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Weeks 1-2 Elo Analysis
Elo ratings for all teams that have played in weeks 1 and 2
Elo ratings for all teams that have played in weeks 1 and 2
Attached Files
-
Matches file (included in report)
matches_week_2_2014.csv
download file
uploaded: 13-03-2014 13:46
filetype: csv
filesize: 229.67kb
downloads: 122
-
Elo report
elo_report_week_2_2014.xlsx
download file
uploaded: 13-03-2014 13:47
filetype: lsx
filesize: 305.91kb
downloads: 513
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Python script
elo.py
download file
uploaded: 13-03-2014 14:34
filetype: .py
filesize: 1.43kb
downloads: 113
Discussion
view entire thread
13-03-2014 14:37
Joe Ross
Re: paper: Weeks 1-2 Elo Analysis
How do the results change if you don't include eliminations?
13-03-2014 14:51
connor.worley
Re: paper: Weeks 1-2 Elo Analysis
Teams that were upset in elims move up a bit (most notably 1114 with a 35 spot jump). Here's a quick look at the top 25 without elims:
Code:
Team Elo Net change 1678 1348.704233 0 1817 1344.119366 3 1024 1343.320635 12 4450 1327.675696 36 33 1324.168502 5 987 1322.929154 13 2468 1320.809335 -4 3393 1319.576459 12 624 1315.602349 -2 1114 1315.295585 35 3683 1315.061656 36 16 1314.684274 -6 1403 1314.394943 18 3604 1313.925403 36 2337 1313.398484 -11 118 1313.160747 -7 4488 1312.959919 -6 176 1312.405035 9 525 1310.636828 -7 254 1310.254616 -18 1736 1305.365745 34 1023 1303.956975 49 1876 1303.95267 46 294 1303.850808 22 3009 1301.648885 27
13-03-2014 16:29
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
I took a look at this last year just for giggles. Included is perl code I used. Also note that I used a k-factor of 32. I normally don't concern myself with rankings/OPR/etc., but I was bored one day.
Quote:
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Originally Posted by Michael Hill
This thread combined with watching Searching for Bobby Fischer earlier today got me wondering how to apply the Elo Rating to FRC, and I think I figured it out. This is the resulting data from the 7 weeks of the 2013 season (Sorted by rating)
Code:
4650 982.089794296798 4755 998.879722986273 1160 1005.63580696492 4234 1007.80265488653 321 1007.93578705957 4060 1014.18233417492 865 1019.24769809173 204 1020.69112670188 818 1026.19352966173 4398 1026.94694016844 1506 1027.13742298458 3167 1028.83751255313 4573 1029.51467487536 3607 1031.21268304486 3453 1031.409363359 2506 1032.43385656209 4532 1032.58573597814 4471 1033.6777037715 1255 1036.95596581586 3515 1037.28640791865 2902 1037.42220102578 4081 1037.84181433329 4680 1039.48464889698 2171 1040.8630633741 4743 1041.31651481374 2926 1042.093260529 451 1042.62182460209 322 1043.6491404653 2832 1045.7148780529 4517 1047.40106468987 4032 1048.18782072589 581 1049.54403251529 4404 1052.80909969208 3536 1053.85665934844 4653 1056.60256481931 1941 1057.03537072986 3256 1057.419034185 4289 1060.95837747809 2853 1061.25162605869 3302 1061.69907895085 3237 1062.41655580015 3783 1062.87822077035 4454 1063.26768643071 4406 1063.49864842402 1922 1064.38666730322 1522 1064.83589998138 4793 1066.85041465773 3493 1067.18136428509 1675 1067.33292602519 2405 1067.96609174255 1351 1068.64718936007 1661 1069.05052097351 3491 1069.21829793876 4721 1069.35729443129 3719 1069.61730092672 4337 1070.04721840224 2180 1070.50167915705 1607 1071.82120266813 280 1072.28193752885 3716 1072.42100870067 4782 1072.53570071915 907 1072.77895957834 3853 1073.96657546736 3398 1074.12978051664 3831 1074.83144694104 423 1074.93771105545 4387 1075.14320913319 3623 1075.95829915874 4637 1076.99431785768 4785 1077.39028590692 4010 1077.58097698408 3259 1077.66200955262 313 1077.96750350088 752 1078.16212218756 3640 1078.17050159868 2156 1078.77450505749 4373 1079.01398736869 4275 1079.43107862278 2347 1079.61536832881 3055 1080.49350385937 3100 1081.2064890464 1209 1081.44587036605 2458 1081.69975698823 4747 1081.86246365315 548 1082.03753483035 1802 1082.10845458727 3740 1082.5393333918 3706 1082.66358990428 3615 1082.99884972842 4088 1083.3464915471 1989 1083.64787319436 2530 1083.65739551926 4507 1083.79174528648 4639 1084.08420058144 533 1085.14076476803 2107 1085.6233250042 4255 1086.28039414152 1793 1086.63990158416 3929 1086.89315133324 2191 1087.68429042904 3494 1087.90313183886 519 1088.18490654803 1289 1088.36782281918 4395 1088.56800522471 3585 1088.66650374476 857 1089.02084028869 3140 1089.6851438625 3568 1089.8180245225 2945 1090.09134827095 1764 1090.24097469259 73 1090.40285198676 4044 1090.52338655588 4753 1091.05346478885 3603 1091.61933041254 3081 1091.78368162201 3591 1091.98321459319 4779 1092.33068291562 3988 1092.36348562938 1881 1092.74872026685 3635 1092.81734459584 3861 1092.92803848603 3566 1093.4281570555 2083 1093.52538448422 2944 1093.53911741688 4131 1093.67536152029 4652 1093.74723929319 709 1094.03997707831 2917 1094.53167873938 1422 1094.56191474946 4171 1094.57727130836 3197 1094.62924479297 3451 1094.86168861649 1561 1094.9630856137 1099 1095.10908758044 4090 1095.17189499012 4083 1095.45198757451 4834 1095.55371195256 3083 1095.66946863574 2856 1096.34627763784 2838 1096.43318095319 1230 1096.4349285908 256 1096.61169329686 4849 1096.67558771439 3402 1096.76389419352 1518 1097.18679135328 1754 1097.87583607985 4300 1098.17013341134 4456 1098.19424768811 4293 1098.61185022255 4547 1098.67318070806 4317 1099.09060314272 4161 1099.20861089011 3180 1099.32442737796 3388 1099.34055814799 3022 1099.46749688019 4403 1099.53870310003 1817 1099.76583418906 4380 1100.04566326468 1528 1100.23736924777 4555 1100.31988326256 4726 1100.41776108631 4105 1100.43931577878 3728 1100.54906331261 1529 1100.66929220804 3602 1100.75055144086 1446 1100.77564419029 4856 1101.63239304157 3175 1101.9981405542 3169 1102.00840529749 4807 1102.18542834292 2075 1102.34543882834 1537 1102.64399793526 4774 1102.86871945862 3667 1103.1218418768 1723 1103.13925498594 371 1103.49120376432 2910 1103.55594157467 2234 1103.64397887364 695 1103.80312438578 41 1104.07730737463 4041 1104.3298532874 4154 1104.5932557378 4479 1104.62904161116 3513 1104.75997758067 3811 1104.97968839489 1257 1105.00442979457 2815 1105.1607201723 4344 1105.23226510311 3321 1105.26495457806 3981 1105.69951323104 3570 1105.95378552135 3969 1106.0154688691 2382 1106.01564504937 811 1106.04754670705 467 1106.07365350854 3699 1106.11403969191 529 1106.14605747221 4750 1106.26307329814 2342 1106.26776219767 2136 1106.38974007382 4372 1106.48508435435 1994 1106.97069886758 2874 1107.17929644413 1649 1107.32863944582 1617 1107.33797689857 1633 1107.50116491359 1137 1107.51606024809 2104 1107.53877538552 4675 1107.60213007288 63 1107.68408303326 1823 1107.71573241874 4470 1107.72759674141 4078 1107.91082565798 3973 1108.12323540307 4277 1108.14108751741 3337 1108.25488577378 4787 1108.26229647447 3035 1108.26500924424 2660 1108.28865759995 319 1108.3199317638 4773 1108.35835814322 4382 1108.41089118593 1058 1108.41672535955 1729 1108.91463502038 4478 1108.99204822242 4053 1108.99700357095 4377 1109.0264437023 3646 1109.03616832717 606 1109.52997827214 3788 1109.61153338867 3822 1109.64835718264 2895 1109.66526065837 4480 1109.66794025485 3283 1109.72171943257 3026 1109.77903930616 3575 1109.8337117978 4202 1109.83383180133 1972 1109.94716524097 3754 1110.02131721571 877 1110.10456031646 3168 1110.33939000611 3218 1110.60211576571 4671 1110.89361245317 4160 1110.98872836854 4672 1111.28350140025 4600 1111.32092415261 3201 1111.35554263891 988 1111.55203562623 3976 1111.73986196145 223 1111.82629743883 2498 1112.00819339418 2725 1112.01843636642 4165 1112.02227421547 4483 1112.06888761806 2455 1112.2320417372 1847 1112.51387556671 3800 1112.56999807922 3469 1112.66084022159 3705 1112.68338018752 2207 1112.75398379075 4748 1112.85552992071 1178 1112.93802787508 2423 1113.17018843453 3527 1113.25330083813 4050 1113.28369571121 2186 1113.31608281745 2404 1113.49989039187 3224 1113.56330639136 3381 1113.58518288808 4796 1113.61698112973 3639 1113.76525833464 2993 1113.78893544838 854 1113.8002233083 2070 1113.87550192555 614 1113.91283859423 4271 1113.93011576015 3555 1113.93909314656 3390 1114.10461173202 3668 1114.43388049551 2761 1114.5208212981 4608 1114.53833235578 2879 1114.80413477142 4034 1114.81184536521 3054 1114.85050185298 1389 1114.92244008114 3940 1115.17764241306 1280 1115.23810961201 2909 1115.25233719677 4685 1115.30074192017 4141 1115.57035389715 4209 1115.61855546881 590 1115.66757821772 3379 1115.87494240893 571 1115.94506923896 488 1115.95387186558 2912 1115.99432320944 433 1116.2067690365 1546 1116.28544908823 4768 1116.40533115538 3967 1116.43952328273 1126 1116.44009612737 4314 1116.53944856438 2803 1117.46529844291 1245 1117.72529301458 2261 1117.8043673863 619 1117.82828609388 835 1117.8989366004 1258 1118.6618775821 3743 1118.93378077197 751 1119.15672468365 3543 1119.44170603868 4810 1119.52092376664 3009 1119.54572255335 2224 1119.60552201394 4786 1119.61577576642 1304 1119.62672586039 457 1119.63574285791 2340 1119.87608281233 617 1120.0349540844 4643 1120.24544030326 2495 1120.3889744376 3353 1120.67595098316 292 1120.79194943679 4252 1120.95491896701 4076 1120.97094029801 4720 1121.01128511953 4811 1121.03119282398 3815 1121.08194590371 2432 1121.08392856245 691 1121.25053277638 3509 1121.56112238182 2367 1121.57249278055 3415 1121.57986718985 1721 1121.59854414128 3366 1121.61139038932 2358 1121.7994231 3876 1121.97614540607 53 1122.08488939136 1811 1122.12447053853 1014 1122.33615512431 3318 1122.4423448386 4246 1122.56620512879 3368 1122.62781014975 2010 1122.64224177735 2830 1122.77958232268 937 1122.81526825817 4467 1122.94634073777 4390 1122.94868106553 4846 1123.13300295534 2022 1123.13818700882 4835 1123.55145563676 4197 1123.83876144016 2811 1123.84784804467 3037 1123.86249375673 4833 1123.88222989458 2537 1123.98196857956 3521 1123.99340494413 4572 1123.99455527509 3029 1124.12485780296 3996 1124.31232212453 3951 1124.31712537787 4497 1124.39025940925 4114 1124.42873888487 3532 1124.64021597458 4396 1124.66244939679 4023 1124.70094339864 3735 1124.73972298578 4804 1124.79248490191 2747 1124.84620019496 3128 1124.87343115242 3357 1124.88449455382 2980 1124.98039650169 4621 1125.30686137498 4489 1125.39306023175 4104 1125.4757321273 3049 1125.52471101168 4238 1125.56000493963 4051 1125.59033290961 4240 1125.74974882145 2544 1125.77386410566 4723 1125.85270404079 665 1125.94296280064 117 1126.09098497072 4593 1126.09846385299 4854 1126.19486187291 1785 1126.19734986916 3637 1126.24229968996 1396 1126.34669262602 4725 1126.44849672692 1748 1126.46644284942 166 1126.50389158326 4189 1126.62626324781 2205 1126.90995980571 4376 1126.96422190851 4235 1127.08146092703 2240 1127.09311872742 3729 1127.20861681004 2942 1127.22056405988 2849 1127.25197709012 4107 1127.26392119278 4719 1127.29336875316 4546 1127.30119210111 4585 1127.33137856279 4216 1127.34129833445 3023 1127.35717777988 4400 1127.50311794377 1942 1127.51054529995 4013 1127.59298828622 4036 1127.69258767289 3794 1127.77712657412 4767 1127.8118361406 4262 1127.81888372012 2134 1128.10243966058 4349 1128.32499707399 2662 1128.41016653741 1143 1128.56972143302 714 1128.60348288075 4064 1128.60791813184 1700 1128.77835103524 2412 1128.79693053383 4047 1128.82569745581 4091 1128.92414430544 4280 1129.08937450395 4272 1129.41514505836 2591 1129.68250786 88 1129.70767705192 4604 1130.04304419249 692 1130.04591547876 339 1130.11150667682 4510 1130.22847090006 157 1130.54589495766 4554 1130.77880583878 2861 1130.86702183227 3936 1131.08390301678 3098 1131.35615081971 3340 1131.38908017229 4193 1131.73501409751 3225 1131.82182692271 2839 1132.0378043708 1124 1132.04374782001 4843 1132.06854216563 2172 1132.23429225976 1703 1132.25313058243 3516 1132.43721232589 1156 1132.45128175716 2465 1132.52934505209 81 1132.70141930537 4851 1132.70232544743 4664 1132.75449767075 3152 1132.76302896686 4838 1132.83470089359 1182 1132.88814147209 2785 1132.93885368371 4020 1132.96349140125 2337 1132.99812341583 484 1133.16057533758 4830 1133.17375468716 1631 1133.26136656671 3987 1133.37341478829 2600 1133.52427458765 2846 1133.83096655337 4633 1134.03231294989 3182 1134.03535955453 3597 1134.13966780856 2473 1134.48551940768 3767 1134.53442941965 4353 1134.80458931333 4260 1134.80832197996 3880 1134.84145489137 3975 1134.84260247014 3559 1134.97560676169 357 1135.03823526221 2819 1135.16640880511 4586 1135.20572089565 1774 1135.22514716772 271 1135.49698548722 1642 1135.51298095052 771 1135.58828161515 1604 1135.68585710195 4226 1135.72656356091 2900 1135.79399449046 768 1135.84582473902 2477 1135.84649675504 1303 1135.84919196811 3953 1135.89714896979 141 1135.90014880396 4666 1136.0689885917 2167 1136.0856164406 1254 1136.40396313889 3833 1136.40452870554 3103 1136.53581386347 3281 1136.72210099405 1791 1136.73938816667 3828 1136.77743130474 4769 1136.78407372899 2817 1136.80728216582 302 1136.87792039188 2658 1136.95319771839 4217 1136.98837904212 2503 1137.00878718604 4556 1137.21102345393 3798 1137.32501486933 3530 1137.68747428216 2185 1137.88064986667 1072 1137.91463256153 4771 1137.93171352201 1307 1138.11823203582 3136 1138.12804958135 4713 1138.26572949528 4808 1138.31499585144 4598 1138.38515461681 2737 1138.43334261694 3243 1138.4359735702 2923 1138.44688475226 4836 1138.62509667444 4261 1138.68534187476 3419 1138.70264264397 3229 1138.72819724404 3045 1138.7485025971 4263 1139.01825577877 1391 1139.05299094762 4029 1139.21456277186 1051 1139.25578995844 3745 1139.35836346362 834 1139.37564942425 4389 1139.39493284325 1033 1139.41581725563 1808 1139.49493377649 2933 1139.51536364018 4711 1139.51564686851 2039 1139.63185039296 1274 1139.68801366771 3272 1139.75819221862 2969 1139.787778779 3814 1139.79334845991 1188 1139.80792604304 3053 1139.87224577181 613 1139.89529228172 2425 1139.96944529087 3782 1140.02532372531 4705 1140.13884281152 2472 1140.32955372616 2554 1140.36914172906 4167 1140.40134575295 352 1140.40717844545 3562 1140.5045701631 1601 1140.57066605605 2987 1140.87662252822 3690 1140.91391464484 4859 1140.91825536466 3294 1140.96388122722 1379 1140.9958026186 640 1141.00283000596 4251 1141.01960945303 4111 1141.03773350231 894 1141.09488551451 4348 1141.1211725928 4136 1141.16281359348 2855 1141.24777504059 4703 1141.26576093999 3142 1141.365194835 2029 1141.37582777157 1846 1141.41994656638 1203 1141.48409634923 4355 1141.48800034575 3632 1141.49623526039 4296 1141.49822020607 4211 1141.51498468485 3979 1141.59128202486 272 1141.64507293338 4410 1141.69178683471 3765 1141.74182920284 3176 1141.77068290111 3926 1141.79379902706 3749 1141.80338434396 3382 1141.85354969536 3275 1141.91639055868 4486 1141.93560850983 3290 1141.94635161456 2444 1142.13876343155 3482 1142.16993677783 3533 1142.22834512673 3247 1142.30752451742 4409 1142.38439709454 1739 1142.43036582849 2183 1142.47568399063 4784 1142.50149603286 3397 1142.59158524174 3475 1142.60105025924 1677 1142.75693293549 4283 1142.79103818027 585 1142.90133282818 4163 1142.91070696072 4195 1142.94470297434 4228 1143.08014215923 1148 1143.11582613392 337 1143.11633886144 4058 1143.3409274469 2122 1143.47048653797 4178 1143.52764696299 4722 1143.61218925218 3000 1143.93276613032 4778 1144.02463726571 2161 1144.05327603255 4052 1144.07836240164 1672 1144.09712610693 1438 1144.10179482169 1997 1144.12092370351 2262 1144.1821028788 4267 1144.21432958415 1795 1144.2359929468 1827 1144.24150264485 4327 1144.55126104441 4128 1144.56273996054 4016 1144.66447152114 4338 1144.7923284902 3872 1144.88779882877 384 1144.96136509384 2982 1144.99863725656 4745 1145.15967413172 3658 1145.17469949042 4616 1145.19031646509 4550 1145.24859604471 3619 1145.29501901995 4777 1145.30582631384 3550 1145.36890087707 4566 1145.51495400684 2882 1145.60419826667 4628 1145.65109766582 1777 1145.69946740773 3618 1145.73159112334 1712 1145.76489490089 2200 1145.87223487943 2370 1145.87445839156 4535 1145.90209413913 4795 1146.03828902451 2081 1146.07276956078 4580 1146.0937225378 4463 1146.24566621425 2085 1146.57813905531 4151 1146.75994493287 2004 1146.78066808963 4538 1146.78629385588 4230 1146.93032292252 4839 1146.96341090907 4825 1147.01795295115 3418 1147.0693394107 4030 1147.09639194407 1095 1147.12351183817 3177 1147.13092014832 4487 1147.29150365805 4145 1147.29803847431 3636 1147.34324066287 1071 1147.39142955772 597 1147.51733234368 2757 1147.82578420199 4021 1147.85353271807 2978 1148.00873029208 4200 1148.01724333088 675 1148.04871208152 2625 1148.1018958307 237 1148.19752407376 1302 1148.32082037207 173 1148.47906552369 4827 1148.50518719898 2535 1148.54186835132 8 1148.55669846065 3763 1148.75134368026 3354 1148.77104473434 4368 1148.82836446407 2493 1148.89054809757 1810 1148.92966838874 1612 1148.99136153525 2121 1149.09104650593 3560 1149.53987629661 4254 1149.71576843316 4781 1149.71598385133 4735 1149.7482810424 3600 1149.90240394465 4004 1149.93831121785 1075 1149.94175373478 4559 1150.02519467038 3024 1150.10045897425 615 1150.18815217934 1769 1150.53655238446 3161 1150.62097605311 3552 1150.665219852 3062 1150.68957240715 342 1150.77091363339 3192 1150.79076035205 4316 1150.81574164928 499 1150.86287228793 4594 1151.00457434442 1398 1151.15397085353 4490 1151.23954195648 4018 1151.3119354128 3620 1151.315949744 4634 1151.38172551554 1197 1151.43505243704 4457 1151.53652175561 509 1151.59567394061 102 1151.60310041278 2795 1151.81116974371 2429 1152.20146133769 1944 1152.2077421217 3673 1152.36125775814 1448 1152.36644493984 4321 1152.41239267128 1361 1152.41876418085 4818 1152.53475264832 3150 1152.57755304498 348 1152.64405558607 743 1152.93332875784 4561 1153.12234389565 896 1153.25143316006 178 1153.28318523935 4371 1153.31482156647 4341 1153.57863300081 2556 1153.6398385815 2773 1153.71748295527 4649 1153.72543286362 2230 1153.743027491 1740 1153.78797951895 3612 1153.85399925561 4037 1153.86644210856 3282 1153.90236697073 4654 1154.04045197726 1571 1154.08159241595 1865 1154.11131696723 3797 1154.11152027076 4459 1154.1436191137 2833 1154.30114191175 3681 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1160.74648237014 2424 1160.74812618401 2064 1160.7868301232 1025 1160.82057327655 190 1160.84510646176 3204 1161.27375363575 867 1161.28929631232 74 1161.30381825156 1711 1161.35821647649 2445 1161.37940909229 4516 1161.4168328922 1643 1161.4436825774 263 1161.55174721942 3685 1161.55681666465 1915 1161.60894343639 703 1161.62191541543 4175 1161.64511061788 3006 1161.75147109093 3288 1161.91889927405 2216 1162.13647262269 4732 1162.29188833652 3179 1162.49441713067 884 1162.53016363054 3884 1162.73776676928 4207 1162.74348565946 4025 1162.75174702705 4232 1162.86324463433 4035 1163.08912824528 4103 1163.14397646053 31 1163.19418908257 4099 1163.20992182575 4696 1163.30490059229 3454 1163.59707826584 3510 1163.64756587597 2988 1163.91812024162 2115 1163.92624768544 3954 1163.97720250026 3070 1163.99375640632 2479 1164.05051829561 3992 1164.07482900247 4841 1164.16204016054 2659 1164.16850659056 4087 1164.20149036037 3345 1164.23721688909 3647 1164.26856542503 852 1164.27316711811 2560 1164.39855736063 1745 1164.43513756711 1554 1164.45013817567 2673 1164.66426264869 4412 1164.72955351177 144 1164.87883641572 2655 1164.95256779157 1510 1165.09702165977 4698 1165.21144465656 3484 1165.29030095208 4529 1165.31228845394 3695 1165.31937451729 4798 1165.40813671457 369 1165.46437641944 4780 1165.47494331293 87 1165.56035073578 3865 1165.59819152704 3574 1165.66342677934 1691 1165.7513151959 4005 1165.75965729924 3212 1165.79833578824 3206 1165.93921468332 1965 1166.03823016061 4730 1166.06356698833 4840 1166.11151450111 2523 1166.25476498539 3352 1166.28406855925 354 1166.51611581746 1293 1166.62636800731 4331 1166.69148472087 3223 1166.74385901025 2151 1166.74793801075 2963 1166.80280422826 3042 1167.03111269554 4695 1167.09105944207 2128 1167.18138258783 2520 1167.30376090097 2634 1167.33782783659 1308 1167.36553685238 4332 1167.38667000949 2869 1167.4267120266 2847 1167.58682932728 1872 1167.62397874526 2480 1167.66141953009 1818 1167.70186978016 2781 1167.73043435126 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1171.55259262785 2852 1171.56058774371 2667 1171.59654365519 4557 1171.79540036657 2450 1171.80440518091 2577 1171.80889703207 848 1171.81920568967 2027 1171.82541994674 4477 1171.86344693711 3655 1171.98739434426 4528 1171.99545292774 538 1171.99965453194 4674 1172.07719136555 3786 1172.09683475539 1277 1172.1353283255 2517 1172.14777138149 2239 1172.19370591802 4369 1172.3338468716 3339 1172.3689209753 4474 1172.38829319067 938 1172.39032086484 3577 1172.4241421836 1247 1172.52513249484 2918 1172.63063227196 3704 1172.65457160194 4361 1172.72057962524 45 1172.72301133413 3267 1172.77713332742 1317 1172.78635410336 3298 1172.81727759178 4335 1172.8576392772 2890 1172.88859214522 114 1172.92509521913 4533 1172.92617575169 2221 1173.02580116343 4537 1173.11464634968 181 1173.12509554848 3610 1173.22769031277 4746 1173.27775251891 4079 1173.29620341117 3630 1173.41965864795 1831 1173.44644551332 1370 1173.50586275257 4852 1173.6052343879 2344 1173.73591829108 2451 1173.77560236794 3751 1173.84275208557 3465 1174.21288209472 4676 1174.2284056361 2389 1174.27899207288 4374 1174.37066303259 2197 1174.45707694446 3703 1174.53848240136 4106 1174.77135592279 4468 1174.79928047616 4231 1174.89229271544 4514 1174.93900243999 663 1174.94615860421 4206 1174.97893766948 1692 1175.01054988268 4577 1175.01349388133 1850 1175.06992874581 1787 1175.12390346661 4330 1175.42630780185 3258 1175.44295391446 4669 1175.58410928977 3350 1175.71861519516 3457 1175.84504225294 578 1175.87992542262 1322 1175.95514759691 702 1176.08676215391 3270 1176.19000376642 4625 1176.19419858282 2973 1176.2045603863 3576 1176.20878155569 2911 1176.28668098888 4391 1176.37083326194 3544 1176.37935135682 2840 1176.40313702576 1763 1176.426953649 1340 1176.44394619127 1816 1176.51870396911 4462 1176.66623212113 2487 1176.72788088421 2437 1176.73277341297 1984 1176.79889908095 2421 1176.85417584657 2491 1177.01758958396 2435 1177.02987346941 3709 1177.14407860779 4072 1177.20764452569 2876 1177.3121750711 888 1177.55584693971 3546 1177.75483938369 3010 1177.85949270476 4783 1177.94184249394 449 1178.14550134383 2410 1178.43833929656 3567 1178.44742242179 1780 1178.46769957588 1710 1178.52189662094 4192 1178.52689474343 3614 1178.53655069801 4006 1178.56414935086 3952 1178.71085667828 1940 1178.77603166715 4185 1178.91203812593 2084 1179.11694038236 97 1179.12670924387 2496 1179.1385446695 4253 1179.15484614137 3496 1179.2745144448 3497 1179.29930653239 4068 1179.37640354659 3801 1179.48514297619 1870 1179.51212822131 3875 1179.56056891591 1228 1179.6433072654 3511 1179.87528953352 4627 1179.94320078371 3949 1179.99024571197 3792 1180.06963223905 3240 1180.26799689447 4196 1180.32747327517 4622 1180.35105438094 1789 1180.38585745864 4066 1180.4013181764 3537 1180.44154196326 858 1180.5337161148 276 1180.5624841937 3215 1180.61558159078 2965 1180.75173000601 4609 1180.78797978283 4118 1180.81455814354 4789 1180.85127323254 949 1181.21709002165 1765 1181.28417860636 2915 1181.33340480263 1973 1181.3885190493 647 1181.41790804046 2654 1181.47268595051 2657 1181.5330073556 3011 1181.60349643924 3110 1181.6306183097 4775 1181.64706221452 4520 1181.66783685736 4794 1181.75000684866 4645 1181.78384190675 3927 1181.81031186062 4132 1182.16559609969 4218 1182.16737214535 4098 1182.21784061675 4290 1182.22090624886 4820 1182.27527319276 3452 1182.31569531843 1348 1182.36230766268 4823 1182.48251964251 3408 1182.48536935872 2809 1182.56020405546 4408 1182.57803849225 1266 1182.80702792277 1591 1183.02087511315 3616 1183.11454433978 2091 1183.149614399 4612 1183.32983070122 2051 1183.35990324571 3712 1183.4075183448 3405 1183.41508202296 4790 1183.42877599409 3756 1183.49559645744 4592 1183.64062618868 3080 1183.68998233187 4662 1183.78781052475 2797 1183.86824620801 4352 1183.92473654247 4498 1183.96051076521 2034 1184.09313773768 4144 1184.18405606017 4156 1184.22502999776 2411 1184.23459763167 3151 1184.24782848137 3813 1184.32971043582 23 1184.34130858306 2202 1184.34804296657 4024 1184.36500591621 95 1184.44898623275 4095 1184.49876070764 668 1184.52525420996 1515 1184.54903366269 3370 1184.62534399299 4816 1184.70089881474 3796 1184.7310559866 4152 1184.77486747025 3043 1184.82745772176 21 1184.91278746326 4458 1184.9172430532 3526 1184.95367201416 3838 1185.15709665619 1502 1185.26959306528 4522 1185.27834759512 68 1185.29613421459 716 1185.36428267007 174 1185.42476429315 3634 1185.45929560829 4386 1185.4702884176 4762 1185.47756780316 3464 1185.56308732363 4761 1185.59054362967 3320 1185.73506200797 1828 1185.8012646588 2825 1185.80469185857 2037 1185.83184835723 3840 1185.83224144575 1747 1185.88936514411 4311 1185.90570997635 4847 1185.98943767919 3930 1186.00517479541 253 1186.10731383589 4525 1186.13717687468 2135 1186.21951767506 4708 1186.23424144233 832 1186.30781066441 3963 1186.42169106159 1369 1186.42480167674 4351 1186.42791662358 4727 1186.43715536608 2212 1186.48862923914 812 1186.58814182893 3488 1186.63729515628 1799 1186.68821996961 4582 1186.69603094094 3413 1186.75163712767 3557 1186.78994464288 2192 1186.82253219246 291 1186.97819595594 4108 1187.11387318533 4611 1187.19880333453 501 1187.22367477895 3821 1187.25905893268 4223 1187.37523409291 2147 1187.42641286233 4069 1187.51446410958 2883 1187.65526697409 4048 1187.67108274046 1311 1187.78892443102 2152 1187.93605092409 3472 1187.9547172637 4754 1187.98476245368 3966 1188.0104693853 3534 1188.02806573266 4508 1188.34795290824 1493 1188.35000611066 4279 1188.46547728672 2375 1188.5071377154 4744 1188.55844975682 2583 1188.56707760528 4359 1188.58655723949 2823 1188.59865030275 395 1188.60265226428 2102 1188.71762514971 4082 1188.79147677889 1168 1188.81909584429 346 1188.87219533475 2399 1189.06830041315 4364 1189.12214967484 2246 1189.18297021332 3707 1189.25108981648 3004 1189.2723809434 172 1189.28545895657 442 1189.31978196345 4284 1189.36914377489 753 1189.42456539978 1474 1189.45000540747 1091 1189.57588132221 2986 1189.79862426188 2559 1189.81235075102 4815 1189.85870239641 226 1189.95608072905 3789 1190.03551804924 1023 1190.20275131341 601 1190.23227389427 4385 1190.37931000252 3696 1190.43935911372 3661 1190.47324036492 3498 1190.6177107137 1860 1190.65134064209 3686 1190.65952714316 3714 1190.8096036421 910 1190.81894034378 2283 1191.02998313357 3998 1191.09875265664 1225 1191.17748060625 2398 1191.19949848172 2441 1191.21157094722 3844 1191.23697632739 4552 1191.30079056105 2265 1191.34221904299 1750 1191.36300241719 4832 1191.36321864805 3137 1191.38015555757 3502 1191.42175322037 3299 1191.55000291719 246 1191.60455413576 4560 1191.61293496944 2854 1191.66281926933 2898 1191.69716196755 3851 1191.75920401556 244 1191.88821753204 1008 1191.89311208486 2106 1192.02257900458 2348 1192.17861222474 2229 1192.21885292123 2264 1192.28768396795 522 1192.50249865598 2550 1192.58993332323 3829 1192.66037789027 1466 1192.69189321847 2767 1192.75369086259 3650 1192.76891437511 554 1192.81178626894 3487 1192.87464539881 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1540.37859616682 1984 1176.79889908095 1985 1404.12577305486 1986 1696.82704216305 1987 1243.19824352584 1989 1083.64787319436 1991 1259.25870102443 1994 1106.97069886758 1997 1144.12092370351 2000 1433.42748392377 2001 1170.97728561531 2002 1207.15090570157 2004 1146.78066808963 2010 1122.64224177735 2013 1330.84744303641 2016 1304.77158226126 2021 1231.36218991602 2022 1123.13818700882 2027 1171.82541994674 2028 1160.72521369021 2029 1141.37582777157 2034 1184.09313773768 2035 1217.42690300255 2036 1248.38057312534 2037 1185.83184835723 2039 1139.63185039296 2040 1218.77368200966 2046 1300.19494478288 2051 1183.35990324571 2052 1445.68913015397 2053 1253.50745928083 2054 1508.534964774 2056 1709.75985745116 2059 1254.36173350003 2062 1372.88869347596 2064 1160.7868301232 2067 1237.94934255195 2068 1194.15977179903 2070 1113.87550192555 2073 1204.34726623342 2075 1102.34543882834 2077 1258.61777304736 2078 1157.61599711142 2079 1195.2442154954 2080 1193.79866271343 2081 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1132.96349140125 4021 1147.85353271807 4023 1124.70094339864 4024 1184.36500591621 4025 1162.75174702705 4026 1340.1003966832 4027 1270.28127404597 4028 1257.6128002538 4029 1139.21456277186 4030 1147.09639194407 4031 1218.36648761205 4032 1048.18782072589 4034 1114.81184536521 4035 1163.08912824528 4036 1127.69258767289 4037 1153.86644210856 4038 1241.8919025018 4039 1259.17524059378 4041 1104.3298532874 4042 1155.73174325098 4043 1217.5113616196 4044 1090.52338655588 4045 1208.06437730369 4046 1193.75062479176 4047 1128.82569745581 4048 1187.67108274046 4049 1260.78635090342 4050 1113.28369571121 4051 1125.59033290961 4052 1144.07836240164 4053 1108.99700357095 4054 1267.94917158175 4055 1170.83001091818 4056 1210.49054728383 4057 1210.0294613153 4058 1143.3409274469 4060 1014.18233417492 4061 1239.86203200487 4063 1395.08467436553 4064 1128.60791813184 4065 1157.54310154477 4066 1180.4013181764 4067 1160.19196285458 4068 1179.37640354659 4069 1187.51446410958 4070 1193.77257961248 4071 1211.00811838871 4072 1177.20764452569 4073 1257.8988322137 4074 1198.8763936583 4075 1169.98103856783 4076 1120.97094029801 4077 1221.70385482641 4078 1107.91082565798 4079 1173.29620341117 4080 1292.37620565784 4081 1037.84181433329 4082 1188.79147677889 4083 1095.45198757451 4085 1270.12660782544 4086 1239.6318945328 4087 1164.20149036037 4088 1083.3464915471 4089 1286.84977573591 4090 1095.17189499012 4091 1128.92414430544 4092 1221.02432480033 4093 1156.8325344058 4095 1184.49876070764 4096 1258.84078294089 4097 1197.83287047986 4098 1182.21784061675 4099 1163.20992182575 4102 1196.25662574458 4103 1163.14397646053 4104 1125.4757321273 4105 1100.43931577878 4106 1174.77135592279 4107 1127.26392119278 4108 1187.11387318533 4110 1158.87435417186 4111 1141.03773350231 4112 1198.92107851594 4113 1199.93916386671 4114 1124.42873888487 4115 1160.10484596122 4118 1180.81455814354 4119 1196.02403367279 4120 1221.24325778993 4121 1203.26785314456 4122 1206.5028011909 4123 1159.26375183 4124 1285.88752515142 4125 1206.52878585579 4126 1230.55502581136 4127 1252.31362642756 4128 1144.56273996054 4130 1280.61200675159 4131 1093.67536152029 4132 1182.16559609969 4134 1245.00033317713 4135 1265.89524910317 4136 1141.16281359348 4137 1214.46706871909 4138 1158.79343631485 4139 1292.21742744764 4140 1208.11075978761 4141 1115.57035389715 4142 1207.74044864765 4143 1263.67703407651 4144 1184.18405606017 4145 1147.29803847431 4146 1214.86722847924 4148 1215.1626077893 4149 1199.89970626228 4150 1228.90040539814 4151 1146.75994493287 4152 1184.77486747025 4153 1227.03798408939 4154 1104.5932557378 4155 1167.98018608798 4156 1184.22502999776 4158 1364.51023895093 4159 1232.80720798067 4160 1110.98872836854 4161 1099.20861089011 4163 1142.91070696072 4165 1112.02227421547 4166 1200.10895494731 4167 1140.40134575295 4171 1094.57727130836 4173 1158.80829092968 4174 1244.6437748292 4175 1161.64511061788 4176 1199.87263214658 4178 1143.52764696299 4179 1169.93278677919 4180 1171.29548151843 4181 1205.53846827138 4182 1231.09961038465 4183 1226.30644385149 4184 1215.13111369246 4185 1178.91203812593 4186 1194.54690240063 4187 1156.04901497873 4188 1238.8506979105 4189 1126.62626324781 4191 1225.85812313045 4192 1178.52689474343 4193 1131.73501409751 4195 1142.94470297434 4196 1180.32747327517 4197 1123.83876144016 4198 1234.77614653502 4200 1148.01724333088 4201 1200.81571888892 4202 1109.83383180133 4203 1216.13121645636 4205 1251.3845019251 4206 1174.97893766948 4207 1162.74348565946 4209 1115.61855546881 4210 1233.96692123796 4211 1141.51498468485 4212 1202.43190627967 4213 1193.25341653238 4215 1233.4106961783 4216 1127.34129833445 4217 1136.98837904212 4218 1182.16737214535 4219 1170.96696738048 4223 1187.37523409291 4224 1251.64502514995 4225 1219.15009527221 4226 1135.72656356091 4228 1143.08014215923 4229 1167.93254011617 4230 1146.93032292252 4231 1174.89229271544 4232 1162.86324463433 4234 1007.80265488653 4235 1127.08146092703 4237 1218.23295216381 4238 1125.56000493963 4239 1241.19820953204 4240 1125.74974882145 4241 1193.23970074999 4242 1234.61651945402 4243 1168.84360506419 4244 1202.41963956922 4245 1155.9861823853 4246 1122.56620512879 4247 1170.43914301603 4251 1141.01960945303 4252 1120.95491896701 4253 1179.15484614137 4254 1149.71576843316 4255 1086.28039414152 4256 1243.1234425866 4259 1212.93557384306 4260 1134.80832197996 4261 1138.68534187476 4262 1127.81888372012 4263 1139.01825577877 4264 1230.99406829513 4265 1409.9440029336 4266 1202.75212148264 4267 1144.21432958415 4268 1232.03803975293 4269 1250.63914078739 4270 1232.25358336403 4271 1113.93011576015 4272 1129.41514505836 4275 1079.43107862278 4276 1258.958117401 4277 1108.14108751741 4279 1188.46547728672 4280 1129.08937450395 4281 1224.86760545985 4282 1242.59308897157 4283 1142.79103818027 4284 1189.36914377489 4285 1294.32728837542 4286 1199.26493855126 4288 1170.32945851768 4289 1060.95837747809 4290 1182.22090624886 4291 1212.4461273552 4292 1212.21283741856 4293 1098.61185022255 4294 1211.98324169093 4295 1170.31652941163 4296 1141.49822020607 4298 1196.52770861629 4299 1202.02298674275 4300 1098.17013341134 4301 1168.4672397442 4302 1193.60902675849 4304 1156.46506534882 4306 1205.57923223841 4309 1214.02692070495 4310 1168.07292042071 4311 1185.90570997635 4314 1116.53944856438 4316 1150.81574164928 4317 1099.09060314272 4319 1225.67185605113 4320 1391.45977062742 4321 1152.41239267128 4322 1228.82414720516 4324 1199.71875993154 4325 1277.61948738663 4327 1144.55126104441 4328 1197.06492981312 4329 1219.42734659645 4330 1175.42630780185 4331 1166.69148472087 4332 1167.38667000949 4334 1354.66774259513 4335 1172.8576392772 4336 1204.30520980126 4337 1070.04721840224 4338 1144.7923284902 4341 1153.57863300081 4342 1333.66717196389 4343 1339.1218049285 4344 1105.23226510311 4345 1226.26448211157 4346 1204.42732526463 4348 1141.1211725928 4349 1128.32499707399 4351 1186.42791662358 4352 1183.92473654247 4353 1134.80458931333 4354 1203.37814683414 4355 1141.48800034575 4356 1227.087209501 4359 1188.58655723949 4360 1200.69952989961 4361 1172.72057962524 4362 1218.56108097627 4364 1189.12214967484 4366 1158.18837305729 4368 1148.82836446407 4369 1172.3338468716 4371 1153.31482156647 4372 1106.48508435435 4373 1079.01398736869 4374 1174.37066303259 4375 1204.48469846592 4376 1126.96422190851 4377 1109.0264437023 4378 1157.47796732389 4380 1100.04566326468 4381 1232.20390605812 4382 1108.41089118593 4383 1231.8754748329 4384 1232.2858583201 4385 1190.37931000252 4386 1185.4702884176 4387 1075.14320913319 4388 1229.04022866951 4389 1139.39493284325 4390 1122.94868106553 4391 1176.37083326194 4392 1207.88778109414 4395 1088.56800522471 4396 1124.66244939679 4397 1202.9276307185 4398 1026.94694016844 4400 1127.50311794377 4401 1199.96233566664 4402 1203.37953319008 4403 1099.53870310003 4404 1052.80909969208 4405 1242.62344122337 4406 1063.49864842402 4408 1182.57803849225 4409 1142.38439709454 4410 1141.69178683471 4412 1164.72955351177 4450 1220.75934266221 4451 1384.11517670854 4452 1304.57588522283 4453 1208.97670181348 4454 1063.26768643071 4455 1231.87978884757 4456 1098.19424768811 4457 1151.53652175561 4458 1184.9172430532 4459 1154.1436191137 4460 1263.84200505859 4461 1243.84476919904 4462 1176.66623212113 4463 1146.24566621425 4464 1246.84878160961 4466 1225.49554539186 4467 1122.94634073777 4468 1174.79928047616 4469 1169.3499169776 4470 1107.72759674141 4471 1033.6777037715 4472 1260.74799264512 4473 1252.68758092147 4474 1172.38829319067 4475 1154.63774122398 4476 1202.92083749695 4477 1171.86344693711 4478 1108.99204822242 4479 1104.62904161116 4480 1109.66794025485 4481 1167.86045010138 4482 1211.43644965811 4483 1112.06888761806 4484 1155.41556728644 4485 1200.37611224542 4486 1141.93560850983 4487 1147.29150365805 4488 1241.39056086186 4489 1125.39306023175 4490 1151.23954195648 4491 1199.82439244588 4492 1197.51309533545 4495 1214.38893373547 4496 1171.19430814511 4497 1124.39025940925 4498 1183.96051076521 4499 1234.43994123891 4500 1231.42237658703 4501 1227.32781242596 4502 1249.15306348751 4504 1234.51210418383 4505 1202.76964151083 4506 1193.46482535282 4507 1083.79174528648 4508 1188.34795290824 4509 1306.92373423803 4510 1130.22847090006 4511 1199.62073979204 4512 1240.98225694567 4513 1209.63007298514 4514 1174.93900243999 4516 1161.4168328922 4517 1047.40106468987 4518 1224.26214187652 4519 1203.75735237475 4520 1181.66783685736 4521 1253.46919148897 4522 1185.27834759512 4523 1236.8624202622 4525 1186.13717687468 4526 1170.66727663226 4528 1171.99545292774 4529 1165.31228845394 4531 1204.40965753658 4532 1032.58573597814 4533 1172.92617575169 4534 1208.11105787777 4535 1145.90209413913 4536 1197.01158473417 4537 1173.11464634968 4538 1146.78629385588 4539 1274.0623019172 4541 1235.12921224568 4542 1160.23207281433 4543 1169.41752193169 4545 1232.7254811531 4546 1127.30119210111 4547 1098.67318070806 4548 1157.03216933959 4549 1235.20502123818 4550 1145.24859604471 4551 1199.31607150523 4552 1191.30079056105 4553 1227.28829262458 4554 1130.77880583878 4555 1100.31988326256 4556 1137.21102345393 4557 1171.79540036657 4559 1150.02519467038 4560 1191.61293496944 4561 1153.12234389565 4562 1159.32973714491 4563 1167.94153678735 4564 1195.80026166222 4565 1204.2721345148 4566 1145.51495400684 4567 1229.78057176523 4568 1160.74648237014 4570 1202.3050937973 4571 1258.78563274589 4572 1123.99455527509 4573 1029.51467487536 4574 1197.22164754954 4575 1262.96256109382 4576 1280.09485723417 4577 1175.01349388133 4578 1229.7177111047 4579 1311.97218269573 4580 1146.0937225378 4581 1159.34504782362 4582 1186.69603094094 4583 1260.06302648731 4585 1127.33137856279 4586 1135.20572089565 4587 1277.69675403827 4589 1193.63731106403 4590 1303.88165522934 4591 1245.28253643857 4592 1183.64062618868 4593 1126.09846385299 4594 1151.00457434442 4595 1160.57327196873 4596 1193.4188242425 4597 1217.66563545631 4598 1138.38515461681 4600 1111.32092415261 4601 1194.66824295581 4603 1196.48093792906 4604 1130.04304419249 4606 1199.34866775818 4607 1285.39564629046 4608 1114.53833235578 4609 1180.78797978283 4610 1251.13031482905 4611 1187.19880333453 4612 1183.32983070122 4615 1215.92163780681 4616 1145.19031646509 4618 1213.73217141105 4619 1201.81326599767 4621 1125.30686137498 4622 1180.35105438094 4623 1228.58929601434 4624 1229.61630685263 4625 1176.19419858282 4626 1199.77823482446 4627 1179.94320078371 4628 1145.65109766582 4629 1228.78544873997 4630 1221.16443445515 4632 1199.00576410709 4633 1134.03231294989 4634 1151.38172551554 4635 1158.68304259053 4637 1076.99431785768 4638 1198.88796180891 4639 1084.08420058144 4640 1212.86118513518 4641 1223.74860696041 4642 1199.81469569968 4643 1120.24544030326 4645 1181.78384190675 4646 1244.24520715043 4648 1202.43464694694 4649 1153.72543286362 4650 982.089794296798 4651 1171.55259262785 4652 1093.74723929319 4653 1056.60256481931 4654 1154.04045197726 4655 1169.88432138157 4656 1201.92977116439 4657 1154.90273600888 4659 1237.46785513438 4661 1217.12438158791 4662 1183.78781052475 4663 1221.24223164386 4664 1132.75449767075 4665 1171.52451288264 4666 1136.0689885917 4667 1200.72944938546 4668 1206.19114146863 4669 1175.58410928977 4670 1209.1988549885 4671 1110.89361245317 4672 1111.28350140025 4673 1170.98581058936 4674 1172.07719136555 4675 1107.60213007288 4676 1174.2284056361 4678 1168.27917684811 4680 1039.48464889698 4681 1249.4716946694 4682 1223.41922420855 4683 1169.47864207891 4684 1212.93048205135 4685 1115.30074192017 4687 1215.45359326252 4688 1194.4065205897 4689 1198.19776426133 4690 1225.62561963749 4692 1212.94881720966 4693 1199.22499109885 4694 1171.09005869826 4695 1167.09105944207 4696 1163.30490059229 4698 1165.21144465656 4701 1200.69060532397 4702 1196.00629027072 4703 1141.26576093999 4704 1201.0762811594 4705 1140.13884281152 4706 1233.44015640996 4707 1159.75504933466 4708 1186.23424144233 4711 1139.51564686851 4713 1138.26572949528 4714 1169.61538872201 4715 1200.95033231691 4716 1260.81704415184 4717 1169.65851004199 4718 1209.93014842886 4719 1127.29336875316 4720 1121.01128511953 4721 1069.35729443129 4722 1143.61218925218 4723 1125.85270404079 4724 1197.19823703816 4725 1126.44849672692 4726 1100.41776108631 4727 1186.43715536608 4728 1168.14737293399 4730 1166.06356698833 4731 1229.0200386629 4732 1162.29188833652 4733 1225.61405873162 4734 1201.08206473769 4735 1149.7482810424 4736 1214.57824569301 4737 1193.76150791181 4738 1197.1615147755 4740 1244.44169143776 4741 1201.91186017079 4742 1168.07650716011 4743 1041.31651481374 4744 1188.55844975682 4745 1145.15967413172 4746 1173.27775251891 4747 1081.86246365315 4748 1112.85552992071 4749 1221.35842325523 4750 1106.26307329814 4751 1216.12189968493 4753 1091.05346478885 4754 1187.98476245368 4755 998.879722986273 4757 1156.11347032437 4758 1209.71817951448 4761 1185.59054362967 4762 1185.47756780316 4765 1158.31665070312 4767 1127.8118361406 4768 1116.40533115538 4769 1136.78407372899 4770 1155.50193681833 4771 1137.93171352201 4772 1225.33534018324 4773 1108.35835814322 4774 1102.86871945862 4775 1181.64706221452 4776 1207.35075431759 4777 1145.30582631384 4778 1144.02463726571 4779 1092.33068291562 4780 1165.47494331293 4781 1149.71598385133 4782 1072.53570071915 4783 1177.94184249394 4784 1142.50149603286 4785 1077.39028590692 4786 1119.61577576642 4787 1108.26229647447 4789 1180.85127323254 4790 1183.42877599409 4791 1226.77289361863 4792 1214.42095830569 4793 1066.85041465773 4794 1181.75000684866 4795 1146.03828902451 4796 1113.61698112973 4797 1332.99162879393 4798 1165.40813671457 4799 1197.62673412403 4800 1211.17511453921 4803 1214.76163042569 4804 1124.79248490191 4805 1255.73839796082 4807 1102.18542834292 4808 1138.31499585144 4809 1202.24581825252 4810 1119.52092376664 4811 1121.03119282398 4812 1252.25141636152 4814 1214.25999977625 4815 1189.85870239641 4816 1184.70089881474 4817 1199.68445669747 4818 1152.53475264832 4819 1230.46897335443 4820 1182.27527319276 4821 1210.0816360906 4823 1182.48251964251 4824 1274.00412127724 4825 1147.01795295115 4827 1148.50518719898 4828 1278.93111983802 4829 1210.37691627317 4830 1133.17375468716 4832 1191.36321864805 4833 1123.88222989458 4834 1095.55371195256 4835 1123.55145563676 4836 1138.62509667444 4838 1132.83470089359 4839 1146.96341090907 4840 1166.11151450111 4841 1164.16204016054 4842 1221.94635528239 4843 1132.06854216563 4845 1198.5312620239 4846 1123.13300295534 4847 1185.98943767919 4848 1204.42495894197 4849 1096.67558771439 4850 1214.51286765616 4851 1132.70232544743 4852 1173.6052343879 4853 1169.5893564853 4854 1126.19486187291 4855 1241.04231318184 4856 1101.63239304157 4859 1140.91825536466 Code:
#!/usr/bin/perl
my %rating = ();
my @data = <STDIN>;
my $K = 32;
my $defaultElo = 1200;
# Just make sure a team number and default value of 1200 exists for each hash.
foreach(@data) {
my ($match, $red1, $red2, $red3, $blue1, $blue2, $blue3, $res) = split;
if (! exists $rating{$red1}) {
$rating{$red1} = $defaultElo
}
if (! exists $rating{$red2}) {
$rating{$red2} = $defaultElo
}
if (! exists $rating{$red3}) {
$rating{$red3} = $defaultElo
}
if (! exists $rating{$blue1}) {
$rating{$blue1} = $defaultElo
}
if (! exists $rating{$blue2}) {
$rating{$blue2} = $defaultElo
}
if (! exists $rating{$blue3}) {
$rating{$blue3} = $defaultElo
}
}
foreach (@data) {
my ($match, $red1, $red2, $red3, $blue1, $blue2, $blue3, $res) = split;
my $Ered = 1 / (1 + 10**((($rating{$blue1}+$rating{$blue2}+$rating{$blue3})/3-($rating{$red1}+$rating{$red2}+$rating{$red3})/3)/400));
my $Eblue = 1 / (1 + 10**((($rating{$red1}+$rating{$red2}+$rating{$red3})/3-($rating{$blue1}+$rating{$blue2}+$rating{$blue3})/3)/400));
if ($res eq 'RED') {
$rating{$red1} = $rating{$red1} + $K*(1 - $Ered);
$rating{$red2} = $rating{$red2} + $K*(1 - $Ered);
$rating{$red3} = $rating{$red3} + $K*(1 - $Ered);
$rating{$blue1} = $rating{$blue1} + $K*(0 - $Eblue);
$rating{$blue2} = $rating{$blue2} + $K*(0 - $Eblue);
$rating{$blue3} = $rating{$blue3} + $K*(0 - $Eblue);
}
if ($res eq 'BLUE') {
$rating{$red1} = $rating{$red1} + $K*(0 - $Ered);
$rating{$red2} = $rating{$red2} + $K*(0 - $Ered);
$rating{$red3} = $rating{$red3} + $K*(0 - $Ered);
$rating{$blue1} = $rating{$blue1} + $K*(1 - $Eblue);
$rating{$blue2} = $rating{$blue2} + $K*(1 - $Eblue);
$rating{$blue3} = $rating{$blue3} + $K*(1 - $Eblue);
}
if ($res eq 'TIE') {
$rating{$red1} = $rating{$red1} + $K*(0.5 - $Ered);
$rating{$red2} = $rating{$red2} + $K*(0.5 - $Ered);
$rating{$red3} = $rating{$red3} + $K*(0.5 - $Ered);
$rating{$blue1} = $rating{$blue1} + $K*(0.5 - $Eblue);
$rating{$blue2} = $rating{$blue2} + $K*(0.5 - $Eblue);
$rating{$blue3} = $rating{$blue3} + $K*(0.5 - $Eblue);
}
}
while(($key, $value) = each(%rating)) {
print $key . "t" . $value . "n";
}
(Edit: Had mistake in my calculation) |
13-03-2014 18:14
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
Included is perl code I used.
|
Code:
BEGIN {FS=","; ln10=log(10); kFactor=24;}
(NR>1) && (($4=="Q")||($4=="E")) {
for(i=8;i<=13;++i){if(!($i in Elo)){Elo[$i]=1200}}
avgRedElo = (Elo[$8] + Elo[$9] + Elo[$10])/3;
avgBlueElo = (Elo[$11] + Elo[$12] + Elo[$13])/3;
x = ((avgBlueElo - avgRedElo)/400)*ln10; Ea = 1/(1 + exp(x));
x = ((avgRedElo - avgBlueElo)/400)*ln10; Eb = 1/(1 + exp(x));
if($6>$7){Sa=1; Sb=0} else if($7>$6){Sa=0; Sb=1} else {Sa=0.5; Sb=0.5}
dRa = kFactor*(Sa-Ea);
dRb = kFactor*(Sb-Eb);
Elo[$8]+=dRa;
Elo[$9]+=dRa;
Elo[$10]+=dRa;
Elo[$11]+=dRb;
Elo[$12]+=dRb;
Elo[$13]+=dRb;
}
END{
PROCINFO["sorted_in"] = "@val_num_desc";
for (TeamNum in Elo) {print TeamNum "," Elo[TeamNum]}}
13-03-2014 20:01
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Free good rep to the first person to post FORTRAN or COBOL code of this.
13-03-2014 20:12
Andrew Schreiber
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
Free good rep to the first person to post FORTRAN or COBOL code of this.
|
13-03-2014 20:38
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
Free good rep to the first person to post FORTRAN or COBOL code of this.
|
13-03-2014 22:16
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
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Originally Posted by Ether
How about Pascal? Would you give reps for that?
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17-03-2014 00:18
Redo91
Re: paper: Weeks 1-2 Elo Analysis
I was curious how the data looked. I just threw it onto Google Docs(after making it into an Excel file because Docs does not like that amount of characters being directly pasted into it). Here it is.
Edit: Realized this isn't terribly relevant after rereading the thread title. Still, a good visual I think.
17-03-2014 00:28
Redo91
Re: paper: Weeks 1-2 Elo Analysis
Here is a visual using the data for the first 2 weeks using the data from the paper.
08-10-2014 19:08
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
I was somewhat bored this evening and decided to try something different. I decided to try the Microsoft TrueSkill algorithm to rank teams. If you're unfamiliar with TrueSkill, it's the algorithm used on XBoxLive to determine fair matchups. It's based on the Glicko rating system, which was developed as an enhanced Elo rating. Glicko introduces Bayesian statistics to the Elo system and TrueSkill takes it a step further and includes team-based play. The results were...interesting. The first column is team #, second column is the team's skill rating, the third is sigma (standard deviation)
Code:
3478 32.1901547 3.20363857 1678 32.0112708 2.399343622 1319 31.87906344 3.315070058 1619 31.75256228 3.470732969 2912 31.58129439 4.715476202 4509 31.40973953 5.133444261 2363 31.31808794 2.836302053 118 31.29619384 2.538432629 1230 31.15380747 3.547815035 2056 31.14569129 2.576563062 1718 31.11263159 2.109044982 195 31.10461402 2.192780006 254 31.04528151 2.330684176 967 31.01357444 3.745206881 225 30.96307625 1.973250808 4539 30.94319405 4.865262985 1310 30.83621852 2.755701999 870 30.83507163 3.272737755 16 30.81035963 2.664498783 1114 30.80861686 2.360223 695 30.77693275 4.33806769 4415 30.77316599 4.730511852 79 30.75791237 2.826369003 1987 30.67232661 3.625521206 1982 30.60625983 4.670991754 383 30.59868127 4.8017054 2485 30.59596864 2.743650604 1410 30.45837899 3.416039844 148 30.43365623 2.481575794 3741 30.41991712 4.512545091 3102 30.41881484 5.213708006 3472 30.40490716 4.859007573 3612 30.3931785 3.722623394 3658 30.37491946 4.472326569 294 30.33797426 2.756791626 971 30.30915264 2.618289057 180 30.30718968 2.695798753 1736 30.20581023 3.308573931 354 30.2000696 5.039422075 1023 30.19938536 2.035922773 3834 30.14868708 4.586989693 2614 30.12043279 2.804402804 696 30.10697699 3.694183464 334 30.08551724 2.806576511 4930 30.0675904 2.735389892 1519 30.05333958 2.241897536 1323 30.00312004 2.643458512 4587 29.99732998 3.348657276 3824 29.98859858 2.932023783 5089 29.95855914 4.922216515 2809 29.92320705 3.297946178 3393 29.8910423 2.20798222 5184 29.88130369 4.091101226 4913 29.8774892 4.678576218 3193 29.86982285 3.311722746 1717 29.85482878 2.7075201 67 29.8301642 2.09103307 4096 29.80669386 4.516803273 2883 29.79046227 3.722170155 3009 29.78901767 3.375059235 3794 29.76813191 3.217671954 33 29.67701471 1.932827532 1318 29.64508078 2.003948916 3038 29.63862012 4.982429233 1775 29.63055641 2.76632969 624 29.61103972 2.557791883 399 29.61042143 2.40927544 4188 29.60319508 5.072906277 231 29.5981198 3.075990159 3981 29.57025821 4.737150581 2388 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4497 26.94534136 4.015393445 5022 26.94221794 4.557214861 1665 26.94031736 4.062860172 4486 26.92883022 3.033922803 5171 26.92278019 2.960178428 3243 26.92229348 3.543979661 337 26.92121878 2.755772318 2130 26.91756492 4.162389046 4564 26.91264432 2.313979038 4643 26.91161161 4.421546577 4416 26.90968669 4.706190029 3492 26.8973508 3.106241224 1051 26.89552508 4.784645939 614 26.89490683 3.783699458 2978 26.88280851 2.892174787 3954 26.88192043 4.564649717 3700 26.87944652 5.077072103 1266 26.87415628 2.732309132 3145 26.86943249 4.217926087 1071 26.86307891 3.041826812 4391 26.85999486 2.126762123 2506 26.85880432 3.519656717 263 26.85647446 3.432507801 5173 26.85341995 3.835720652 2153 26.85006695 4.350400574 1922 26.84705275 3.385452066 2529 26.84166569 5.007046708 247 26.84137887 2.589735815 4 26.83710989 3.429090135 3516 26.83482084 3.502605036 514 26.83402782 3.597450234 830 26.83108191 3.206053206 3479 26.82967472 3.059106717 5122 26.82520067 2.075697625 2630 26.81980043 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26.69978959 3.398508821 4701 26.69846987 4.990413383 4935 26.6980541 2.868786401 5026 26.69137599 3.173532459 2021 26.69053522 4.894621575 1294 26.6894296 2.091324199 2642 26.68664321 2.715561349 3609 26.68511214 3.424561158 4669 26.67957914 4.188563583 2180 26.67821656 1.892455435 1557 26.67668948 4.757889229 3610 26.67531388 4.808360052 175 26.67425164 1.972006176 4678 26.6741384 3.093210987 2016 26.67230231 2.151934085 2191 26.66816976 2.40625519 5096 26.6673863 4.435244145 2950 26.66646675 3.442808299 3133 26.66493004 5.021828517 1600 26.66204201 5.070840488 2164 26.66142283 3.5167828 2093 26.66020488 3.000570692 1760 26.65371123 4.590304257 1732 26.65264887 2.634672347 4915 26.65253477 2.154791283 3646 26.65143023 4.164106131 3511 26.65005461 4.513631392 2204 26.64882534 4.389093472 4945 26.64859154 2.751365963 1279 26.64647645 2.076699475 5288 26.64582895 2.950977784 4178 26.64277584 4.097338398 2838 26.64231064 4.358353061 2491 26.63869237 3.760823919 3063 26.63804164 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4.77185758 3355 26.55408008 4.339033224 781 26.55281223 2.321084198 852 26.54544057 4.402179437 3130 26.54436797 3.655664034 2070 26.53950535 2.795090854 2918 26.53299981 4.847858712 3335 26.53167691 3.556444272 1850 26.53091319 4.199841027 1712 26.52622092 2.313215425 2658 26.52555363 4.58014148 2781 26.520205 4.238725952 341 26.5153957 1.960689534 3718 26.51363791 3.13288558 2502 26.50592992 2.857917171 3538 26.50418822 2.85019668 2659 26.50404065 4.320624106 981 26.5030513 4.756344059 3314 26.50036359 2.126667212 3313 26.49888769 2.975780661 3055 26.49654744 4.629299993 701 26.49527553 3.415676533 217 26.49513811 2.324275342 4176 26.48713797 2.557065908 3928 26.48685658 2.772081516 4193 26.48426138 5.014335283 1647 26.48406936 2.405817716 114 26.48294896 3.139332858 5317 26.4773966 5.010097249 4216 26.47722887 3.289788249 1540 26.47557967 1.914931561 456 26.4720496 3.593828254 2478 26.47128247 2.78421771 3303 26.46733441 4.765651755 3120 26.46718971 3.752947844 649 26.46611486 3.614287975 4325 26.45404532 3.170948289 4774 26.45070888 4.83056045 4061 26.4450231 2.1158179 5028 26.43947213 5.049080515 2393 26.43858883 4.431104523 4362 26.43277966 2.023338421 234 26.43022874 3.229762608 2945 26.42794337 4.677309273 2443 26.41989028 2.67603015 2102 26.41357778 3.447311026 703 26.40561579 3.145189362 2445 26.40053614 4.599299778 545 26.39588105 4.591458956 5019 26.3935473 3.305490562 4080 26.39173086 4.98949808 533 26.38814781 3.518061749 4187 26.3876894 4.506171354 2986 26.38746886 4.591761709 3277 26.3844842 4.834320822 5001 26.38335364 4.790979461 2601 26.38045227 3.821239332 1306 26.37569034 4.126236148 2345 26.37231681 4.683611479 3930 26.37158085 2.280587476 5010 26.36776106 3.203808361 4310 26.36513022 4.392151319 3131 26.36104256 2.307524277 1523 26.35990588 3.193121182 66 26.35931637 2.904202074 4988 26.35123865 2.424577194 1452 26.35000555 4.567905224 3802 26.34957493 3.618602139 1923 26.34609455 2.308692464 988 26.34539555 3.527299983 3710 26.34178986 3.594718187 213 26.33867398 2.895277965 3494 26.33305305 3.314351538 3633 26.33280352 4.755907162 3784 26.33050355 3.429139147 2264 26.32931357 5.092493407 2377 26.32927136 3.668313923 4159 26.32797063 2.687717714 53 26.32779461 3.281633297 2534 26.32605278 3.630859058 5084 26.31468779 2.973523501 3576 26.31288377 3.247221898 3688 26.30397925 2.299409366 3666 26.29930437 3.538829509 207 26.29804409 4.720588381 4481 26.29669207 3.12702241 2767 26.29554752 3.084955806 997 26.29230668 2.170275191 4626 26.28962591 4.839928889 3485 26.28868562 4.512323559 2522 26.28468504 1.864673156 4825 26.28429385 4.645386896 503 26.28368661 2.094137524 1089 26.27722291 2.132970122 3319 26.27688829 4.8638227 2513 26.26845259 4.910206236 888 26.26793863 3.610515561 190 26.26646387 2.256284924 4196 26.26600408 4.493002054 4592 26.26318028 3.370753848 272 26.25752449 2.402619101 4990 26.25638167 4.232298953 806 26.2558093 4.993130704 1403 26.25343604 2.389524935 818 26.2521952 2.978226058 2733 26.24912354 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26.15166814 2.696934866 3593 26.14737191 3.577894319 1584 26.14545418 4.968485871 4909 26.14425502 2.454670072 4767 26.14399505 4.691651869 3360 26.1438338 2.872728079 1920 26.13485534 4.929267772 28 26.13379925 3.162373535 834 26.13339575 3.418706136 2657 26.13018711 4.37322872 4610 26.12536067 3.624940794 1777 26.12044677 4.61442098 3847 26.11830988 2.692131428 1895 26.1166409 4.873866379 525 26.11559579 2.604670177 4207 26.11214616 4.946985888 4532 26.10981601 4.565538661 3789 26.09940516 2.39438938 3975 26.09621294 4.770695839 4267 26.09285388 4.985953903 2872 26.08740157 4.284170978 3171 26.08432072 3.579544181 4167 26.08368429 4.879688429 2234 26.08091728 2.652214629 3598 26.08071127 3.322460536 4580 26.07776388 4.564311954 871 26.07757124 4.481655167 5085 26.0744573 2.240517286 4034 26.07318428 3.1253295 2474 26.06930848 2.377078534 4797 26.06918165 5.158795888 1259 26.0682702 3.571395181 4778 26.06740772 3.166051236 3147 26.06299559 2.669411697 3729 26.0584137 4.702797096 5254 26.05509478 4.265924585 4484 26.0548508 4.455726089 2004 26.05453772 4.763668828 4633 26.05020964 4.005286843 1815 26.04983267 4.663266242 3534 26.04706623 2.388449645 245 26.0453876 2.115680298 1750 26.04293435 4.76870836 973 26.03913264 2.714604862 4283 26.03424007 3.129550525 4601 26.03215301 3.537598454 2423 26.02399272 3.052377281 3765 26.02091945 5.133492585 4127 26.01507353 2.449883627 5302 26.01348526 4.193129223 4910 26.01214001 4.956101754 1952 26.00823002 4.829085143 555 26.00738109 2.475346292 4513 26.00516059 3.113976573 2439 26.00449134 3.397106684 3958 25.99785175 3.419857228 1438 25.99394787 4.655325771 3340 25.99028638 2.859971601 2177 25.98959104 2.858639482 4139 25.98772837 3.348619787 1157 25.98318857 4.823218855 1014 25.97303174 3.238123515 4653 25.96958585 2.488406342 3103 25.96586623 2.722495932 4952 25.96320817 4.8488014 4381 25.95668772 2.672570854 2574 25.95100705 3.689420592 743 25.94629998 3.725348569 2158 25.9406868 2.803883339 829 25.93858261 3.335568116 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4175 25.83384099 4.349167177 4726 25.83320278 2.977810115 4676 25.82594744 4.315738267 316 25.82481492 2.273709941 5161 25.82327837 3.045787057 1891 25.82166143 4.099315737 1739 25.82139118 3.419477996 2910 25.81443519 3.374864624 4201 25.81330262 3.401463618 4343 25.81215503 3.37375928 3352 25.80437606 3.441060808 999 25.80430157 2.350787378 48 25.80258738 2.382335397 1692 25.80172521 4.624153001 4849 25.79694313 4.610311768 2704 25.7942631 3.319372868 2457 25.79075761 4.666099819 2149 25.79020623 2.41177977 453 25.78789702 2.38818413 3881 25.78662744 3.441167939 810 25.78404993 3.730171249 1350 25.78399234 2.841195365 4800 25.78117337 4.580236285 2869 25.78019509 4.878641097 3709 25.78002205 4.793501878 34 25.77725812 4.751276857 3555 25.77571947 3.483371002 4027 25.77183415 4.486230455 4091 25.76451189 4.697675647 4624 25.76377657 4.695358626 835 25.76232095 2.970896703 606 25.7620557 4.570989037 2823 25.76194156 4.880508492 1796 25.75828223 3.717976596 3965 25.75750696 3.561090342 4694 25.75480253 4.416583686 4534 25.75381381 4.699388735 2973 25.7486724 3.748649123 3792 25.74617129 4.235462911 3481 25.7456566 3.04631725 1250 25.74391386 2.37587626 4777 25.74319086 4.04647475 2531 25.74141852 4.632646496 1761 25.73871853 2.953334359 5230 25.73860625 2.963977863 100 25.73487455 3.133382358 1137 25.7336749 4.887332239 5003 25.73248562 5.020100817 4717 25.72964521 4.582595251 1261 25.72858201 2.81889641 2584 25.72410757 4.638031775 1633 25.72390211 4.99450338 4384 25.72351402 3.085015565 4973 25.72267697 4.647138626 1073 25.71769281 2.365944176 3357 25.71614237 3.66067293 2526 25.71370525 5.007304738 378 25.71205725 2.638254401 4102 25.7117055 4.437586924 1361 25.70598967 4.821173608 2084 25.70585107 2.541179523 5144 25.69921737 3.005643551 2992 25.69783516 3.653019213 3561 25.69536358 4.983700967 3460 25.6931703 4.523746471 3374 25.69132795 4.301707291 178 25.69052589 2.1545598 3571 25.68758326 3.648516709 5012 25.68651749 2.731842173 1989 25.68614161 2.460306339 501 25.68455023 2.979488487 3140 25.68404945 3.717867335 386 25.68116149 3.42413329 1502 25.68024141 2.676003794 2847 25.67984833 4.755306211 1553 25.67958708 4.87999649 2603 25.67765839 4.79711919 3999 25.6753191 3.705666205 4928 25.67526694 4.753734617 4795 25.67439086 4.610460528 4255 25.67175231 4.260518063 2890 25.67020932 4.649282044 1758 25.67001989 3.664607988 538 25.66820431 4.57451238 3255 25.66538562 3.443509708 4473 25.66388121 2.206872697 358 25.66330158 3.064885593 3660 25.65773871 3.067528095 4646 25.65409878 3.544512616 4461 25.65399259 3.272188888 4264 25.65391465 4.645461031 4135 25.64285596 3.512537247 4827 25.64059679 3.075858951 2198 25.64011025 3.297096596 1711 25.63735726 2.345621307 5340 25.63597618 5.000337098 3767 25.63561587 2.987549523 4765 25.63508275 4.210027308 4011 25.6342395 4.853041648 4625 25.63166803 4.133051859 4009 25.63099902 4.956826279 4593 25.63064101 5.017402572 5190 25.62712305 3.201753278 2187 25.62662565 4.7130277 4782 25.62645409 4.784694553 3868 25.62476913 4.402621424 4549 25.62252939 3.692639183 2972 25.62229042 3.366534934 3882 25.62220325 4.774745384 4954 25.62022793 2.372455853 1927 25.6194747 5.130251585 1984 25.61886177 4.715334182 3760 25.61092496 4.751900681 2395 25.60922567 4.453403738 858 25.60623625 3.125635574 5119 25.60162795 4.795939761 1302 25.60032367 2.264116783 3320 25.59706068 5.097648999 2192 25.59699299 3.004169133 5143 25.59644426 5.079989327 2929 25.59557055 3.2731385 5242 25.58995457 4.51154077 5106 25.5875175 4.677039755 1033 25.58050913 4.874723116 433 25.57937821 2.372069504 5145 25.5793524 3.279545023 1197 25.57291957 3.522335782 5166 25.57100763 3.256311916 4110 25.5700043 2.78098605 3617 25.5697536 3.22227272 4575 25.56901276 2.821268881 5251 25.5666995 4.422932374 3142 25.56619221 2.267311135 1156 25.56496852 2.82018508 3512 25.55801056 3.484010787 3546 25.55549339 3.776975241 839 25.55411759 2.875154711 3382 25.55147892 4.618733376 4054 25.55129373 5.124226428 3128 25.54854102 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25.46267481 3.493153169 3714 25.46138919 4.627633861 342 25.45573477 3.658140807 2374 25.43979125 2.97333266 2551 25.43860263 4.234717662 2974 25.43642674 2.896112102 2493 25.43566144 3.565427759 5191 25.42986489 3.025447621 2537 25.42866873 3.669773188 670 25.42829303 3.520492582 3946 25.42632596 4.86296507 5162 25.42608084 2.628944356 4290 25.42491821 4.51777209 3711 25.42310084 2.358362282 2498 25.42248088 4.961637635 3961 25.4224772 3.708770861 5111 25.42160592 2.364452459 5194 25.41988109 3.28110173 587 25.41771344 3.599839454 1577 25.41729918 4.963829127 3164 25.41628042 3.381147794 1983 25.41589346 2.113843094 95 25.41345456 3.228008016 884 25.41259937 3.026332984 704 25.40731064 3.513257631 2403 25.40076238 2.94738915 57 25.40040438 3.631456184 3387 25.40012204 3.700419082 2001 25.39735382 4.531829645 3826 25.39481891 3.418292776 371 25.39277366 3.547696623 1908 25.39163255 4.773467765 2611 25.39101768 3.177697682 63 25.3858905 3.660390074 2871 25.38325119 3.062227278 2990 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3265 22.86275131 5.1857766 3191 22.86168338 3.055931131 3239 22.8596735 4.359985097 2346 22.85555936 4.735232634 4107 22.85464817 4.97969329 5241 22.85361078 5.009294843 5078 22.85289497 4.141668689 3876 22.8521794 3.038134791 3977 22.85136431 4.79172194 5292 22.84745578 4.160163329 4295 22.84663854 4.576265409 2352 22.84310349 3.616063688 5081 22.84245795 2.899137511 1541 22.84170628 5.102896172 5182 22.83494842 3.924412466 3300 22.83306687 3.44909885 4627 22.83163254 3.248267546 4655 22.82662644 3.26863325 3796 22.82205993 4.720235287 4792 22.82096173 3.551683939 5178 22.80811343 4.511264808 5293 22.80745521 5.069288874 1868 22.79264757 3.221139356 2984 22.78707503 3.411088259 4985 22.7862486 3.297607233 2916 22.78578693 4.876356386 5339 22.78413368 3.278229729 4753 22.7779757 4.509773464 2034 22.76858258 4.465230281 4608 22.76401756 3.217552893 1723 22.76297381 2.739328771 4823 22.76237189 3.606962615 4182 22.7600776 4.851204436 2227 22.75837774 3.207353139 3192 22.74430562 2.825327598 3146 22.7430643 2.985072672 4538 22.74003007 4.761121569 4042 22.73598203 3.136320052 2765 22.73499518 4.659815097 2827 22.73412864 4.464475056 2040 22.73184726 3.363776739 2465 22.72414585 4.507195406 4570 22.72164894 3.43735011 832 22.72124228 3.765559142 5152 22.71951071 3.239985445 691 22.7190356 3.573873706 94 22.71874451 2.931097954 4923 22.71865102 4.167839633 4137 22.71183328 4.83036367 4516 22.71157189 3.831299862 4523 22.71069957 4.596263492 1095 22.71021206 4.837194811 3135 22.7086883 3.236563478 3510 22.70622892 4.770887168 3676 22.70258839 4.554915294 3415 22.70057072 3.223141787 3936 22.69786884 3.209439995 3414 22.69427147 2.972597425 949 22.6942485 3.022238809 5181 22.69235128 3.003837506 840 22.68875693 3.247671405 3024 22.68866833 3.164978673 2785 22.68229946 3.029787774 4495 22.68114345 3.103027455 3838 22.6706894 4.370975216 4328 22.66088399 4.42870014 2398 22.65994369 4.525274429 5279 22.6595921 4.888372538 5297 22.64848483 3.191684578 1687 22.64749428 3.039622291 2051 22.64542987 4.51254483 4853 22.63935202 4.279404905 5134 22.63823483 3.154131132 3722 22.63610335 4.783673076 5159 22.63533865 4.134024848 3080 22.63275466 5.166202551 5052 22.63018596 3.233842044 4234 22.6300626 4.524645686 5277 22.62878378 4.553314815 4742 22.62714009 4.721144775 5252 22.62583115 3.270148028 1573 22.62374461 4.911025426 4163 22.62018785 4.93346379 5091 22.61981389 4.571853963 4692 22.61774943 3.042085572 4378 22.61452928 4.913161666 4482 22.61224332 3.047764216 435 22.61141443 3.565180082 751 22.61064935 3.135775345 1757 22.59116088 3.24841796 1528 22.59001796 3.36387388 4150 22.58834534 4.679019567 4104 22.58461647 3.139744787 4675 22.57218481 4.658475246 2342 22.57015496 3.356096607 2404 22.56906282 4.646685721 2911 22.56871234 3.321601181 1591 22.5667452 4.31744546 5147 22.56628862 4.45610129 4060 22.56507513 2.280845048 3585 22.5634921 3.032281708 3780 22.54992919 3.238823482 4528 22.54918283 4.988259368 4814 22.5484073 4.027406426 585 22.54561222 3.363552318 4629 22.54357214 5.222233961 2555 22.54349973 3.298174079 3413 22.54188706 4.601642957 4585 22.53930453 4.205412223 1677 22.53513519 3.080029482 4355 22.53085204 3.162054319 3196 22.52875682 3.664132317 5157 22.52757886 4.56337677 4733 22.52683497 4.090614219 73 22.52482515 4.354145579 2262 22.52346858 3.087507333 3606 22.51831938 4.815172298 2425 22.51783164 4.978832383 3972 22.51721584 4.412103248 499 22.51388036 5.004622164 4903 22.50584196 4.084701436 620 22.50094579 3.517879374 5008 22.50031144 2.913114929 4661 22.49757949 5.063711716 5221 22.49406479 3.988847586 2148 22.4935146 3.024679894 2353 22.49289794 4.572276131 3831 22.49151302 3.103255676 3865 22.4863187 4.526669306 4454 22.4857252 2.930256277 4489 22.48210034 3.774494262 1807 22.48045771 3.131307532 3370 22.47903627 4.290221537 4405 22.47752615 3.084987052 4939 22.4712902 4.437235981 1188 22.4708665 3.185435492 5233 22.46574578 3.717292617 3043 22.46292147 4.377858839 5197 22.45700999 2.7407773 2405 22.44408788 2.993284316 4021 22.44217448 4.923043789 2654 22.44027462 4.861479785 2836 22.42691706 3.195320709 5100 22.42616319 4.513799649 41 22.41937889 2.626590867 3723 22.41534876 4.853372607 5227 22.38743678 3.151623974 2819 22.38705638 4.777284512 3484 22.38548411 4.650666578 1466 22.38476277 4.554233352 2194 22.38137755 3.298269371 2259 22.37574379 4.626574383 4288 22.37402732 3.137601198 4964 22.37365329 4.602269141 4134 22.36395934 4.009443186 2817 22.36171024 4.809395926 3679 22.35950301 5.326110557 2438 22.35859327 4.556356869 1289 22.35375359 3.155308976 1293 22.3531644 4.736375435 2453 22.3474932 4.579510287 5116 22.34568225 3.967971676 5043 22.33934001 4.768211134 4789 22.33655311 4.923471995 4809 22.32910871 4.587073132 4842 22.32896827 3.652366063 4284 22.32817898 3.928059111 5016 22.32651061 3.16901492 4838 22.32581035 3.817160205 2171 22.32561904 3.344757535 4496 22.32252069 4.965575225 2480 22.31343845 5.065944572 4751 22.31006599 4.063487602 4998 22.30879081 2.949602237 1308 22.30540134 4.723775695 4619 22.30368876 4.630826979 3821 22.3005249 3.974431423 2348 22.29714115 4.72062159 2585 22.28822583 4.671222236 1967 22.28736094 3.291998835 590 22.28600905 5.121886737 3168 22.27825932 4.905244988 5104 22.27769378 3.410307309 4904 22.27598581 4.321434831 3036 22.27067935 4.62538734 3261 22.25965684 4.906192239 932 22.25005479 2.855571149 2582 22.24388996 4.705782907 1799 22.23671684 4.816703299 4383 22.22351601 4.849062032 4637 22.22002485 2.464672058 1307 22.21622362 2.882928494 4198 22.21332879 4.864447217 5287 22.21332382 4.608268176 5236 22.21293297 4.254240267 3275 22.20954081 4.789029898 4263 22.20755941 4.91102686 2660 22.19231098 3.079969498 2408 22.19001028 4.285376054 3237 22.18737319 3.227048012 4268 22.18639578 4.270790567 4786 22.18426932 3.393739941 3680 22.18298523 4.480331157 4816 22.17901877 4.732607541 3681 22.17861053 2.992693079 4368 22.17579858 3.172632711 5286 22.17414411 3.044811704 295 22.16929191 3.469684833 4942 22.1679048 4.801320651 253 22.16779445 4.39277166 3984 22.16576379 4.508629283 1601 22.162078 4.737670869 238 22.15207413 3.046953194 1710 22.14417038 3.368577732 5272 22.1334624 4.410070161 3356 22.13092537 4.726776895 2141 22.12988424 3.281955563 5223 22.12967272 2.871283797 5168 22.12935262 5.363641513 5027 22.12303217 4.290522647 1389 22.12048748 3.675319666 1605 22.11208906 4.487707361 3323 22.11191417 3.03026464 4590 22.11104989 4.829741704 1248 22.10990245 4.712673878 1740 22.10842915 2.897765752 3985 22.1050504 3.609828463 4375 22.10434813 3.209494054 4683 22.10099723 3.116783342 4667 22.10017328 4.779107212 1219 22.09797899 4.721369933 4830 22.09151712 4.223585634 5070 22.09132538 4.411696826 3750 22.08308808 4.660900563 5260 22.06501158 3.174815922 1896 22.06474384 3.130751745 3885 22.06192295 4.449715043 1940 22.06180574 4.040934031 5174 22.06061714 4.983714441 1743 22.0489179 4.577050629 653 22.04546511 3.776709409 3627 22.04393295 4.981837804 5018 22.04198776 4.077253044 4854 22.03723021 2.905369618 3811 22.03545958 4.550000154 1432 22.03391146 2.798030005 752 22.01943546 3.19320387 3177 22.01536518 4.22859294 5204 22.0151309 3.229154772 4921 22.00754821 4.256978245 4796 22.00522775 3.192588464 4674 22.00437964 4.758273739 5064 22.0026786 4.318797721 4211 21.99907953 3.311227641 5072 21.99685874 3.062012802 1518 21.99681701 4.219418878 3350 21.99498296 3.650518201 4459 21.99121924 5.010803856 87 21.99101952 3.09473909 4987 21.98802152 4.628658426 4561 21.98725421 4.559825538 3875 21.97908155 2.937532159 589 21.97044148 4.562032903 117 21.96624297 4.577355658 4056 21.96341094 4.394690979 3182 21.96274212 3.298772988 4364 21.96079454 4.434711018 4787 21.95804536 4.325088359 2586 21.95226447 3.069903077 4151 21.94623648 3.378201142 1915 21.94518396 4.814385365 2634 21.94303896 4.380986079 3788 21.94019946 5.073412555 3783 21.92486177 3.694664341 2145 21.91869853 2.769794473 4832 21.91415305 4.931843194 1422 21.91114451 4.757968938 1404 21.90615908 4.690378585 4685 21.89141182 4.884522936 991 21.89020295 5.028260893 4968 21.88837691 4.42238154 4995 21.88472171 3.145048574 4640 21.88308895 5.08101941 1382 21.88000941 5.003712457 2783 21.8785289 3.281029259 1159 21.86849191 4.634241185 322 21.86473135 2.996562348 4919 21.84944487 4.54648442 3532 21.84247016 4.741359033 2747 21.84164782 4.570072272 4291 21.83967727 4.566615738 3257 21.83596021 4.301882779 3800 21.81162613 4.551109345 4639 21.80921833 4.623142475 3242 21.80216569 3.457767619 4471 21.79438152 3.435491452 3122 21.79214279 5.009075594 2903 21.79206971 2.324033894 1290 21.76671946 4.99459911 2895 21.75195854 4.909622996 1880 21.74772702 5.246528601 3417 21.74659217 4.508207 3157 21.7387222 4.244118035 3575 21.73826148 3.180512605 4371 21.7349426 4.558890445 5141 21.72862721 4.617924857 3361 21.72361219 5.059123885 4979 21.71848734 3.024835253 4025 21.69940462 4.592180003 1504 21.69589071 3.085479355 4408 21.68579676 3.271954388 2583 21.68055127 4.524550242 2077 21.67170631 4.543136891 2036 21.66438772 4.898812983 1178 21.65331963 4.401538343 3639 21.64419237 3.816461305 4270 21.63621983 4.551707436 5055 21.62782057 4.745034055 3807 21.62039496 4.817210707 4245 21.61590445 4.67510016 714 21.59075277 2.670359992 4553 21.5855391 4.856607338 3986 21.58387227 3.682497538 1277 21.57038595 3.119320275 3685 21.55638401 4.607028266 4397 21.54625512 5.136488661 4757 21.54307459 4.89210837 3035 21.54306103 4.967821152 5306 21.54258367 4.594438027 1943 21.52956653 4.851311554 522 21.52574939 4.994814467 5175 21.52537839 3.102782056 4309 21.50994471 3.08309742 4302 21.50853574 4.236725154 4215 21.50292316 4.865887049 2964 21.4956509 3.697963716 4793 21.49450508 4.245563169 4565 21.49083817 5.144127478 3274 21.49054901 5.093662984 3863 21.48137177 4.777152107 5215 21.47370977 3.22069172 2027 21.44760176 4.366770482 1994 21.43972987 4.750737103 3952 21.43484489 4.47236129 4041 21.41595345 2.967101762 877 21.41179428 4.787985601 3845 21.40848723 4.541872123 601 21.39685157 4.475333597 2039 21.39581163 3.379038545 4106 21.39537829 4.160526143 4630 21.38437352 4.463742004 5121 21.37983429 4.293707194 3643 21.37650303 5.034886134 3933 21.36985611 3.272435484 5130 21.36698952 4.871276019 5068 21.35245502 4.310251515 1599 21.34901055 5.176705717 1027 21.3489523 2.997870771 1446 21.34780443 4.67755418 3344 21.3475913 5.126309454 2662 21.34006106 4.98250531 4224 21.33050119 3.994020769 4547 21.33037418 3.203428486 3814 21.32236762 4.283181654 3082 21.32116122 4.848600871 3991 21.31785457 3.630087434 4285 21.31468156 3.103773405 5156 21.31423375 3.348861433 2676 21.30814954 3.194380719 4155 21.3078797 4.633550192 5017 21.30096465 3.305793609 4912 21.2978298 4.548408817 3630 21.29754138 4.998866814 4466 21.29740372 4.785732087 4533 21.29386296 3.446496501 4354 21.28892726 4.536608983 395 21.28336399 3.848249324 2151 21.28068234 4.500279208 3359 21.27758968 4.841163321 1529 21.27642641 3.243283798 3180 21.25992397 4.462610375 753 21.25913395 3.460586959 5118 21.25593764 3.970630138 3488 21.24335832 4.365234818 1763 21.24332196 4.654309297 3295 21.22865208 4.388670725 1414 21.21703214 4.99481088 1474 21.21549678 3.448261672 4123 21.20780838 4.577309113 3703 21.20091858 4.646266974 2854 21.1913235 4.194972631 4663 21.18941761 4.851033915 5117 21.18820596 4.21356447 5187 21.18596079 4.272125718 4817 21.17692475 4.649660578 5273 21.173849 4.89670621 4664 21.17291107 4.819354549 4010 21.17124083 2.747217862 2360 21.16075999 4.585532052 5218 21.15090927 4.866989684 4304 21.14652998 3.37115834 2982 21.13994161 5.066436853 4141 21.13915291 4.821611787 3329 21.13685735 5.069576529 4581 21.12759357 4.675741163 4611 21.11521746 4.800812629 3878 21.1138723 4.501611382 5146 21.08428644 4.211355099 3354 21.07704768 2.685275302 5335 21.06012328 4.080701449 4018 21.05931428 4.919112335 4149 21.05717351 4.814004355 854 21.04734925 3.41538174 3799 21.03083937 4.305360695 4804 21.01942597 4.490884223 3225 21.01416542 4.217633583 619 20.99989342 4.927975014 2143 20.98466196 4.970786085 5246 20.96967684 4.104676424 4859 20.96489022 4.257149195 4648 20.94640939 4.833549723 156 20.94555147 4.652610035 5226 20.93968662 3.115619483 4316 20.93896763 4.830446444 4186 20.93589489 4.032210787 3062 20.92655915 4.563959792 3957 20.92041376 4.675008504 5007 20.90423664 4.13060361 3927 20.89983223 3.240823443 5225 20.85090698 3.143680396 4776 20.8479108 3.262063496 896 20.84758177 4.50114434 4043 20.82319454 2.930768404 115 20.81697907 3.218887154 5249 20.79850177 4.73208868 5006 20.79493825 2.717846667 31 20.79385077 4.831878256 3379 20.78643169 4.625677167 3544 20.7687236 4.765015272 173 20.74532193 2.947850502 5092 20.74256545 4.584668152 4738 20.70476614 4.420157425 3839 20.69743558 4.875044566 2357 20.68302233 4.782461347 4634 20.66783734 4.153589823 3951 20.65718599 3.992471403 4702 20.62515841 4.320257542 3749 20.62179377 4.553489848 4032 20.59169305 4.702833828 4246 20.57083704 4.307840417 2985 20.55021355 5.065814374 3856 20.54097072 4.709572569 4470 20.52399516 4.411489758 3176 20.52208439 3.283907754 4015 20.51887181 4.362644621 4989 20.508978 4.494458826 3215 20.50159523 4.784623063 1765 20.48261734 4.390054158 974 20.48249769 4.775726924 136 20.48068622 4.512964347 2221 20.46907134 5.016719803 4670 20.44329369 4.941664942 352 20.43943739 4.527657173 4966 20.43497007 4.737671775 4336 20.43318843 4.913644463 5278 20.40047309 4.919373702 1660 20.37517344 5.142832076 4105 20.36905545 3.828472397 4920 20.32738779 4.114863254 1246 20.31108094 4.819283221 4711 20.29370333 4.358252638 4728 20.29300677 4.740396312 5169 20.29277159 4.858911358 5259 20.28312638 4.574089323 5067 20.25958097 3.927867108 4360 20.25813998 4.776763064 2477 20.25795419 4.579814405 4846 20.24459106 4.661480764 5329 20.19141231 4.190114638 4714 20.17125084 4.867346437 3110 20.16375122 4.418730565 2922 20.14115757 3.106269793 3023 20.13862869 4.809368998 3381 20.12996489 3.477462198 4195 20.12314932 4.932339995 3341 20.10482871 4.473821764 3345 20.07522164 5.004159653 2503 20.07143388 5.075185528 3202 20.05791935 4.941794465 2544 20.04573078 4.775037264 4798 20.03497174 4.267007361 2989 20.01757204 4.967193993 3283 20.01572011 4.818010449 4960 19.96001892 4.854257242 3502 19.94178834 4.902109685 3752 19.92516463 5.06167185 4595 19.89406327 3.090992729 3224 19.87622243 5.062065581 4517 19.87436638 4.159004906 3091 19.75414816 5.168307401 5217 19.74444312 3.22244583 5250 19.73695704 4.471346384 1604 19.72607703 5.058885127 1123 19.67365046 4.713400863 5009 19.6402823 4.807841978 4396 19.61667916 4.697495313 4095 19.61262627 4.248177689 5269 19.60259206 4.786578845 1254 19.60082642 4.009390825 2261 19.55763904 4.941666138 2389 19.51428737 4.476945134 4996 19.48763311 4.566497254 5202 19.40411802 5.086210806 1872 19.36393635 5.096624757 4019 19.35554454 4.526344484 4684 19.30942417 5.02132926 4087 19.27447363 4.962870211 4126 19.19054108 5.046593161 2952 19.16971411 5.224935251 5075 19.16296996 4.892465659 4142 19.04934212 4.793109701 2667 19.04587466 4.860844453 2382 18.9203 4.571932289 2998 18.9054508 4.905657549 5099 18.88527598 4.554081496 615 18.82720953 4.804459265 3740 18.81277744 5.177990025 4093 18.68793669 4.447856246 4144 18.61942464 4.442683844 2879 18.21441237 4.961698142 4671 18.16199962 4.753591698 5049 17.88317913 4.650154039 3258 17.50461155 5.122638833 3648 17.49845565 4.678098732 5205 17.26544666 4.530085423 996 17.24465971 4.990684298
Code:
from trueskill import *
import csv
import sys
filename = str(sys.argv[1])
nteams = 10000
teams = []
nmatches = []
for count in xrange(nteams):
x = Rating()
n = 0
teams.append(x)
nmatches.append(n)
for row in open(filename, 'rb'):
r1, r2, r3, b1, b2, b3, rs, bs = row.split('t')
rt = [teams[int(r1)], teams[int(r2)], teams[int(r3)]]
bt = [teams[int(b1)], teams[int(b2)], teams[int(b3)]]
if (int(rs) > int(bs)):
(teams[int(r1)], teams[int(r2)], teams[int(r3)]), (teams[int(b1)], teams[int(b2)], teams[int(b3)]) = rate([rt, bt], ranks=[0, 1])
if (int(rs) < int(bs)):
(teams[int(r1)], teams[int(r2)], teams[int(r3)]), (teams[int(b1)], teams[int(b2)], teams[int(b3)]) = rate([rt, bt], ranks=[1, 0])
else:
(teams[int(r1)], teams[int(r2)], teams[int(r3)]), (teams[int(b1)], teams[int(b2)], teams[int(b3)]) = rate([rt, bt], ranks=[0, 0])
nmatches[int(r1)] += 1
nmatches[int(r2)] += 1
nmatches[int(r3)] += 1
nmatches[int(b1)] += 1
nmatches[int(b2)] += 1
nmatches[int(b3)] += 1
rankedteams = []
teamnums = []
for count in range(nteams):
if nmatches[count] > 0:
rankedteams.append(teams[count])
teamnums.append(count)
for count in range(len(teamnums)):
print teamnums[count], rankedteams[count].mu, rankedteams[count].sigma
08-10-2014 19:38
connor.worley
Re: paper: Weeks 1-2 Elo Analysis
Very interesting results, thanks for reviving this!
08-10-2014 19:58
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
I think there are quite a few biases still because of the way we do regionals/districts. Teams that only compete in a week 1 or 2 regional and do well (but not well enough to go to championship), will be rated artificially high because the only teams they're compared against are the other teams at the regional who still have the default rating. There is no opportunity to mark them down later on if they don't compete again (but other teams from that regional do). What would be possible is to use results from prior years as well, but shift them toward the mean at the beginning of each season. This would account for good teams tend to consistently be good teams (to paraphrase Jim Zondag). This sort of thing is done in the Elo rankings of NFL teams by Nate Silver (http://fivethirtyeight.com/datalab/i...l-elo-ratings/) There are some other things we can take away from Silver as well. For example, we could possibly modify the algorithm to weigh eliminations more than the qualifications, something that's also done in the World Football Elo Ratings. See this wiki article: http://en.wikipedia.org/wiki/World_F...n_princ iples Basically, the K value (the factor that determins how much to change a participating team's elo rating) is modified based on how important a match is.
08-10-2014 20:02
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
The file should be a tab delimited file of red1 red2 red3 blue1 blue2 blue3 redscore bluescore
|
08-10-2014 20:16
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Ether
Would you please post a ZIP of your input data file?
|
https://dl.dropboxusercontent.com/u/5193107/scores.zip
You'll need to install the trueskill package ('pip install trueskill') to use it.
11-10-2014 09:31
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
So I decided to take this data a little bit further. What I did was to take all of these calculations and run them through the data this year and try to predict matches. For this, I also included a modified Elo system that has diminishing returns for large margins of victory (Calling this Elo Mod). I got some rather surprising results.
My baseline was just using OPR for predicting match outcomes, it was able to predict about 77.1% of the matches this year. This was calculated by adding up the OPRs of each alliance and comparing with the result of the match. TrueSkill was able to predict 79.0% of the matches, a pretty good improvement. I need to develop the prediction model a bit better because it currently doesn't take into account the standard deviation as a measure of certainty. The modified Elo system was able to predict 79.5% of matches, an improvement over TrueSkill. The baseline, unadulterated Elo system as used in this thread was able to predict a whopping 81.4% of matches, by far the best out of any of these models. There is still room for improvement with the TrueSkill and Modified Elo. With the modified Elo, there are some constants that can be tuned for better results. But overall, the results are somewhat interesting. It seems that no matter the ranking model used, about 1 in 5 qualification matches will result in an upset.
Here is the spreadsheet I used: https://dl.dropboxusercontent.com/u/...Trueskill.xlsx
11-10-2014 10:55
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
What I did was to take all of these calculations and run them through the data this year and try to predict matches.
|
11-10-2014 12:25
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Ether
Since you used the word "predict", is it safe to say that what you did was to use the data from weeks 1 through n-1 to predict the matches in week n?
|
11-10-2014 13:20
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
My baseline was just using OPR for predicting match outcomes, it was able to predict about 77.1% of the matches this year. This was calculated by adding up the OPRs of each alliance and comparing with the result of the match. TrueSkill was able to predict 79.0% of the matches, a pretty good improvement. I need to develop the prediction model a bit better because it currently doesn't take into account the standard deviation as a measure of certainty. The modified Elo system was able to predict 79.5% of matches, an improvement over TrueSkill. The baseline, unadulterated Elo system as used in this thread was able to predict a whopping 81.4% of matches, by far the best out of any of these models.
|
12-10-2014 09:52
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
I've tried the L1 optimization problem, but l1-magic is giving me fits. For some reason, it blows up after 10 iterations.
However, I have done the analysis that I wanted. I calculated all the rating systems using data from events prior to CMP, then I used that data to predict CMP matches.
In summary:
OPR: 72.46% Correct
TrueSkill: 69.31% Correct
Elo: 72.90% Correct
Elo Mod: 71.71% Correct
TL;DR: We're okay, but not great at predicting matches. OPR is okay at it, but Elo is better.
I'm still somewhat surprised that Elo is slightly better.
Updated Spreadsheet: https://dl.dropboxusercontent.com/u/...skill%202.xlsx
13-10-2014 00:36
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
I've tried the L1 optimization problem, but l1-magic is giving me fits. For some reason, it blows up after 10 iterations.
|
13-10-2014 00:38
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
In summary:
OPR: 72.46% Correct TrueSkill: 69.31% Correct Elo: 72.90% Correct Elo Mod: 71.71% Correct |
13-10-2014 01:06
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Ether
What solver are you using ?
|
Quote:
|
Originally Posted by Ether
Try CCWM.
|
13-10-2014 08:58
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
I'm using the l1eq_pd.m function
|
Code:
% l1eq_pd.m % % Solve % min_x ||x||_1 s.t. Ax = b
Secondly, what you want to find is the min L1 norm of the residuals, not of the solution vector itself.
For the set of overdetermined linear equations Ax ≈ b, x is the solution vector. The residuals are b-Ax. So you want find a solution vector x which minimizes the L1 norm of b-Ax.
13-10-2014 15:35
Ether
Re: paper: Weeks 1-2 Elo Analysis
Attached is a comparison of b-Ax residuals for L2 and L1 OPR.
Alliance scores computed from L1 OPR are within +/-10 points of the actual scores 33.5% of the time.
Alliance scores computed from L2 OPR are within +/-10 points of the actual scores only 22.4% of the time.
It is on that basis that I postulate that L1 OPR might be a better predictor of match outcome.
[EDIT]Cannot add attachments to threads associated with papers. Brandon: can you please change this setting to allow attachments? Thank you.[/EDIT]
13-10-2014 20:21
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
My baseline was just using OPR for predicting match outcomes, it was able to predict about 77.1% of the matches this year.
|
Our numbers are very close, but I had expected them to be identical.
Here's a link to an XLS spreadsheet.
14-10-2014 06:26
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Ether
I just ran the OPR numbers using the data you linked in your earlier post. I came up with 6919 of 8921 matches correctly "postdicted", or 77.56%
Our numbers are very close, but I had expected them to be identical. Here's a link to an XLS spreadsheet. |
14-10-2014 06:46
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Ether
Attached is a comparison of b-Ax residuals for L2 and L1 OPR. Alliance scores computed from L1 OPR are within +/-10 points of the actual scores 33.5% of the time. Alliance scores computed from L2 OPR are within +/-10 points of the actual scores only 22.4% of the time. It is on that basis that I postulate that L1 OPR might be a better predictor of match outcome. [EDIT]Cannot add attachments to threads associated with papers. Brandon: can you please change this setting to allow attachments? Thank you.[/EDIT] |
14-10-2014 11:13
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
The differences are how we're calling tied matches.
|
77.11% correct (counting ties as incorrect)
77.93% correct (counting ties as correct)
14-10-2014 13:45
Michael Hill
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Ether
77.75% correct (discarding ties)
77.11% correct (counting ties as incorrect) 77.93% correct (counting ties as correct) |
14-10-2014 18:34
Ether
Re: paper: Weeks 1-2 Elo Analysis
Quote:
|
Originally Posted by Michael Hill
...the L1 stuff [is] a new concept to me...
|
Ax ≈ b,
where A is the (binary) design matrix of alliances, b is a column vector of alliance scores, and x is what you are trying to find: a column vector of team "OPR" scores.
There is no exact solution for x, since the system is overdetermined. So the idea is to find the "best" solution (in some sense of the word "best").
Notice that the left-hand side (Ax) is a column vector of alliance scores computed from whatever solution x you come up with.
The residuals are b-Ax: a column vector of the differences between the actual alliance scores (b) and the computed alliance scores (Ax).
Looking at it that way, it becomes clear that what you are trying to do is find a solution x which minimizes the residuals (in some sense of the word "minimize").
The most common way to do this is to find x which minimizes the L2 norm of the residuals. The L2 norm of a vector is the square root of the sum of the squares of the vector's elements. The L2 norm solution is also known as the "least squares" solution (for obvious reasons).
It turns out that finding the x which minimizes the L2 norm of b-Ax is computationally straightforward.
In Octave, it's one line of code: x = Ab. The backslash in this context is known as "left division". The syntax is simple, but under the hood there's a lot going on.
For the Ax ≈ b overdetermined linear systems were are dealing with in FRC to compute OPR scores, it turns out that there is a computationally faster way to compute the least squares solution for x. Here's how:
Multiply both sides of Ax ≈ b by the transpose of A to get A'Ax = A'b, or Nx =d where N=A'A and d = A'b.But "least squares" (min L2 norm of residuals) is not the only possible "best fit" solution to the overdetermined system Ax ≈ b.
Nx =d is known as the system of "Normal Equations", and its solution x = Nd gives the same answer as Ab (within rounding error) and is faster to compute.
For example, there's the "Least Absolute Deviations (LAD)" solution (min L1 norm of residuals). The L1 norm of a vector is the sum of the absolute values of the vector's elements.
Finding an LAD solution for Ax ≈ b is more computationally intensive than least squares.
Perhaps the best way to proceed is to convert the problem to a "Linear Program" (LP) and then use one of the many LP solvers.
For example, here's the AMPL code I used to compute the LAD OPR for your data:
Code:
param m;
param n;
set I := {1..m};
set J := {1..n};
param A{I,J};
param b{I};
var x{J};
var t{I} >= 0;
minimize sum_dev:
sum {i in I} t[i];
subject to lower_bound {i in I}:
-t[i] <= b[i] - sum {j in J} A[i,j]*x[j];
subject to upper_bound {i in I}:
b[i] - sum {j in J} A[i,j]*x[j] <= t[i];
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