.33 28/121 5-0
71 Purdue 0 1281.75 81.94 41/106 9-5
72 Emory 0 1277.36 93.14 38/109 10-5
73 Truman State 0 1276.3 116.41 32/120 11-3
74 South Florida 0 1263.77 103.47 39/135 7-5
75 Colorado State 0 1262.57 86.15 43/113 11-4
76 Portland 0 1252.55 61.96 50/106 8-2
77 Texas State 0 1240.46 103.07 41/118 9-4
78 Central Florida 0 1236.59 94.95 38/120 8-7
79 Temple 0 1226.54 86.4 42/122 8-6
80 St Olaf 0 1219.07 89.26 40/130 8-4
81 Boston College 0 1218.22 141.03 34/152 4-4
82 Oberlin 0 1218.02 104.91 41/122 6-6
83 Clemson 0 1202.24 119.64 39/135 5-8
84 Notre Dame 0 1188.39 124.88 34/148 0-5
85 Haverford/Bryn Mawr 0 1184.08 91.65 48/129 9-6
86 San Diego State University 0 1174.11 78.12 52/119 12-5
87 Texas A&M 0 1161.1 101.14 51/137 12-2
88 Richmond 0 1136.95 203.2 33/180 6-1
89 Brown 0 1135.99 67.72 57/124 4-8
90 Southern California 0 1124.67 53.8 70/122 6-8
91 Colby 0 1123.64 101.74 46/134 6-5
92 Auburn 0 1117.81 99.14 51/138 7-6
93 Tennessee 0 1107.96 86.61 58/128 10-9
94 Kentucky 0 1102.08 118.91 48/156 3-3
95 Brandeis 0 1097.6 105.97 48/142 4-3
96 Occidental 0 1088.5 57.94 72/126 14-3
97 Lehigh 0 1081.24 242.51 27/200 7-1
98 North Georgia 0 1072.34 77.66 64/144 10-11
99 Cornell 0 1069.72 134.76 47/158 4-2
100 Cal State-Long Beach 0 1064.93 73.03 70/143 10-4
101 Connecticut 0 1058.76 109.63 51/154 8-5
102 NYU 0 1056.49 149.18 39/183 9-5
103 Mississippi State 0 1054.64 82.11 63/139 8-6
104 Delaware 0 1049.03 158.91 29/187 4-1
105 Appalachian State 0 1043.87 207.12 29/191 0-5
106 Indiana 0 1043.16 109.81 54/162 4-2
107 Georgetown 0 1034.49 65.77 75/140 6-6
108 Wesleyan 0 1033.65 73.98 73/138 4-2
109 Carnegie Mellon 0 1025.99 59.88 82/139 3-3
110 Cincinnati 0 1022.65 70.34 73/141 9-3
111 Maryland 0 1017.61 75.04 69/143 5-8
112 Yale 0 1014.19 127.94 55/173 3-4
113 Michigan State 0 1011.92 106.15 54/162 4-1
114 Pacific Lutheran 0 1000.51 84.03 60/151 4-4
115 American 0 992.6 69.95 69/148 10-3
116 SUNY-Geneseo 0 987.55 88.83 64/151 4-4
117 Iowa State 0 959.25 53.57 91/137 8-6
118 Syracuse 0 951.11 106.09 72/159 8-6
119 Rice 0 942.13 89.21 76/168 7-6
120 San Diego State University-B 0 936.81 103.17 72/174 2-1
121 Denver 0 928.84 63.53 93/148 14-4
122 Trinity 0 928.51 77.74 82/156 9-5
123 Tulane 0 919.01 110.15 64/175 7-6
124 Swarthmore 0 916.06 79.5 84/157 8-4
125 California-San Diego-B 0 908.98 60.5 94/148 9-8
126 Chico State 0 908.96 81.98 89/167 7-6
127 SUNY-Stony Brook 0 906.2 117.6 74/176 3-4
128 Alabama-Huntsville 0 901.36 61.07 95/150 4-9
129 Alabama-Birmingham 0 884.89 116.42 69/175 2-5
130 Western Washington-B 0 878.34 76.81 93/164 3-2
131 Harvard 0 862.04 130.47 83/189 0-6
132 Northern Arizona 0 861.82 79.18 84/170 8-6
133 MIT 0 841.85 121.11 73/180 7-7
134 George Mason 0 840.98 79.6 99/171 7-6
135 Oregon State 0 839.4 60.26 109/166 6-7
136 Catholic 0 829.99 101.49 77/181 6-7
137 John Brown 0 825.02 71.98 99/168 6-8
138 Montana State University 0 823.08 76.41 91/178 5-3
139 Iowa 0 817.29 62.28 104/164 4-4
140 Dayton 0 810.66 200.72 56/218 8-5
141 Mary Washington 0 806.2 113.75 75/194 4-2
142 Santa Clara 0 802.09 83.1 97/179 5-7
143 LSU 0 801.8 99.91 95/183 6-4
144 Colorado-B 0 795 68.19 105/176 7-8
145 East Carolina 0 790.05 85.13 100/175 2-5
146 Nevada-Reno 0 776.46 66.54 114/168 7-6
147 Michigan Tech 0 774.57 87.34 102/176 2-2
148 UCLA-B 0 766.28 72.77 113/180 8-9
149 Drexel 0 763.07 71.9 112/173 2-4
150 Georgia State 0 760.92 73.16 115/173 3-4
151 Arizona State 0 733.56 77.44 109/181 5-8
152 Texas-B 0 722.12 71 120/184 6-7
153 Rutgers 0 709.29 79.64 112/184 2-3
154 Georgia College 0 703.93 100.46 118/195 5-12
155 Stanford-B 0 700.01 99.81 102/194 5-2
156 Illinois 0 692.87 107.95 110/199 4-2
157 Wisconsin-Milwaukee 0 690.05 64.31 119/180 5-10
158 Bowdoin 0 687.13 63.64 124/180 1-3
159 Vermont-B 0 656.74 62.02 133/184 2-5
160 Washington-B 0 638.96 79.68 117/200 2-3
161 Amherst 0 637.23 42.74 146/181 6-12
162 Humboldt State 0 619.64 136.71 92/212 3-3
163 Williams 0 604.77 97.09 124/204 2-5
164 Maryland-Baltimore County 0 597.06 87.76 135/198 15-7
165 St Benedict 0 592.68 67.87 136/197 2-4
166 Claremont 0 589.87 76.68 132/203 2-8
167 Wisconsin-Eau Claire 0 577.2 130.32 119/219 4-3
168 Sonoma State 0 562.53 63.34 136/196 4-8
169 Pittsburgh-B 0 562.25 79 136/199 3-7
170 Tennessee-Chattanooga 0 557.12 78.17 138/215 5-6
171 West Virginia 0 555.33 105.39 128/211 9-11
172 Air Force 0 550.71 81.07 140/204 7-10
173 Virginia Commonwealth 0 545.55 74.73 143/209 4-7
174 Florida-B 0 534.58 55.32 154/199 7-8
175 Rhode Island 0 528.84 137.69 112/233 3-4
176 California-Irvine 0 525.66 104.16 136/211 3-4
177 Wake Forest 0 521.63 110.99 115/221 5-3
178 Jacksonville State 0 520.26 103.04 128/209 1-6
179 Northeastern-B 0 518.93 90.21 146/210 5-3
180 Lewis & Clark 0 498.88 90.85 148/210 0-6
181 Portland State 0 489.22 89.41 147/213 1-7
182 Cedarville 0 484.26 124.37 127/221 1-4
183 Tulsa 0 484.26 72.08 153/212 6-6
184 Baylor 0 477.23 66.91 160/221 2-5
185 George Washington-B 0 476.24 80.02 152/216 10-4
186 Macalester 0 473.02 67.4 156/217 5-6
187 Charleston 0 462.09 122.16 136/230 0-6
188 Arizona 0 445.82 78.34 155/213 3-9
189 Texas Christian 0 443.19 69.37 153/218 4-8
190 Washington University-B 0 437.83 144.05 111/237 3-4
191 Pennsylvania-B 0 432.01 112.73 146/224 6-1
192 Cal Poly SLO-B 0 421.63 116.25 139/233 1-11
193 Boise State 0 402.66 93.19 153/226 3-5
194 Princeton 0 393.43 100.35 148/225 0-5
195 Arkansas 0 387.72 76.04 166/221 5-9
196 Minnesota-Duluth 0 380.78 104.35 151/236 2-5
197 Grinnell 0 323.78 89.21 163/231 4-9
198 Georgia Southern 0 320.88 114.44 158/237 1-5
199 SUNY-Fredonia 0 317.47 150.98 131/238 2-5
200 Wooster 0 311.29 60.23 178/222 0-3
201 Miami (Ohio) 0 310.86 108.29 159/230 5-7
202 California-B 0 302.06 78.84 173/230 2-11
203 Montana 0 299.52 76.77 175/228 1-6
204 Georgetown-B 0 288.79 86.55 169/240 4-2
205 Belmont 0 272.48 110.44 164/240 1-11
206 Oklahoma 0 266.36 80.79 174/231 4-9
207 Luther 0 253.84 123.85 162/237 4-3
208 SUNY-Albany 0 251.37 38.41 188/222 5-8
209 California-Davis-B 0 230.13 87.38 177/237 2-11
210 Allegheny 0 218.24 138.66 152/246 6-2
211 Idaho 0 213.69 32.42 199/224 0-6
212 Marist 0 211.97 91.29 178/240 5-1
213 Nebraska 0 209.71 131.21 158/245 4-8
214 DePaul 0 203.03 160.8 130/247 5-2
215 Columbia-B 0 200.24 62.65 193/233 4-7
216 University of North Carolina - Asheville 0 164.26 43.27 204/230 1-1
217 Colorado School of Mines 0 158.93 119.03 169/245 1-8
218 North Carolina-B 0 151.14 127.59 159/245 1-5
219 Berry 0 146.46 127.65 174/243 3-3
220 Wisconsin-La Crosse 0 118.05 193.11 147/252 0-4
221 Sam Houston State 0 114.48 97.02 185/240 1-5
222 Brown-B 0 86.45 62.53 198/238 3-3
223 Christopher Newport 0 81.54 115.28 190/245 2-5
224 Virginia-B 0 79.69 152.09 173/252 2-10
225 Pacific Lutheran-B 0 68.84 206.67 117/255 0-4
226 North Texas 0 66.58 129.78 188/252 0-11
227 Michigan-B 0 63.75 178.75 168/254 2-3
228 Georgia Tech-B 0 40.81 159.57 174/252 2-4
229 Ithaca 0 19.11 135.3 179/248 2-4
230 Wisconsin-Oshkosh 0 5.32 160.52 175/254 1-5
231 Wisconsin 0 4.43 191.14 163/256 2-5
232 William & Mary-B 0 -0.57 51.49 217/242 1-6
233 Shippensburg 0 -7.35 75.87 208/246 2-4
234 Florida Tech 0 -31.26 58.24 218/245 1-4
235 Knox 0 -44.24 224.87 144/260 1-5
236 Johns Hopkins 0 -55.81 86.12 211/249 7-9
237 Missouri 0 -132.47 105.46 211/254 2-10
238 FSU-B 0 -134.81 127.75 209/255 2-8
239 RIT 0 -136.14 210.52 136/260 0-6
240 Drake University 0 -163.32 163.74 206/258 1-6
241 Miami 0 -193.11 175.59 202/260 1-6
242 SUNY Cortland 0 -196.81 78.52 228/252 5-6
243 Kansas State 0 -204.51 151.76 203/259 1-6
244 Franciscan 0 -246.77 259.77 160/262 1-4
245 Towson-B 0 -248.26 116.65 219/256 2-13
246 Hofstra 0 -261.76 102.52 226/257 2-5
247 Lehigh-B-B 0 -266.94 180.99 201/260 2-4
248 Messiah 0 -316.13 63.65 237/255 3-5
249 Houston 0 -339.12 232.95 184/262 0-6
250 College of New Jersey 0 -389.74 94.94 237/260 0-6
251 Emory-B-B 0 -394.03 196.94 203/262 0-10
252 Northwestern-B 0 -417.33 169.65 208/262 0-7
253 American-B 0 -514.99 145.33 234/261 1-12
254 Salisbury 0 -574 225.19 222/263 1-6
255 Temple-B-B 0 -576.3 123.82 242/261 1-4
256 Ohio State-B 0 -652.53 239.41 214/263 3-10
257 Haverford/Bryn Mawr-B 0 -668.17 234.92 224/263 1-4
258 Goucher 0 -748.45 210.36 239/263 2-11
259 Akron 0 -803.63 399.48 183/263 3-4
260 SUNY-Buffalo 0 -863.92 179.51 249/263 1-12
261 Xavier 0 -994.91 446.19 206/263 1-6
262 Oberlin-B 0 -1076.59 304.88 243/263 0-6
263 Ohio Wesleyan 0 -1338.89 618.21 148/263 0-6

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)