College Basketball Sectionals Page


Jeff Sagarin'stm College Basketball Sectionals Page



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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.

Last updated: 2016 January 29 Friday  07:40:50.515  Central Standard Time  = GMT/UTC-06:00
              2016 January 29 Friday  13:40:50.515  Greenwich Mean Time    = GMT/UTC
JULIAN DATE= 2457417

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 33 are),there are 5*4 / 2 = 10 possible pairs of teams. In a 6-team sectional (which 31 are) there are 6*5 / 2 = 15 possible pairs of teams. 33 sectionals with 5 teams = 165 teams 33 * 10 = 330 pairs 31 sectionals with 6 teams = 186 teams 31 * 15 = 465 pairs ------------- ----------- 351 teams 795 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=106455.2673 total pairs=795 average golden miles between pairs of teams=133.91 suggested T0=.381498566 total linear miles=70955.2185 total pairs=795 average linear miles between pairs of teams=89.25 suggested T0=.254278767 total miles squared=32087272.7387 total pairs=795 square root(mean miles squared) between pairs of teams=200.90 suggested T0=114.989599307 ____________________________________________________________________________________________________ SECTIONAL# 1 total miles=296 average distance between teams=20 pairs=15 teams=6 6 Boston College 42.335653 -71.171165 $ 4 Boston U. 42.333987 -71.104774 $ 5 Harvard 42.378430 -71.116441 $ 12 Holy Cross 42.238982 -71.807849 $ 3 Northeastern 42.339820 -71.087552 $ 7 UMass Lowell 42.655528 -71.324208 $ ____________________________________________________________________________________________________ SECTIONAL# 2 total miles=267 average distance between teams=27 pairs=10 teams=5 8 Brown 41.826211 -71.397556 $ 10 Bryant College 41.921264 -71.537983 $ 13 Connecticut 41.809265 -72.253690 $ 9 Providence 41.843711 -71.437836 $ 11 Rhode Island 41.486212 -71.548116 $ ____________________________________________________________________________________________________ SECTIONAL# 3 total miles=1478 average distance between teams=148 pairs=10 teams=5 14 Dartmouth 43.704793 -72.292591 $ 1 Maine 44.899236 -68.669199 $ 15 Massachusetts 42.388979 -72.528699 $ 2 New Hampshire 43.135641 -70.932837 $ 21 Vermont 44.477549 -73.193183 $ ____________________________________________________________________________________________________ SECTIONAL# 4 total miles=393 average distance between teams=26 pairs=15 teams=6 17 Cent. Connecticut State 41.690100 -72.768152 $ 23 Fairfield 41.160652 -73.257615 $ 18 Quinnipiac 41.418986 -72.894268 $ 22 Sacred Heart 41.221485 -73.241504 $ 20 Stony Brook-NY 40.917321 -73.124554 $ 19 Yale 41.311208 -72.926491 $ ____________________________________________________________________________________________________ SECTIONAL# 5 total miles=640 average distance between teams=64 pairs=10 teams=5 26 Albany-NY 42.660016 -73.771364 $ 33 Army 41.387872 -73.964306 $ 16 Hartford 41.795655 -72.715094 $ 31 Marist 41.722038 -73.934304 $ 25 Siena 42.718412 -73.753731 $ ____________________________________________________________________________________________________ SECTIONAL# 6 total miles=189 average distance between teams=13 pairs=15 teams=6 37 Fairleigh Dickinson 40.898432 -74.028195 $ 29 Fordham 40.861211 -73.885969 $ 24 Hofstra 40.714546 -73.600684 $ 27 Iona 40.925932 -73.787077 $ 30 Manhattan 40.889544 -73.901525 $ 28 St. John's 40.722047 -73.795134 $ ____________________________________________________________________________________________________ SECTIONAL# 7 total miles=123 average distance between teams=8 pairs=15 teams=6 32 Columbia 40.808990 -73.961249 $ 34 Long Island U. 40.690000 -73.981667 $ 40 NJIT(New Jersey Tech) 40.742323 -74.178756 $ 38 Saint Peter's 40.727324 -74.071253 $ 35 St. Francis-NY 40.693294 -73.991535 $ 39 Wagner 40.614548 -74.094308 $ ____________________________________________________________________________________________________ SECTIONAL# 8 total miles=513 average distance between teams=34 pairs=15 teams=6 49 Lafayette 40.698154 -75.207399 $ 36 Monmouth-NJ 40.278167 -74.006527 $ 43 Princeton 40.342885 -74.656825 $ 44 Rider 40.279275 -74.739327 $ 42 Rutgers 40.499549 -74.444319 $ 41 Seton Hall 40.742601 -74.247369 $ ____________________________________________________________________________________________________ SECTIONAL# 9 total miles=88 average distance between teams=6 pairs=15 teams=6 47 Drexel 39.954002 -75.192957 $ 46 La Salle 40.038723 -75.154065 $ 48 Pennsylvania 39.950946 -75.193513 $ 50 Saint Joseph's 39.995371 -75.239062 $ 45 Temple 39.980946 -75.152955 $ 51 Villanova 40.038166 -75.344632 $ ____________________________________________________________________________________________________ SECTIONAL#10 total miles=847 average distance between teams=85 pairs=10 teams=5 56 Delaware 39.679556 -75.752991 $ 54 Delaware State 39.185668 -75.544091 $ 52 Lehigh 40.606487 -75.380180 $ 55 Md.-Eastern Shore 38.207344 -75.686038 $ 63 Navy 38.982056 -76.483016 $ ____________________________________________________________________________________________________ SECTIONAL#11 total miles=782 average distance between teams=78 pairs=10 teams=5 57 Binghamton-NY 42.089797 -75.968254 $ 70 Bucknell 40.955363 -76.884133 $ 53 Colgate 42.817292 -75.535735 $ 62 Cornell 42.447017 -76.482996 $ 58 Syracuse 43.037844 -76.134646 $ ____________________________________________________________________________________________________ SECTIONAL#12 total miles=702 average distance between teams=47 pairs=15 teams=6 61 Hampton 37.019869 -76.338833 $ 59 Norfolk State 36.849592 -76.262717 $ 60 Old Dominion 36.890148 -76.304386 $ 80 Richmond 37.576257 -77.537487 $ 79 Va. Commonwealth 37.547646 -77.456095 $ 68 William & Mary 37.271536 -76.711624 $ ____________________________________________________________________________________________________ SECTIONAL#13 total miles=284 average distance between teams=19 pairs=15 teams=6 67 Coppin State 39.310384 -76.658303 $ 66 Loyola-Maryland 39.346496 -76.619135 $ 64 Morgan State 39.345940 -76.583022 $ 77 Mount St. Mary's 39.681764 -77.353042 $ 65 Towson 39.392329 -76.605801 $ 69 UMBC(Md-Balt) 39.255384 -76.711637 $ ____________________________________________________________________________________________________ SECTIONAL#14 total miles=130 average distance between teams=9 pairs=15 teams=6 75 American U. 38.937055 -77.086922 $ 76 George Mason 38.834002 -77.308596 $ 73 George Washington 38.898723 -77.045810 $ 74 Georgetown 38.907334 -77.072200 $ 72 Howard 38.923722 -77.021366 $ 71 Maryland 38.985944 -76.938586 $ ____________________________________________________________________________________________________ SECTIONAL#15 total miles=1067 average distance between teams=71 pairs=15 teams=6 88 Campbell 35.409883 -78.740295 $ 93 Duke 35.997527 -78.942317 $ 78 East Carolina 35.600439 -77.364409 $ 92 NC Central 35.974276 -78.898605 $ 87 NC State 35.786589 -78.670735 $ 82 NC Wilmington 34.226837 -77.876930 $ ____________________________________________________________________________________________________ SECTIONAL#16 total miles=817 average distance between teams=82 pairs=10 teams=5 89 Buffalo 42.953113 -78.820868 $ 90 Canisius 42.925336 -78.852535 $ 95 Niagara 43.138666 -79.038933 $ 81 Penn State 40.803950 -77.857224 $ 84 St. Bonaventure 42.079787 -78.482522 $ ____________________________________________________________________________________________________ SECTIONAL#17 total miles=556 average distance between teams=56 pairs=10 teams=5 91 James Madison 38.438180 -78.873360 $ 97 Liberty 37.350977 -79.180579 $ 83 Longwood 37.300430 -78.395551 $ 98 VMI 37.789576 -79.439482 $ 85 Virginia 38.035417 -78.503346 $ ____________________________________________________________________________________________________ SECTIONAL#18 total miles=448 average distance between teams=30 pairs=15 teams=6 99 Elon 36.107080 -79.505856 $ 107 High Point 35.972081 -79.993650 $ 100 N.C. A&T 36.073746 -79.776419 $ 101 NC Greensboro 36.070969 -79.811143 $ 96 North Carolina 35.899514 -79.043930 $ 111 Wake Forest 36.133471 -80.277273 $ ____________________________________________________________________________________________________ SECTIONAL#19 total miles=870 average distance between teams=58 pairs=15 teams=6 106 Duquesne 40.436180 -79.992831 $ 104 Pittsburgh 40.442847 -79.959219 $ 108 Robert Morris 40.438958 -79.993664 $ 86 St. Francis-Pa. 40.504237 -78.637518 $ 103 West Virginia 39.634248 -79.954508 $ 116 Youngstown State 41.104225 -80.647019 $ ____________________________________________________________________________________________________ SECTIONAL#20 total miles=1125 average distance between teams=75 pairs=15 teams=6 109 Charleston Southern 32.977127 -80.069864 $ 105 Citadel 32.796010 -79.959256 $ 94 Coastal Carolina 33.793782 -79.011979 $ 102 College of Charleston 32.784065 -79.937033 $ 123 Savannah State 32.022434 -81.055112 $ 119 South Carolina State 33.498444 -80.848123 $ ____________________________________________________________________________________________________ SECTIONAL#21 total miles=859 average distance between teams=86 pairs=10 teams=5 132 Appalachian State 36.214573 -81.680385 $ 117 Charlotte 35.305142 -80.732014 $ 118 Davidson 35.500136 -80.845073 $ 115 Radford 37.139015 -80.549502 $ 114 Virginia Tech 37.228740 -80.423662 $ ____________________________________________________________________________________________________ SECTIONAL#22 total miles=1118 average distance between teams=112 pairs=10 teams=5 110 Florida Atlantic 26.371188 -80.102543 $ 133 Florida Gulf Coast 26.471045 -81.764672 $ 113 Florida International 25.754267 -80.381998 $ 112 Miami-Florida 25.719546 -80.278662 $ 142 South Florida 28.062795 -82.412315 $ ____________________________________________________________________________________________________ SECTIONAL#23 total miles=1077 average distance between teams=72 pairs=15 teams=6 122 Bethune-Cookman 29.210259 -81.035056 $ 124 Central Florida(UCF) 28.600277 -81.202010 $ 139 Florida 29.648579 -82.349271 $ 129 Jacksonville 30.352462 -81.605371 $ 127 North Florida(UNF) 30.269963 -81.507033 $ 125 Stetson 29.035540 -81.303396 $ ____________________________________________________________________________________________________ SECTIONAL#24 total miles=772 average distance between teams=51 pairs=15 teams=6 130 Gardner-Webb 35.247625 -81.670374 $ 135 Presbyterian College 34.465072 -81.868978 $ 120 South Carolina 33.999044 -81.026481 $ 137 USC Upstate 34.995684 -81.968813 $ 121 Winthrop 34.940700 -81.028411 $ 136 Wofford 34.959011 -81.935382 $ ____________________________________________________________________________________________________ SECTIONAL#25 total miles=901 average distance between teams=90 pairs=10 teams=5 128 Akron 41.076167 -81.511505 $ 131 Cleveland State 41.503107 -81.672908 $ 126 Kent State 41.147834 -81.338441 $ 146 Ohio State 39.996175 -83.018795 $ 138 Ohio U. 39.323129 -82.095422 $ ____________________________________________________________________________________________________ SECTIONAL#26 total miles=1093 average distance between teams=73 pairs=15 teams=6 145 Clemson 34.677049 -82.838754 $ 140 East Tennessee State 36.303440 -82.369029 $ 141 Furman 34.841784 -82.401789 $ 144 NC Asheville 35.618167 -82.565683 $ 157 Tennessee 35.954249 -83.930740 $ 148 Western Carolina 35.310933 -83.181811 $ ____________________________________________________________________________________________________ SECTIONAL#27 total miles=691 average distance between teams=46 pairs=15 teams=6 154 Bowling Green 41.375886 -83.639656 $ 147 Detroit 42.332260 -83.037976 $ 153 Eastern Michigan 42.246983 -83.622716 $ 156 Michigan 42.275872 -83.736052 $ 149 Oakland-Mich. 42.675866 -83.217713 $ 152 Toledo 41.661994 -83.614380 $ ____________________________________________________________________________________________________ SECTIONAL#28 total miles=1530 average distance between teams=153 pairs=10 teams=5 160 Florida A&M 30.426867 -84.285177 $ 161 Florida State 30.440756 -84.291844 $ 134 Georgia Southern 32.425456 -81.783445 $ 155 Mercer 32.831806 -83.649903 $ 181 Troy 31.800713 -85.957173 $ ____________________________________________________________________________________________________ SECTIONAL#29 total miles=888 average distance between teams=89 pairs=10 teams=5 162 Eastern Kentucky 37.738135 -84.301599 $ 168 Kentucky 38.030355 -84.499383 $ 179 Louisville 38.215071 -85.759129 $ 143 Marshall 38.423139 -82.430431 $ 151 Morehead State 38.186748 -83.433240 $ ____________________________________________________________________________________________________ SECTIONAL#30 total miles=654 average distance between teams=65 pairs=10 teams=5 174 Chattanooga 35.046185 -85.300235 $ 150 Georgia 33.951226 -83.373769 $ 163 Georgia State 33.752884 -84.386038 $ 164 Georgia Tech 33.772884 -84.393816 $ 170 Kennesaw State 34.037600 -84.585211 $ ____________________________________________________________________________________________________ SECTIONAL#31 total miles=489 average distance between teams=33 pairs=15 teams=6 169 Cincinnati 39.131448 -84.516332 $ 159 Dayton 39.739781 -84.178273 $ 171 Miami-Ohio 39.509220 -84.734120 $ 165 Northern Kentucky 39.031970 -84.459136 $ 158 Wright State 39.783670 -84.063547 $ 166 Xavier-Ohio 39.149782 -84.477998 $ ____________________________________________________________________________________________________ SECTIONAL#32 total miles=987 average distance between teams=99 pairs=10 teams=5 172 Central Michigan 43.591419 -84.775014 $ 173 IPFW 41.116715 -85.097192 $ 167 Michigan State 42.730868 -84.478587 $ 184 Notre Dame 41.703104 -86.239173 $ 178 Western Michigan 42.283651 -85.611951 $ ____________________________________________________________________________________________________ SECTIONAL#33 total miles=578 average distance between teams=58 pairs=10 teams=5 175 Ball State 40.199488 -85.412471 $ 182 Butler 39.838930 -86.172488 $ 183 IUPUI 39.776432 -86.185265 $ 188 Indiana 39.166158 -86.526386 $ 196 Purdue 40.428091 -86.922510 $ ____________________________________________________________________________________________________ SECTIONAL#34 total miles=1157 average distance between teams=77 pairs=15 teams=6 201 Alabama 33.215118 -87.546673 $ 185 Alabama State 32.364027 -86.295524 $ 176 Auburn 32.602079 -85.484949 $ 180 Jacksonville State 33.822323 -85.766632 $ 190 Samford 33.465107 -86.793323 $ 193 UAB 33.504828 -86.799990 $ ____________________________________________________________________________________________________ SECTIONAL#35 total miles=837 average distance between teams=56 pairs=15 teams=6 189 Alabama A&M 34.785646 -86.569159 $ 191 Belmont 36.135613 -86.794721 $ 192 Lipscomb 36.105614 -86.799444 $ 186 Middle Tennessee 35.852288 -86.369992 $ 177 Tennessee Tech 36.174505 -85.503865 $ 194 Vanderbilt 36.148113 -86.803055 $ ____________________________________________________________________________________________________ SECTIONAL#36 total miles=1342 average distance between teams=89 pairs=15 teams=6 198 Austin Peay 36.533382 -87.353897 $ 200 Evansville 37.971709 -87.531681 $ 213 Murray State 36.611445 -88.322261 $ 195 Tennessee State 36.167279 -86.830555 $ 216 Tennessee-Martin 36.341452 -88.864227 $ 187 Western Kentucky 36.987542 -86.451658 $ ____________________________________________________________________________________________________ SECTIONAL#37 total miles=334 average distance between teams=22 pairs=15 teams=6 202 Chicago State 41.718090 -87.608659 $ 204 DePaul 41.922810 -87.653110 $ 203 Illinois-Chicago 41.871977 -87.649220 $ 205 Loyola-Chicago 42.000587 -87.658112 $ 206 Northwestern 42.055586 -87.674503 $ 197 Valparaiso 41.462539 -87.043641 $ ____________________________________________________________________________________________________ SECTIONAL#38 total miles=932 average distance between teams=93 pairs=10 teams=5 209 Marquette 43.037514 -87.929807 $ 214 Northern Illinois 41.937529 -88.775921 $ 208 Wis.-Green Bay 44.529993 -87.920934 $ 207 Wis.-Milwaukee 43.075568 -87.878973 $ 220 Wisconsin 43.073885 -89.410953 $ ____________________________________________________________________________________________________ SECTIONAL#39 total miles=767 average distance between teams=77 pairs=10 teams=5 223 Bradley 40.698093 -89.617043 $ 210 Eastern Illinois 39.480590 -88.175596 $ 212 Illinois 40.108643 -88.228382 $ 217 Illinois State 40.512536 -88.997576 $ 199 Indiana State 39.468648 -87.408631 $ ____________________________________________________________________________________________________ SECTIONAL#40 total miles=1354 average distance between teams=135 pairs=10 teams=5 228 Jackson State 32.295980 -90.207866 $ 230 MVSU(Mississippi Valley St.) 33.515120 -90.338696 $ 215 Mississippi State 33.454844 -88.788664 $ 211 South Alabama 30.694912 -88.179725 $ 219 Southern Mississippi 31.326563 -89.332285 $ ____________________________________________________________________________________________________ SECTIONAL#41 total miles=1044 average distance between teams=104 pairs=10 teams=5 242 Missouri 38.945872 -92.327684 $ 221 SE Missouri State 37.312551 -89.530926 $ 225 SIU-Edwardsville 38.796333 -89.999826 $ 229 Saint Louis 38.635329 -90.233723 $ 218 Southern Illinois 37.713106 -89.218695 $ ____________________________________________________________________________________________________ SECTIONAL#42 total miles=726 average distance between teams=48 pairs=15 teams=6 236 LSU 30.414636 -91.176218 $ 226 New Orleans 30.027980 -90.067016 $ 234 Nicholls State 29.794375 -90.802037 $ 231 SE Louisiana 30.515191 -90.471200 $ 237 Southern University 30.523522 -91.190386 $ 227 Tulane 29.939927 -90.119518 $ ____________________________________________________________________________________________________ SECTIONAL#43 total miles=1630 average distance between teams=109 pairs=15 teams=6 243 Ark.-Little Rock 34.721759 -92.341264 $ 240 Ark.-Pine Bluff 34.242320 -92.019585 $ 232 Arkansas State 35.843130 -90.677056 $ 244 Central Arkansas 35.079252 -92.457102 $ 224 Memphis 35.118701 -89.937311 $ 222 Mississippi 34.366773 -89.535360 $ ____________________________________________________________________________________________________ SECTIONAL#44 total miles=660 average distance between teams=66 pairs=10 teams=5 235 Alcorn State 31.877105 -91.141220 $ 247 Grambling 32.525428 -92.715152 $ 246 Louisiana Tech 32.527372 -92.646260 $ 241 Louisiana-Monroe 32.526532 -92.074578 $ 248 Northwestern State 31.753220 -93.097664 $ ____________________________________________________________________________________________________ SECTIONAL#45 total miles=1109 average distance between teams=111 pairs=10 teams=5 253 Drake 41.601378 -93.651886 $ 238 Iowa 41.661683 -91.536280 $ 252 Iowa State 42.026097 -93.648552 $ 245 Northern Iowa 42.515818 -92.457410 $ 233 Western Illinois 40.464208 -90.683742 $ ____________________________________________________________________________________________________ SECTIONAL#46 total miles=1230 average distance between teams=123 pairs=10 teams=5 254 Lamar 29.879382 -93.926837 $ 239 Louisiana-Lafayette 30.215479 -92.019009 $ 249 McNeese State 30.180485 -93.217376 $ 263 Sam Houston State 30.714360 -95.549388 $ 257 Stephen F. Austin 31.621568 -94.649376 $ ____________________________________________________________________________________________________ SECTIONAL#47 total miles=586 average distance between teams=39 pairs=15 teams=6 259 Houston 29.720507 -95.343549 $ 262 Houston Baptist 29.694786 -95.517220 $ 267 Prairie View A&M 30.092163 -95.989678 $ 261 Rice 29.719118 -95.397439 $ 269 Texas A&M 30.617700 -96.338296 $ 260 Texas Southern 29.722729 -95.360772 $ ____________________________________________________________________________________________________ SECTIONAL#48 total miles=1708 average distance between teams=114 pairs=15 teams=6 265 Creighton 41.265276 -95.947514 $ 258 Kansas 38.958058 -95.247750 $ 270 Kansas State 39.200400 -96.588400 $ 271 Nebraska 40.817779 -96.701683 $ 268 Nebraska-Omaha 41.257087 -96.008717 $ 256 UMKC 39.035005 -94.577178 $ ____________________________________________________________________________________________________ SECTIONAL#49 total miles=1953 average distance between teams=130 pairs=15 teams=6 255 Arkansas 36.068691 -94.172149 $ 251 Missouri State 37.198382 -93.278520 $ 276 Oklahoma State 36.121995 -97.070313 $ 266 Oral Roberts 36.049262 -95.951105 $ 264 Tulsa 36.152316 -95.946106 $ 281 Wichita State 37.719180 -97.293378 $ ____________________________________________________________________________________________________ SECTIONAL#50 total miles=2156 average distance between teams=216 pairs=10 teams=5 250 Minnesota 44.974410 -93.233002 $ 277 North Dakota 47.927668 -97.071444 $ 274 North Dakota State 46.894687 -96.803415 $ 275 South Dakota 42.783118 -96.924328 $ 272 South Dakota State 44.319431 -96.783275 $ ____________________________________________________________________________________________________ SECTIONAL#51 total miles=543 average distance between teams=54 pairs=10 teams=5 278 Baylor 31.544889 -97.119446 $ 280 North Texas 33.211508 -97.150013 $ 273 SMU 32.845127 -96.784167 $ 283 TCU 32.709298 -97.361684 $ 279 Texas-Arlington 32.729298 -97.126677 $ ____________________________________________________________________________________________________ SECTIONAL#52 total miles=1975 average distance between teams=132 pairs=15 teams=6 288 Incarnate Word 29.468072 -98.469261 $ 285 Texas 30.286041 -97.738894 $ 282 Texas A&M-CorpusChristi 27.714198 -97.324713 $ 286 Texas State 29.889941 -97.939450 $ 287 Texas-Pan American 26.309793 -98.174177 $ 289 Texas-San Antonio 29.577172 -98.622799 $ ____________________________________________________________________________________________________ SECTIONAL#53 total miles=3245 average distance between teams=324 pairs=10 teams=5 290 Abilene Christian 32.470381 -99.709113 $ 300 New Mexico State 32.283428 -106.753336 $ 284 Oklahoma 35.203956 -97.444478 $ 291 Texas Tech 33.585918 -101.871834 $ 298 UTEP 31.777608 -106.506099 $ ____________________________________________________________________________________________________ SECTIONAL#54 total miles=1085 average distance between teams=72 pairs=15 teams=6 293 Air Force 38.990270 -104.858313 $ 296 Colorado 40.005541 -105.264434 $ 295 Colorado State 40.574982 -105.083867 $ 294 Denver 39.676654 -104.962203 $ 292 Northern Colorado 40.409981 -104.693021 $ 297 Wyoming 41.311923 -105.576378 $ ____________________________________________________________________________________________________ SECTIONAL#55 total miles=1936 average distance between teams=194 pairs=10 teams=5 301 Arizona 32.231187 -110.952591 $ 308 Arizona State 33.417268 -111.935421 $ 310 Grand Canyon 33.510017 -112.130826 $ 299 New Mexico 35.083936 -106.619191 $ 304 Northern Arizona 35.190012 -111.658217 $ ____________________________________________________________________________________________________ SECTIONAL#56 total miles=1101 average distance between teams=110 pairs=10 teams=5 303 BYU 40.245788 -111.651033 $ 312 Southern Utah 37.676088 -113.068560 $ 307 Utah 40.764946 -111.848546 $ 305 Utah Valley State 40.289398 -111.706315 $ 309 Weber State 41.211055 -111.944385 $ ____________________________________________________________________________________________________ SECTIONAL#57 total miles=2376 average distance between teams=238 pairs=10 teams=5 315 Boise State 43.602945 -116.198450 $ 311 Idaho State 42.866859 -112.433312 $ 313 Montana 46.860202 -113.983720 $ 302 Montana State 45.669652 -111.053003 $ 306 Utah State 41.741042 -111.812721 $ ____________________________________________________________________________________________________ SECTIONAL#58 total miles=582 average distance between teams=58 pairs=10 teams=5 324 CS Fullerton 33.880292 -117.885615 $ 319 San Diego 32.771994 -117.191701 $ 317 San Diego State 32.776717 -117.070864 $ 323 UC Irvine 33.646132 -117.842833 $ 320 UC Riverside 33.973349 -117.330877 $ ____________________________________________________________________________________________________ SECTIONAL#59 total miles=1228 average distance between teams=123 pairs=10 teams=5 322 Eastern Washington 47.489889 -117.582985 $ 321 Gonzaga 47.665725 -117.402435 $ 316 Idaho 46.725721 -117.011276 $ 344 Washington 47.656209 -122.306515 $ 318 Washington State 46.730997 -117.158226 $ ____________________________________________________________________________________________________ SECTIONAL#60 total miles=300 average distance between teams=20 pairs=15 teams=6 329 CS Northridge 34.238615 -118.531197 $ 325 Long Beach State 33.776406 -118.114232 $ 327 Loyola Marymount 33.970846 -118.416744 $ 330 Pepperdine 34.040563 -118.709253 $ 326 Southern California 34.020846 -118.285630 $ 328 UCLA 34.071398 -118.438413 $ ____________________________________________________________________________________________________ SECTIONAL#61 total miles=1730 average distance between teams=173 pairs=10 teams=5 331 CS Bakersfield 35.372504 -119.012900 $ 335 Cal Poly-SLO 35.300808 -120.660727 $ 332 Fresno State 36.812450 -119.746533 $ 334 UC Santa Barbara 34.416107 -119.849027 $ 314 UNLV 36.107750 -115.141665 $ ____________________________________________________________________________________________________ SECTIONAL#62 total miles=1159 average distance between teams=77 pairs=15 teams=6 343 California 37.869648 -122.258858 $ 333 Nevada 39.541577 -119.814914 $ 336 Pacific 37.979645 -121.311336 $ 337 Sacramento State 38.562684 -121.424120 $ 341 Saint Mary's-Cal. 37.841037 -122.108020 $ 338 UC Davis 38.540184 -121.749128 $ ____________________________________________________________________________________________________ SECTIONAL#63 total miles=9767 average distance between teams=977 pairs=10 teams=5 351 Hawaii 21.300278 -157.823056 $ 346 San Francisco 37.775485 -122.450805 $ 339 San Jose State 37.334386 -121.881066 $ 340 Santa Clara 37.349108 -121.939957 $ 342 Stanford 37.427161 -122.170242 $ ____________________________________________________________________________________________________ SECTIONAL#64 total miles=1152 average distance between teams=115 pairs=10 teams=5 349 Oregon 44.035125 -123.084531 $ 350 Oregon State 44.567344 -123.278155 $ 348 Portland 45.572062 -122.724265 $ 347 Portland State 45.512063 -122.683707 $ 345 Seattle 47.607629 -122.313223 $ ____________________________________________________________________________________________________ ____________________________________________________________________________________________________ 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 with 351 teams with 33 sectionals with 5 teams and 31 sectionals with 6 teams, it would be: 351! ____________________________________ = 10^585.4469928238 which is also a number beyond the capacity to (5!)^33 * (6!)^31 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 almost 10^578 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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