College Basketball Sectionals Page


Jeff Sagarin'stm College Basketball Sectionals Page



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All Contents Copyright © 2012 Jeff Sagarintm. All Rights Reserved.

Last updated: 2012 December 19 Wednesday  14:38:39.184  Central Standard Time  = GMT/UTC-06:00
              2012 December 19 Wednesday  20:38:39.184  Greenwich Mean Time    = GMT/UTC
JULIAN DATE= 2456281


This is a very difficult math problem to get the ultimate "perfect" answer - that is, the absolute
minimum distance sum.  The technique used is "simulated annealing". I'll be continually running it and trying to improve the answer.

So check here every once in a while to see if it's been updated.



College Basketball Sectionals


The 1-64 listing of the sectionals is in a rough east-west order. The combining of the sectionals into regionals will be done in the next stage. So don't read anything into the 1-64 ordering now. The goal is to minimize the total mileage - that is, have the teams as close together as possible. Actually, to minimize the product of the average distance times the root-mean-square distance. By mileage, I'm referring to the sum of the mileages from the 64 sectionals. The mileage for a given sectional is the sum of the distances between all possible pairs of teams in a sectional. In a 5-team sectional (which 37 are),there are 5*4 / 2 = 10 possible pairs of teams. In a 6-team sectional (which 27 are) there are 6*5 / 2 = 15 possible pairs of teams. 37 sectionals with 5 teams = 185 teams 37 * 10 = 370 pairs 27 sectionals with 6 teams = 162 teams 27 * 15 = 405 pairs ------------- ----------- 347 teams 775 pairs And the numbers to the left of each team's name are simply the code numbers used by the program for each team. They have no other significance. The suggestion here is that the host role of the sectionals would rotate among the teams so that each team gets to host its sectional every 5(6) years.
total golden miles=104330.8942 total pairs=775 average golden miles between pairs of teams=134.62 suggested T0=.387955356 total linear miles=69308.4323 total pairs=775 average linear miles between pairs of teams=89.43 suggested T0=.257724021 total miles squared=31825692.6423 total pairs=775 square root(mean miles squared) between pairs of teams=202.65 suggested T0=118.344120637 ____________________________________________________________________________________________________ SECTIONAL# 1 total miles=980 average distance between teams=98 pairs=10 teams=5 4 Boston U. 42.333987 -71.104774 $ 5 Harvard 42.378430 -71.116441 $ 1 Maine 44.899236 -68.669199 $ 2 New Hampshire 43.135641 -70.932837 $ 3 Northeastern 42.339820 -71.087552 $ ____________________________________________________________________________________________________ SECTIONAL# 2 total miles=451 average distance between teams=30 pairs=15 teams=6 6 Boston College 42.335653 -71.171165 $ 7 Brown 41.826211 -71.397556 $ 9 Bryant College 41.921264 -71.537983 $ 11 Holy Cross 42.238982 -71.807849 $ 8 Providence 41.843711 -71.437836 $ 10 Rhode Island 41.486212 -71.548116 $ ____________________________________________________________________________________________________ SECTIONAL# 3 total miles=269 average distance between teams=27 pairs=10 teams=5 16 Cent. Connecticut State 41.690100 -72.768152 $ 12 Connecticut 41.809265 -72.253690 $ 15 Hartford 41.795655 -72.715094 $ 17 Quinnipiac 41.418986 -72.894268 $ 18 Yale 41.311208 -72.926491 $ ____________________________________________________________________________________________________ SECTIONAL# 4 total miles=904 average distance between teams=90 pairs=10 teams=5 25 Albany-NY 42.660016 -73.771364 $ 13 Dartmouth 43.704793 -72.292591 $ 14 Massachusetts 42.388979 -72.528699 $ 24 Siena 42.718412 -73.753731 $ 20 Vermont 44.477549 -73.193183 $ ____________________________________________________________________________________________________ SECTIONAL# 5 total miles=599 average distance between teams=40 pairs=15 teams=6 32 Army 41.387872 -73.964306 $ 22 Fairfield 41.160652 -73.257615 $ 23 Hofstra 40.714546 -73.600684 $ 30 Marist 41.722038 -73.934304 $ 21 Sacred Heart 41.221485 -73.241504 $ 19 Stony Brook-NY 40.917321 -73.124554 $ ____________________________________________________________________________________________________ SECTIONAL# 6 total miles=139 average distance between teams=9 pairs=15 teams=6 31 Columbia 40.808990 -73.961249 $ 36 Fairleigh Dickinson 40.898432 -74.028195 $ 28 Fordham 40.861211 -73.885969 $ 26 Iona 40.925932 -73.787077 $ 29 Manhattan 40.889544 -73.901525 $ 27 St. John's 40.722047 -73.795134 $ ____________________________________________________________________________________________________ SECTIONAL# 7 total miles=124 average distance between teams=8 pairs=15 teams=6 33 Long Island U. 40.690000 -73.981667 $ 39 NJIT(New Jersey Tech) 40.742323 -74.178756 $ 37 Saint Peter's 40.727324 -74.071253 $ 40 Seton Hall 40.742601 -74.247369 $ 34 St. Francis-NY 40.693294 -73.991535 $ 38 Wagner 40.614548 -74.094308 $ ____________________________________________________________________________________________________ SECTIONAL# 8 total miles=552 average distance between teams=37 pairs=15 teams=6 48 Lafayette 40.698154 -75.207399 $ 51 Lehigh 40.606487 -75.380180 $ 35 Monmouth-NJ 40.278167 -74.006527 $ 42 Princeton 40.342885 -74.656825 $ 43 Rider 40.279275 -74.739327 $ 41 Rutgers 40.499549 -74.444319 $ ____________________________________________________________________________________________________ SECTIONAL# 9 total miles=88 average distance between teams=6 pairs=15 teams=6 46 Drexel 39.954002 -75.192957 $ 45 La Salle 40.038723 -75.154065 $ 47 Pennsylvania 39.950946 -75.193513 $ 49 Saint Joseph's 39.995371 -75.239062 $ 44 Temple 39.980946 -75.152955 $ 50 Villanova 40.038166 -75.344632 $ ____________________________________________________________________________________________________ SECTIONAL#10 total miles=613 average distance between teams=61 pairs=10 teams=5 55 Delaware 39.679556 -75.752991 $ 53 Delaware State 39.185668 -75.544091 $ 54 Md.-Eastern Shore 38.207344 -75.686038 $ 63 Morgan State 39.345940 -76.583022 $ 62 Navy 38.982056 -76.483016 $ ____________________________________________________________________________________________________ SECTIONAL#11 total miles=782 average distance between teams=78 pairs=10 teams=5 56 Binghamton-NY 42.089797 -75.968254 $ 69 Bucknell 40.955363 -76.884133 $ 52 Colgate 42.817292 -75.535735 $ 61 Cornell 42.447017 -76.482996 $ 57 Syracuse 43.037844 -76.134646 $ ____________________________________________________________________________________________________ SECTIONAL#12 total miles=702 average distance between teams=47 pairs=15 teams=6 60 Hampton 37.019869 -76.338833 $ 58 Norfolk State 36.849592 -76.262717 $ 59 Old Dominion 36.890148 -76.304386 $ 79 Richmond 37.576257 -77.537487 $ 78 Va. Commonwealth 37.547646 -77.456095 $ 67 William & Mary 37.271536 -76.711624 $ ____________________________________________________________________________________________________ SECTIONAL#13 total miles=217 average distance between teams=22 pairs=10 teams=5 66 Coppin State 39.310384 -76.658303 $ 65 Loyola-Maryland 39.346496 -76.619135 $ 76 Mount St. Mary's 39.681764 -77.353042 $ 64 Towson 39.392329 -76.605801 $ 68 UMBC(Md-Balt) 39.255384 -76.711637 $ ____________________________________________________________________________________________________ SECTIONAL#14 total miles=130 average distance between teams=9 pairs=15 teams=6 74 American U. 38.937055 -77.086922 $ 75 George Mason 38.834002 -77.308596 $ 72 George Washington 38.898723 -77.045810 $ 73 Georgetown 38.907334 -77.072200 $ 71 Howard 38.923722 -77.021366 $ 70 Maryland 38.985944 -76.938586 $ ____________________________________________________________________________________________________ SECTIONAL#15 total miles=969 average distance between teams=97 pairs=10 teams=5 87 Campbell 35.409883 -78.740295 $ 93 Coastal Carolina 33.793782 -79.011979 $ 77 East Carolina 35.600439 -77.364409 $ 86 NC State 35.786589 -78.670735 $ 81 NC Wilmington 34.226837 -77.876930 $ ____________________________________________________________________________________________________ SECTIONAL#16 total miles=817 average distance between teams=82 pairs=10 teams=5 88 Buffalo 42.953113 -78.820868 $ 89 Canisius 42.925336 -78.852535 $ 94 Niagara 43.138666 -79.038933 $ 80 Penn State 40.803950 -77.857224 $ 83 St. Bonaventure 42.079787 -78.482522 $ ____________________________________________________________________________________________________ SECTIONAL#17 total miles=1042 average distance between teams=69 pairs=15 teams=6 90 James Madison 38.438180 -78.873360 $ 96 Liberty 37.350977 -79.180579 $ 82 Longwood 37.300430 -78.395551 $ 97 VMI 37.789576 -79.439482 $ 84 Virginia 38.035417 -78.503346 $ 113 Virginia Tech 37.228740 -80.423662 $ ____________________________________________________________________________________________________ SECTIONAL#18 total miles=438 average distance between teams=29 pairs=15 teams=6 92 Duke 35.997527 -78.942317 $ 98 Elon 36.107080 -79.505856 $ 99 N.C. A&T 36.073746 -79.776419 $ 91 NC Central 35.974276 -78.898605 $ 100 NC Greensboro 36.070969 -79.811143 $ 95 North Carolina 35.899514 -79.043930 $ ____________________________________________________________________________________________________ SECTIONAL#19 total miles=870 average distance between teams=58 pairs=15 teams=6 105 Duquesne 40.436180 -79.992831 $ 103 Pittsburgh 40.442847 -79.959219 $ 107 Robert Morris 40.438958 -79.993664 $ 85 St. Francis-Pa. 40.504237 -78.637518 $ 102 West Virginia 39.634248 -79.954508 $ 115 Youngstown State 41.104225 -80.647019 $ ____________________________________________________________________________________________________ SECTIONAL#20 total miles=1058 average distance between teams=71 pairs=15 teams=6 108 Charleston Southern 32.977127 -80.069864 $ 104 Citadel 32.796010 -79.959256 $ 101 College of Charleston 32.784065 -79.937033 $ 133 Georgia Southern 32.425456 -81.783445 $ 122 Savannah State 32.022434 -81.055112 $ 118 South Carolina State 33.498444 -80.848123 $ ____________________________________________________________________________________________________ SECTIONAL#21 total miles=1083 average distance between teams=72 pairs=15 teams=6 131 Appalachian State 36.214573 -81.680385 $ 116 Charlotte 35.305142 -80.732014 $ 117 Davidson 35.500136 -80.845073 $ 106 High Point 35.972081 -79.993650 $ 114 Radford 37.139015 -80.549502 $ 110 Wake Forest 36.133471 -80.277273 $ ____________________________________________________________________________________________________ SECTIONAL#22 total miles=1118 average distance between teams=112 pairs=10 teams=5 109 Florida Atlantic 26.371188 -80.102543 $ 132 Florida Gulf Coast 26.471045 -81.764672 $ 112 Florida International 25.754267 -80.381998 $ 111 Miami-Florida 25.719546 -80.278662 $ 141 South Florida 28.062795 -82.412315 $ ____________________________________________________________________________________________________ SECTIONAL#23 total miles=1077 average distance between teams=72 pairs=15 teams=6 121 Bethune-Cookman 29.210259 -81.035056 $ 123 Central Florida(UCF) 28.600277 -81.202010 $ 138 Florida 29.648579 -82.349271 $ 128 Jacksonville 30.352462 -81.605371 $ 126 North Florida(UNF) 30.269963 -81.507033 $ 124 Stetson 29.035540 -81.303396 $ ____________________________________________________________________________________________________ SECTIONAL#24 total miles=772 average distance between teams=51 pairs=15 teams=6 129 Gardner-Webb 35.247625 -81.670374 $ 134 Presbyterian College 34.465072 -81.868978 $ 119 South Carolina 33.999044 -81.026481 $ 136 USC Upstate 34.995684 -81.968813 $ 120 Winthrop 34.940700 -81.028411 $ 135 Wofford 34.959011 -81.935382 $ ____________________________________________________________________________________________________ SECTIONAL#25 total miles=901 average distance between teams=90 pairs=10 teams=5 127 Akron 41.076167 -81.511505 $ 130 Cleveland State 41.503107 -81.672908 $ 125 Kent State 41.147834 -81.338441 $ 145 Ohio State 39.996175 -83.018795 $ 137 Ohio U. 39.323129 -82.095422 $ ____________________________________________________________________________________________________ SECTIONAL#26 total miles=1093 average distance between teams=73 pairs=15 teams=6 144 Clemson 34.677049 -82.838754 $ 139 East Tennessee State 36.303440 -82.369029 $ 140 Furman 34.841784 -82.401789 $ 143 NC Asheville 35.618167 -82.565683 $ 156 Tennessee 35.954249 -83.930740 $ 147 Western Carolina 35.310933 -83.181811 $ ____________________________________________________________________________________________________ SECTIONAL#27 total miles=691 average distance between teams=46 pairs=15 teams=6 153 Bowling Green 41.375886 -83.639656 $ 146 Detroit 42.332260 -83.037976 $ 152 Eastern Michigan 42.246983 -83.622716 $ 155 Michigan 42.275872 -83.736052 $ 148 Oakland-Mich. 42.675866 -83.217713 $ 151 Toledo 41.661994 -83.614380 $ ____________________________________________________________________________________________________ SECTIONAL#28 total miles=567 average distance between teams=57 pairs=10 teams=5 149 Georgia 33.951226 -83.373769 $ 162 Georgia State 33.752884 -84.386038 $ 163 Georgia Tech 33.772884 -84.393816 $ 169 Kennesaw State 34.037600 -84.585211 $ 154 Mercer 32.831806 -83.649903 $ ____________________________________________________________________________________________________ SECTIONAL#29 total miles=888 average distance between teams=89 pairs=10 teams=5 161 Eastern Kentucky 37.738135 -84.301599 $ 167 Kentucky 38.030355 -84.499383 $ 178 Louisville 38.215071 -85.759129 $ 142 Marshall 38.423139 -82.430431 $ 150 Morehead State 38.186748 -83.433240 $ ____________________________________________________________________________________________________ SECTIONAL#30 total miles=489 average distance between teams=33 pairs=15 teams=6 168 Cincinnati 39.131448 -84.516332 $ 158 Dayton 39.739781 -84.178273 $ 170 Miami-Ohio 39.509220 -84.734120 $ 164 Northern Kentucky 39.031970 -84.459136 $ 157 Wright State 39.783670 -84.063547 $ 165 Xavier-Ohio 39.149782 -84.477998 $ ____________________________________________________________________________________________________ SECTIONAL#31 total miles=1116 average distance between teams=112 pairs=10 teams=5 184 Alabama State 32.364027 -86.295524 $ 175 Auburn 32.602079 -85.484949 $ 159 Florida A&M 30.426867 -84.285177 $ 160 Florida State 30.440756 -84.291844 $ 180 Troy 31.800713 -85.957173 $ ____________________________________________________________________________________________________ SECTIONAL#32 total miles=987 average distance between teams=99 pairs=10 teams=5 171 Central Michigan 43.591419 -84.775014 $ 172 IPFW 41.116715 -85.097192 $ 166 Michigan State 42.730868 -84.478587 $ 183 Notre Dame 41.703104 -86.239173 $ 177 Western Michigan 42.283651 -85.611951 $ ____________________________________________________________________________________________________ SECTIONAL#33 total miles=952 average distance between teams=95 pairs=10 teams=5 188 Alabama A&M 34.785646 -86.569159 $ 173 Chattanooga 35.046185 -85.300235 $ 179 Jacksonville State 33.822323 -85.766632 $ 185 Middle Tennessee 35.852288 -86.369992 $ 176 Tennessee Tech 36.174505 -85.503865 $ ____________________________________________________________________________________________________ SECTIONAL#34 total miles=578 average distance between teams=58 pairs=10 teams=5 174 Ball State 40.199488 -85.412471 $ 181 Butler 39.838930 -86.172488 $ 182 IUPUI 39.776432 -86.185265 $ 187 Indiana 39.166158 -86.526386 $ 195 Purdue 40.428091 -86.922510 $ ____________________________________________________________________________________________________ SECTIONAL#35 total miles=485 average distance between teams=32 pairs=15 teams=6 197 Austin Peay 36.533382 -87.353897 $ 190 Belmont 36.135613 -86.794721 $ 191 Lipscomb 36.105614 -86.799444 $ 194 Tennessee State 36.167279 -86.830555 $ 193 Vanderbilt 36.148113 -86.803055 $ 186 Western Kentucky 36.987542 -86.451658 $ ____________________________________________________________________________________________________ SECTIONAL#36 total miles=334 average distance between teams=22 pairs=15 teams=6 201 Chicago State 41.718090 -87.608659 $ 203 DePaul 41.922810 -87.653110 $ 202 Illinois-Chicago 41.871977 -87.649220 $ 204 Loyola-Chicago 42.000587 -87.658112 $ 205 Northwestern 42.055586 -87.674503 $ 196 Valparaiso 41.462539 -87.043641 $ ____________________________________________________________________________________________________ SECTIONAL#37 total miles=954 average distance between teams=95 pairs=10 teams=5 200 Alabama 33.215118 -87.546673 $ 221 Mississippi 34.366773 -89.535360 $ 214 Mississippi State 33.454844 -88.788664 $ 189 Samford 33.465107 -86.793323 $ 192 UAB 33.504828 -86.799990 $ ____________________________________________________________________________________________________ SECTIONAL#38 total miles=932 average distance between teams=93 pairs=10 teams=5 208 Marquette 43.037514 -87.929807 $ 213 Northern Illinois 41.937529 -88.775921 $ 207 Wis.-Green Bay 44.529993 -87.920934 $ 206 Wis.-Milwaukee 43.075568 -87.878973 $ 219 Wisconsin 43.073885 -89.410953 $ ____________________________________________________________________________________________________ SECTIONAL#39 total miles=767 average distance between teams=77 pairs=10 teams=5 222 Bradley 40.698093 -89.617043 $ 209 Eastern Illinois 39.480590 -88.175596 $ 211 Illinois 40.108643 -88.228382 $ 216 Illinois State 40.512536 -88.997576 $ 198 Indiana State 39.468648 -87.408631 $ ____________________________________________________________________________________________________ SECTIONAL#40 total miles=865 average distance between teams=86 pairs=10 teams=5 199 Evansville 37.971709 -87.531681 $ 212 Murray State 36.611445 -88.322261 $ 220 SE Missouri State 37.312551 -89.530926 $ 217 Southern Illinois 37.713106 -89.218695 $ 215 Tennessee-Martin 36.341452 -88.864227 $ ____________________________________________________________________________________________________ SECTIONAL#41 total miles=1109 average distance between teams=111 pairs=10 teams=5 227 Jackson State 32.295980 -90.207866 $ 225 New Orleans 30.027980 -90.067016 $ 210 South Alabama 30.694912 -88.179725 $ 218 Southern Mississippi 31.326563 -89.332285 $ 226 Tulane 29.939927 -90.119518 $ ____________________________________________________________________________________________________ SECTIONAL#42 total miles=529 average distance between teams=53 pairs=10 teams=5 235 LSU 30.414636 -91.176218 $ 238 Louisiana-Lafayette 30.215479 -92.019009 $ 233 Nicholls State 29.794375 -90.802037 $ 230 SE Louisiana 30.515191 -90.471200 $ 236 Southern University 30.523522 -91.190386 $ ____________________________________________________________________________________________________ SECTIONAL#43 total miles=975 average distance between teams=98 pairs=10 teams=5 242 Ark.-Little Rock 34.721759 -92.341264 $ 239 Ark.-Pine Bluff 34.242320 -92.019585 $ 231 Arkansas State 35.843130 -90.677056 $ 243 Central Arkansas 35.079252 -92.457102 $ 223 Memphis 35.118701 -89.937311 $ ____________________________________________________________________________________________________ SECTIONAL#44 total miles=895 average distance between teams=89 pairs=10 teams=5 234 Alcorn State 31.877105 -91.141220 $ 246 Grambling 32.525428 -92.715152 $ 245 Louisiana Tech 32.527372 -92.646260 $ 240 Louisiana-Monroe 32.526532 -92.074578 $ 229 MVSU(Mississippi Valley St.) 33.515120 -90.338696 $ ____________________________________________________________________________________________________ SECTIONAL#45 total miles=1542 average distance between teams=154 pairs=10 teams=5 241 Missouri 38.945872 -92.327684 $ 250 Missouri State 37.198382 -93.278520 $ 224 SIU-Edwardsville 38.796333 -89.999826 $ 228 Saint Louis 38.635329 -90.233723 $ 255 UMKC 39.035005 -94.577178 $ ____________________________________________________________________________________________________ SECTIONAL#46 total miles=1109 average distance between teams=111 pairs=10 teams=5 252 Drake 41.601378 -93.651886 $ 237 Iowa 41.661683 -91.536280 $ 251 Iowa State 42.026097 -93.648552 $ 244 Northern Iowa 42.515818 -92.457410 $ 232 Western Illinois 40.464208 -90.683742 $ ____________________________________________________________________________________________________ SECTIONAL#47 total miles=1145 average distance between teams=114 pairs=10 teams=5 253 Lamar 29.879382 -93.926837 $ 248 McNeese State 30.180485 -93.217376 $ 247 Northwestern State 31.753220 -93.097664 $ 262 Sam Houston State 30.714360 -95.549388 $ 256 Stephen F. Austin 31.621568 -94.649376 $ ____________________________________________________________________________________________________ SECTIONAL#48 total miles=586 average distance between teams=39 pairs=15 teams=6 258 Houston 29.720507 -95.343549 $ 261 Houston Baptist 29.694786 -95.517220 $ 266 Prairie View A&M 30.092163 -95.989678 $ 260 Rice 29.719118 -95.397439 $ 268 Texas A&M 30.617700 -96.338296 $ 259 Texas Southern 29.722729 -95.360772 $ ____________________________________________________________________________________________________ SECTIONAL#49 total miles=1055 average distance between teams=105 pairs=10 teams=5 264 Creighton 41.265276 -95.947514 $ 257 Kansas 38.958058 -95.247750 $ 269 Kansas State 39.200400 -96.588400 $ 270 Nebraska 40.817779 -96.701683 $ 267 Nebraska-Omaha 41.257087 -96.008717 $ ____________________________________________________________________________________________________ SECTIONAL#50 total miles=2156 average distance between teams=216 pairs=10 teams=5 249 Minnesota 44.974410 -93.233002 $ 276 North Dakota 47.927668 -97.071444 $ 273 North Dakota State 46.894687 -96.803415 $ 274 South Dakota 42.783118 -96.924328 $ 271 South Dakota State 44.319431 -96.783275 $ ____________________________________________________________________________________________________ SECTIONAL#51 total miles=1723 average distance between teams=115 pairs=15 teams=6 254 Arkansas 36.068691 -94.172149 $ 283 Oklahoma 35.203956 -97.444478 $ 275 Oklahoma State 36.121995 -97.070313 $ 265 Oral Roberts 36.049262 -95.951105 $ 263 Tulsa 36.152316 -95.946106 $ 280 Wichita State 37.719180 -97.293378 $ ____________________________________________________________________________________________________ SECTIONAL#52 total miles=543 average distance between teams=54 pairs=10 teams=5 277 Baylor 31.544889 -97.119446 $ 279 North Texas 33.211508 -97.150013 $ 272 SMU 32.845127 -96.784167 $ 282 TCU 32.709298 -97.361684 $ 278 Texas-Arlington 32.729298 -97.126677 $ ____________________________________________________________________________________________________ SECTIONAL#53 total miles=1491 average distance between teams=149 pairs=10 teams=5 284 Texas 30.286041 -97.738894 $ 281 Texas A&M-CorpusChristi 27.714198 -97.324713 $ 285 Texas State 29.889941 -97.939450 $ 286 Texas-Pan American 26.309793 -98.174177 $ 287 Texas-San Antonio 29.577172 -98.622799 $ ____________________________________________________________________________________________________ SECTIONAL#54 total miles=591 average distance between teams=59 pairs=10 teams=5 293 Colorado 40.005541 -105.264434 $ 292 Colorado State 40.574982 -105.083867 $ 291 Denver 39.676654 -104.962203 $ 289 Northern Colorado 40.409981 -104.693021 $ 294 Wyoming 41.311923 -105.576378 $ ____________________________________________________________________________________________________ SECTIONAL#55 total miles=3019 average distance between teams=302 pairs=10 teams=5 290 Air Force 38.990270 -104.858313 $ 296 New Mexico 35.083936 -106.619191 $ 297 New Mexico State 32.283428 -106.753336 $ 288 Texas Tech 33.585918 -101.871834 $ 295 UTEP 31.777608 -106.506099 $ ____________________________________________________________________________________________________ SECTIONAL#56 total miles=1264 average distance between teams=84 pairs=15 teams=6 300 BYU 40.245788 -111.651033 $ 307 Idaho State 42.866859 -112.433312 $ 304 Utah 40.764946 -111.848546 $ 303 Utah State 41.741042 -111.812721 $ 302 Utah Valley State 40.289398 -111.706315 $ 306 Weber State 41.211055 -111.944385 $ ____________________________________________________________________________________________________ SECTIONAL#57 total miles=2297 average distance between teams=230 pairs=10 teams=5 298 Arizona 32.231187 -110.952591 $ 305 Arizona State 33.417268 -111.935421 $ 301 Northern Arizona 35.190012 -111.658217 $ 308 Southern Utah 37.676088 -113.068560 $ 310 UNLV 36.107750 -115.141665 $ ____________________________________________________________________________________________________ SECTIONAL#58 total miles=2337 average distance between teams=156 pairs=15 teams=6 318 Eastern Washington 47.489889 -117.582985 $ 317 Gonzaga 47.665725 -117.402435 $ 312 Idaho 46.725721 -117.011276 $ 309 Montana 46.860202 -113.983720 $ 299 Montana State 45.669652 -111.053003 $ 314 Washington State 46.730997 -117.158226 $ ____________________________________________________________________________________________________ SECTIONAL#59 total miles=841 average distance between teams=56 pairs=15 teams=6 320 CS Fullerton 33.880292 -117.885615 $ 321 Long Beach State 33.776406 -118.114232 $ 315 San Diego 32.771994 -117.191701 $ 313 San Diego State 32.776717 -117.070864 $ 319 UC Irvine 33.646132 -117.842833 $ 316 UC Riverside 33.973349 -117.330877 $ ____________________________________________________________________________________________________ SECTIONAL#60 total miles=564 average distance between teams=38 pairs=15 teams=6 325 CS Northridge 34.238615 -118.531197 $ 323 Loyola Marymount 33.970846 -118.416744 $ 326 Pepperdine 34.040563 -118.709253 $ 322 Southern California 34.020846 -118.285630 $ 330 UC Santa Barbara 34.416107 -119.849027 $ 324 UCLA 34.071398 -118.438413 $ ____________________________________________________________________________________________________ SECTIONAL#61 total miles=2177 average distance between teams=218 pairs=10 teams=5 311 Boise State 43.602945 -116.198450 $ 329 Nevada 39.541577 -119.814914 $ 332 Pacific 37.979645 -121.311336 $ 333 Sacramento State 38.562684 -121.424120 $ 334 UC Davis 38.540184 -121.749128 $ ____________________________________________________________________________________________________ SECTIONAL#62 total miles=1306 average distance between teams=131 pairs=10 teams=5 327 CS Bakersfield 35.372504 -119.012900 $ 331 Cal Poly-SLO 35.300808 -120.660727 $ 328 Fresno State 36.812450 -119.746533 $ 335 San Jose State 37.334386 -121.881066 $ 336 Santa Clara 37.349108 -121.939957 $ ____________________________________________________________________________________________________ SECTIONAL#63 total miles=9741 average distance between teams=974 pairs=10 teams=5 339 California 37.869648 -122.258858 $ 347 Hawaii 21.300278 -157.823056 $ 337 Saint Mary's-Cal. 37.841037 -122.108020 $ 342 San Francisco 37.775485 -122.450805 $ 338 Stanford 37.427161 -122.170242 $ ____________________________________________________________________________________________________ SECTIONAL#64 total miles=1921 average distance between teams=128 pairs=15 teams=6 345 Oregon 44.035125 -123.084531 $ 346 Oregon State 44.567344 -123.278155 $ 344 Portland 45.572062 -122.724265 $ 343 Portland State 45.512063 -122.683707 $ 341 Seattle 47.607629 -122.313223 $ 340 Washington 47.656209 -122.306515 $ ____________________________________________________________________________________________________ ________________________________________________________________________________ Explanation of Data It's really hard to get the exact solution other than literally checking every possible combination but with 402 Indiana high school(345 in NCAA division I) teams, you can see that the factorial issue soon makes that impossible on even the best PC's and in fact for even the fastest super-computers. In fact, for the Indiana High Schools, based on there being 46 sectionals with 6 teams and 18 sectionals with 7 teams, I think it would be: 402! ____________________________________ (6!)^46 * (7!)^18 And the natural logarithm of the answer is 1556.3926512477 and thus the logbase10 of the answer is 675.9327401116 which means the number of possible combinations is 10^675.9327401116 which is an amazingly large number! It would be actually be an exact integer, but I don't have access to a computer that can handle such large integers. I think only the latest "super computers" can. For college basketball, it would be 347! ____________________________________ 10^578.3858179936 which is also a number beyond the capacity to (5!)^37 * (6!)^27 simply "try all the possibilities". NOTE: I originally had underestimated these quantities by having (incorrectly) an additional factor of 64! in the denominators. An observant reader named Loren Maxwell alerted me to this and so it's been corrected. Remember, there are 31.5576 million seconds in an average year or 3.16 * 10^7 seconds. Thus for even a super-computer to check every possibility in one-year, it would have to evaluate more than 10^668 possibilities per second for the high schools and more than 10^570 per second for the colleges. So the simulated annealing technique is used to avoid the impossible task of literally checking every possibility. It was first developed in the early 1950s at Los Alamos by guys like Edward Teller when they (Metropolis, N.; Rosenbluth, A. W.; Rosenbluth, M.; Teller, A. H.; and Teller, E. "Equation of State Calculations by Fast Computing Machines." J. Chem. Phys. 21, 1087-1092, 1953. ) were working on the hydrogen bomb. I was in my early oughts then and so was only consulting with them on an informal basis :-) (just kidding!) at that time.
[ Monte Carlo Landmark Papers ]

[ Equation of State Calculations by Fast Computing Machines ]

> Equation of State Calculations by Fast Computing Machines
> N. Metropolis, A.W.Rosenbluth, M.N.Rosenbluth, A.H.Teller and E. Teller 1953
> The Journal of Chemical Physics, 21, 1087 (1953)
> THE paper. Probably THE most important algorithm of the 20th century, often called the M(RT)2 algorithm from the names of the authors.
  (the paper begins in the middle of page 1087)


The exact same technique could be used to redistrict
for congressional and state districts if you were to treat each
voter as a "team".  And each district would end up with very close to the
same number of voters and those voters would all be close to each other
geographically.  No more ludicrously shaped districts created totally for the
purpose of giving an advantage to the party drawing the lines.
Of course you'd need to use the supercomputers at the major universities
because even using simulated annealing would take a very long time with
several million "teams(voters)" in each state :-D

But the neat thing about this is that each party could have a mathematician
who liked them run the program and they'd either both get the same answer,
or the one with the lower total distance would have the better answer.
The fact that this would literally "take politics out of the equation", is probably
the reason that it wouldn't be adopted;  each party would worry that an honest
redistricting could take away "their" safe seats.
Enjoy!
Jeff Sagarin
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