paper: Weeks 1-2 Elo Analysis

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1

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Weeks 1-2 Elo Analysis
by: connor.worley

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

matches_week_2_2014.csv (230 KB)
elo_report_week_2_2014.xlsx (306 KB)
elo.py (1.43 KB)

Here is the Python code used to calculate the ratings:

import csv

teams = {}

def getElo(team):
    if team not in teams:
        teams[team] = 1200
    return teams[team]

def setElo(team, elo):
    teams[team] = elo

def calculateElo(fileName, kFactor):
    reader = csv.reader(open(fileName, 'r'))

    for row in reader:
        if row[3] == "Q" or row[3] == "E":
            averageRedElo  = (getElo(row[9])  + getElo(row[10]) + getElo(row[11]))/3
            averageBlueElo = (getElo(row[12]) + getElo(row[13]) + getElo(row[14]))/3

            Ea = 1/(1 + 10**((averageBlueElo - averageRedElo)/400))
            Eb = 1/(1 + 10**((averageRedElo - averageBlueElo)/400))

            if int(row[7]) > int(row[8]):
                Sa = 1
                Sb = 0
            elif int(row[8]) > int(row[7]):
                Sa = 0
                Sb = 1
            else:
                Sa = 0.5
                Sb = 0.5       

            dRa = kFactor*(Sa-Ea)
            dRb = kFactor*(Sb-Eb)

            setElo(row[9],  getElo(row[9])  + dRa)
            setElo(row[10], getElo(row[10]) + dRa)
            setElo(row[11], getElo(row[11]) + dRa)
            setElo(row[12], getElo(row[12]) + dRb)
            setElo(row[13], getElo(row[13]) + dRb)
            setElo(row[14], getElo(row[14]) + dRb)
            
calculateElo('matches_week_2_2014.csv', 24)
sortedTeams = sorted(teams, key=teams.get, reverse=True)
for team in sortedTeams:
    print(team, getElo(team))
2

*The usual Twitter data caveats apply :slight_smile:
*
*

3

How do the results change if you don’t include eliminations?

4

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:

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
5

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=Michael Hill;1316903]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)


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
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1422	1094.56191474946
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3197	1094.62924479297
3451	1094.86168861649
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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
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4547	1098.67318070806
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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
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3646	1109.03616832717
606	1109.52997827214
3788	1109.61153338867
3822	1109.64835718264
2895	1109.66526065837
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3283	1109.72171943257
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988	1111.55203562623
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3940	1115.17764241306
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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
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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
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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
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3996	1124.31232212453
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3532	1124.64021597458
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4104	1125.4757321273
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4238	1125.56000493963
4051	1125.59033290961
4240	1125.74974882145
2544	1125.77386410566
4723	1125.85270404079
665	1125.94296280064
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4859	1140.91825536466
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1379	1140.9958026186
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1334	1549.90012172128
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118	1655.58062776287
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33	1663.08681001952
359	1693.81098547929
1986	1696.82704216305
1477	1699.43206031541
2056	1709.75985745116
469	1860.09151515805

Sorted by Team #:


1	1222.5778695651
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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

Here’s the Perl script I used. It takes a standard input file of a match number (just sequential is fine), red teams, blue teams, (“RED”|“BLUE”|“TIE”) (referring to who won.


#!/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 . "	" . $value . "
";
}

Not sure how useful the Elo ratings are, but there is some statistical significance with having teams like 469, 67, 1114 and 2056 near the top. I’m nowhere near good enough with statistics to determine if this is enough data to work with (my instinct says no), but it’s just another interesting way to look at wins/losses

(Edit: Had mistake in my calculation)[/quote]

6

Here’s Connor’s translated to GNU AWK 4.0.1. Input is standard export.csv file.

*
*
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]}}
7

Free good rep to the first person to post FORTRAN or COBOL code of this.

8

Bonus points for shortest viable MUMPS implementation :slight_smile:

9

How about Pascal? Would you give reps for that?

10

lol of course not :stuck_out_tongue:

11

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.

12

Here is a visual using the data for the first 2 weeks using the data from the paper.

13

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)


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	29.53343602	3.505482723
3604	29.50671464	2.387871186
3507	29.41604642	3.473038332
4238	29.40460167	5.128627995
2052	29.39817072	2.852137471
3098	29.37634231	2.100343943
1730	29.35808437	2.866267364
4705	29.35425678	4.328548166
2481	29.34448721	2.597287993
5160	29.3410846	4.407520664
131	29.33269732	2.410860812
461	29.2949643	3.400288017
27	29.2584181	1.963683284
836	29.23384075	2.812459901
1986	29.21831157	2.788409232
2090	29.20563236	4.667521749
5057	29.20529178	3.066809556
610	29.20137097	2.730510579
1825	29.17707902	4.513578798
4028	29.16935309	3.236107507
3227	29.16366806	3.576224541
3386	29.13015577	2.805551126
5261	29.12090884	4.52024528
3018	29.11684387	2.780230959
314	29.1137908	2.155851246
2607	29.10596373	2.474612815
3491	29.09457281	4.732290359
2451	29.08057067	2.705712664
846	29.05322417	2.708043561
401	29.03981884	3.68830887
138	29.03914468	2.433997114
2137	29.0239724	2.096970259
4967	29.0201646	2.121102898
1583	29.01446561	5.085032027
4250	29.00906134	4.589249874
1396	29.00411684	4.983703554
2996	28.99853297	2.637380121
4003	28.99627635	2.418860007
145	28.9865935	4.026913446
1658	28.98607397	4.378878932
2797	28.9772021	5.011390959
364	28.97658572	3.260667401
4911	28.97471817	1.959958519
5289	28.96901789	5.116254183
1164	28.96780246	4.41807995
1165	28.96298327	3.667415147
2613	28.95773029	4.522513711
51	28.95283117	2.04568091
330	28.94137205	2.757355386
2550	28.928286	3.259926747
1065	28.92414986	3.350546227
1418	28.91922536	3.625238161
1245	28.91299834	4.696817574
3299	28.89864893	4.77036342
2122	28.88314202	2.632342013
2590	28.87763451	2.12109764
4050	28.87537735	4.4408568
2337	28.86109549	1.947189895
1075	28.8589027	3.486470276
2059	28.85801696	3.855572027
3056	28.84388821	4.698165799
1640	28.84385094	2.115164223
2472	28.83584063	3.937474327
4265	28.82053179	3.202783641
2470	28.81843083	3.62434634
2200	28.80200222	3.454150345
2853	28.80057617	4.532767299
3683	28.78703528	2.573634595
5172	28.78531008	3.17008341
1592	28.76603843	2.780417592
4039	28.76053783	2.698909212
4488	28.75751498	2.066478142
1218	28.75058556	1.965513343
3230	28.74965528	2.98843785
3158	28.74459617	2.919053474
5290	28.74032139	4.986355668
842	28.7384048	3.390498681
2875	28.73486068	4.393809797
1937	28.72667953	3.159170361
3939	28.72377262	5.014530397
1477	28.72195481	2.645931196
1625	28.71449008	2.572107155
359	28.7106173	2.428574051
558	28.70245237	1.966845141
2508	28.7017193	4.867675197
639	28.69219888	2.793132014
494	28.68548348	2.008560481
346	28.68508561	3.701458387
2528	28.67792171	3.650580436
744	28.66809808	3.423887217
1421	28.6531687	3.758194739
4551	28.64865284	4.168401925
75	28.63578832	2.121493199
3467	28.62975734	2.139867106
2907	28.62606271	2.222687386
2761	28.61954732	3.39224997
2068	28.61136406	3.887963826
3211	28.60418949	3.146403127
3334	28.59815921	4.34943834
5349	28.59570059	4.466291466
1742	28.58203823	4.728482913
3259	28.57764535	4.784459804
3189	28.55687292	3.467863461
2928	28.55016722	1.896961764
4612	28.54101822	4.666243576
339	28.53098874	3.602334025
1817	28.52943668	2.62451883
1262	28.51584333	4.714753286
60	28.51465696	3.658851444
4522	28.51327424	2.496180895
192	28.51009496	2.837694214
1507	28.50904353	2.720309797
250	28.50737526	3.218727996
3525	28.50580939	1.929654217
1756	28.50316361	2.730433292
3044	28.4997126	3.177095472
222	28.49367617	2.025079777
2339	28.48436254	3.301338552
540	28.47933421	3.217824853
862	28.46126207	2.023734676
3389	28.46099026	4.68596841
1379	28.45657369	5.195424462
1675	28.439144	3.261421717
2156	28.43537317	4.275714783
4462	28.42975519	4.550973536
70	28.41177903	1.895989771
135	28.408739	2.636827712
155	28.40706035	2.688336749
469	28.40096089	1.874391042
2183	28.39996952	4.687026597
2078	28.3977569	4.833904451
319	28.39395756	2.083071777
58	28.36280402	2.087280415
3206	28.35801911	3.688675189
3998	28.34404697	4.849336928
1257	28.32025459	2.499704853
3418	28.30933828	4.349595634
3388	28.30259473	4.824801315
1285	28.29458059	2.305152996
597	28.27834188	2.787716954
447	28.26467088	2.561633227
486	28.25232446	2.973760953
3015	28.24856616	2.602491856
3735	28.23414165	3.150216293
1311	28.23280496	2.804190221
1731	28.23135219	2.845290234
246	28.21585028	2.431129206
2107	28.21525663	4.703143024
4266	28.21192071	4.778905794
772	28.20214026	2.383205586
86	28.19176133	3.376964429
3005	28.19093489	4.501310307
4400	28.18151359	4.64052433
2486	28.17937362	2.805844071
3117	28.16664785	3.425938594
3656	28.16562902	3.323462653
3539	28.15919773	1.991295532
1329	28.15724567	3.355881553
2013	28.15667815	2.378503565
1876	28.1516167	3.762993367
5005	28.14456079	4.575925432
3535	28.14181724	2.936168852
3822	28.14036599	4.673917786
1828	28.13139891	3.701192659
4451	28.12510102	3.823729966
2181	28.12212267	4.875266253
2641	28.11901782	3.091051845
4092	28.11055919	3.751631445
125	28.09033155	1.853441856
4498	28.0901825	4.465208775
3572	28.07534664	2.859355582
3588	28.0750612	2.557894259
5282	28.07459544	4.17573687
3482	28.07399642	3.389302297
1111	28.07010785	3.632608132
3268	28.06727843	2.83892901
188	28.06298756	2.656421278
4070	28.05912621	4.502580614
107	28.05697432	2.145286865
4946	28.05596303	2.646533546
4158	28.05315935	4.618358386
3090	28.05005009	4.717190071
3003	28.0498165	3.274335467
2935	28.04793134	4.435358283
1816	28.02961966	2.862994721
4732	28.02384662	4.036594982
1942	28.01633271	4.863433025
1280	28.00219279	3.260433478
279	27.99347211	3.230759844
3763	27.99139831	4.447420555
4073	27.97968297	5.065743872
1885	27.97598351	2.7666224
4085	27.97469156	3.471272455
3614	27.97216098	4.960212238
2190	27.95430507	3.930074667
900	27.94524399	2.707364614
4820	27.9390299	4.688622033
21	27.93410091	3.432868247
3526	27.93169239	4.814848781
1538	27.92486838	2.724456636
857	27.92354123	2.098624606
5023	27.92203199	4.171843831
4656	27.92141755	4.80487981
4598	27.91955858	4.481995239
304	27.90909841	2.322057528
2375	27.90894942	3.603518954
2202	27.90734135	2.633259675
2959	27.89732735	2.007381819
4153	27.89122899	3.463395154
2252	27.88971547	2.756102993
228	27.87601748	2.109778856
3504	27.87224357	2.759226657
1317	27.8666563	4.832387572
78	27.86462222	2.117100866
4828	27.8595393	4.812909586
3620	27.85597677	2.080220628
1025	27.8536183	3.129743052
93	27.85089194	3.633570165
3944	27.84765204	5.019998598
2338	27.84209635	3.279898247
876	27.84083004	3.451462062
1596	27.83996243	3.067789924
3310	27.83584393	2.745422584
1747	27.83319892	3.462503992
4111	27.83258837	4.96614408
2969	27.82606189	5.049974036
343	27.82084209	4.049864518
573	27.81981388	2.053915974
2723	27.81732589	4.473535581
3556	27.81691144	4.724989673
931	27.81294965	3.321652165
3452	27.80865098	3.216628704
56	27.80536408	2.122151409
3691	27.80201138	4.876157444
4020	27.79025435	4.455539186
4623	27.78720433	4.78384784
1806	27.7517166	2.693683812
3187	27.74944306	3.729457122
3966	27.74706817	4.723918981
3937	27.7463367	2.838299502
1676	27.73681218	1.906777071
910	27.73453115	1.839643025
1595	27.72869361	2.131583206
5148	27.72642552	3.057855571
1001	27.7027831	4.807188233
1413	27.70083626	3.650011212
2035	27.69901414	2.468387129
3848	27.69285471	4.7936929
3624	27.69192722	3.422816241
4125	27.69136235	2.084184773
3490	27.68560185	4.88693688
1610	27.68463046	2.878862855
1598	27.6810935	4.898353944
5102	27.67564132	3.59374657
2212	27.66886563	4.932148824
2851	27.66621224	2.211712079
4926	27.66425235	4.486776609
5098	27.65839368	3.2524909
3284	27.65740247	2.779064721
1726	27.6556748	3.640493219
2471	27.65278994	2.073629563
706	27.6489457	3.636591288
4724	27.64813757	4.895060011
3528	27.6466486	2.699204433
308	27.64364871	2.317731374
4550	27.63529197	4.773031531
3786	27.6248589	3.252142018
4253	27.62410298	4.54891385
4269	27.62181187	2.763347388
4762	27.60345114	4.726691298
4024	27.587038	4.953979431
2606	27.5854184	4.759825177
3266	27.58443366	3.33516848
123	27.58366916	3.107219666
3745	27.58308555	5.03764501
4819	27.58059005	2.140147397
1629	27.57655826	2.866371217
2530	27.57235911	4.292038109
578	27.56707996	3.242176494
379	27.56262425	3.263778573
3759	27.55922794	4.725662825
801	27.55703623	2.81305897
1772	27.54950934	3.772181397
1024	27.54631545	2.77994546
1918	27.54444037	2.096471083
2705	27.54324206	3.607748785
2826	27.54323466	3.374980074
4320	27.5416407	4.955658948
4519	27.53393972	3.177129283
5073	27.53195721	3.056701536
4721	27.53178719	5.002346133
2557	27.52718383	1.859384087
948	27.52292412	2.117162186
1810	27.52186287	3.541299176
133	27.51367751	2.181238841
3812	27.51319031	2.276035278
955	27.51172273	2.118769286
3476	27.49188517	2.625971576
2468	27.48591177	2.55648535
2881	27.48475869	3.60131234
193	27.48056474	1.923419091
3990	27.47326123	2.678230152
20	27.47023721	2.512110565
269	27.46996698	3.34061618
2081	27.46847797	2.698981761
4203	27.46819273	3.974481462
167	27.46796329	3.521827513
4242	27.4648404	4.466315763
812	27.45963852	3.607268313
3054	27.45770837	5.070251715
3245	27.45531446	3.352310736
3993	27.44196636	4.671152566
2538	27.4366107	3.623092064
4651	27.4364919	4.943628117
4276	27.43485551	3.514811986
5231	27.43357485	3.157118689
3316	27.43346019	3.194624558
2834	27.42730834	2.006280369
3751	27.42028981	5.235495659
4536	27.41829863	3.4563523
2927	27.40656356	2.451121007
422	27.40401953	2.957876215
4244	27.40382967	4.964119278
2521	27.40297901	2.263793039
2152	27.39881308	3.319318035
987	27.39181513	2.670533041
25	27.38837111	2.092022025
716	27.38776316	2.288914651
126	27.38185912	2.468035797
3844	27.38117587	4.55347509
4412	27.36759876	4.903192216
3041	27.3641515	4.320561615
2852	27.36181757	3.603067341
179	27.36031026	2.764265897
1735	27.35989723	1.993950316
2495	27.35113614	2.281709205
357	27.34839561	2.090330354
4845	27.34496582	5.040937264
3309	27.33911782	2.784755425
1803	27.33817798	4.534051755
4690	27.32390236	4.395296741
3330	27.31036652	4.121911715
1585	27.30806794	4.43348185
302	27.3066819	2.611956867
1108	27.30644498	3.051014111
4978	27.30454681	4.892153553
449	27.30284842	3.681264667
3967	27.29808346	4.400890539
3926	27.29212541	4.956834524
1671	27.28665666	2.712861962
694	27.2866214	3.843752792
2228	27.28628056	3.265406807
4487	27.27681364	4.429716245
4112	27.27183768	5.036259439
2637	27.26241508	3.692491243
4687	27.26209302	4.750044007
68	27.2618129	1.927997223
1492	27.25714713	4.916402006
233	27.25631261	3.740157843
74	27.25393707	2.105938892
1153	27.25260314	2.084194397
1574	27.25087839	3.387533505
5153	27.25077393	4.608179263
935	27.24930406	3.545882152
2410	27.24795339	3.630758937
3081	27.23619843	3.549289927
5256	27.23425654	4.567881724
5326	27.22829143	3.085680302
4976	27.22704881	3.565552127
71	27.22385925	3.376846972
4982	27.21988159	2.902770078
1189	27.21879352	2.264639466
5332	27.2145263	5.151395258
360	27.21278454	2.122032087
4286	27.2054425	5.090189794
2067	27.20208255	1.972400853
3641	27.18138301	2.20185617
5015	27.17966646	4.108038834
4256	27.17853674	2.701200827
4526	27.17741653	4.627958159
1511	27.17552064	2.699270017
3042	27.17326969	2.846021645
1102	27.1690749	5.119039965
2106	27.16845311	4.921549574
4077	27.16580063	2.085375903
303	27.16539337	1.868462747
1243	27.16313232	2.741018804
2075	27.16098569	2.914772306
4377	27.16063445	3.240279998
2175	27.15929009	2.873695325
4403	27.1571352	3.376176124
2576	27.15522799	3.045870789
4241	27.15050979	4.241520254
3513	27.14750039	4.152151171
1985	27.1474009	3.373984391
3557	27.14476542	5.016940213
365	27.14349502	2.102683108
1626	27.13864471	2.491411021
166	27.13472968	2.376839709
3318	27.13034001	3.31491642
2144	27.12964423	3.279564094
868	27.1215306	2.288832244
3305	27.11942578	5.001916144
4635	27.11906131	4.968373912
1683	27.11485614	3.326149264
388	27.11405871	4.696771538
816	27.1061132	3.152338309
3021	27.10403963	4.410618837
937	27.10184037	4.725242296
2791	27.10102025	3.287214718
3562	27.09792896	2.813765267
5167	27.09338954	4.279201021
11	27.08384319	1.899858076
4118	27.0829381	3.3281953
2518	27.08273148	3.574117411
3596	27.0801639	4.306878042
1764	27.0679737	3.361528498
4161	27.06749932	2.974942027
384	27.06285529	3.263764143
2231	27.0618991	4.781034853
3591	27.06083334	3.259676042
1860	27.05631912	4.422026054
4146	27.05486265	3.589106481
4296	27.05434935	2.715197206
5112	27.0541892	3.225554622
2046	27.04797325	2.193351916
4917	27.04757659	2.485976271
3626	27.04680148	4.279470654
1829	27.0461927	4.834005551
3929	27.04452733	2.28332554
1533	27.03763448	3.567085926
81	27.03224647	4.243086126
4130	27.03169297	3.185094972
177	27.02989146	2.119770084
4055	27.02855095	1.963619764
3339	27.02601778	4.957860817
5114	27.02332801	3.08906336
1322	27.01852425	3.100913392
2560	27.01783462	4.544022304
2054	27.01746261	2.077831266
4531	27.01614103	2.775579556
4467	27.01293198	3.545637697
1746	27.01168313	4.915496717
4703	27.00591604	4.535521441
537	27.00141516	3.230865422
1241	27.00033607	2.085828698
4783	27.00012671	4.902858438
2437	26.99825107	3.343888432
1212	26.98872696	5.059435509
3065	26.98735302	3.185071078
4450	26.97528813	2.541819829
2064	26.97067106	2.3755279
4924	26.96554856	4.798305317
1138	26.96504067	2.695993322
5095	26.95999497	4.76882588
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	4.89766032
2283	26.81666798	2.852185302
1571	26.81455005	3.186739281
2655	26.81377099	2.856122133
4476	26.8117957	2.740825183
1648	26.81077216	3.900878942
4308	26.80760758	4.522536491
2811	26.80529708	2.104282348
5285	26.80430575	4.317120518
1539	26.80049036	3.766136712
2449	26.79801845	5.108322587
236	26.79575946	2.645218979
2386	26.79425295	3.544634915
1425	26.78894295	2.136572227
230	26.78377087	1.954592572
2612	26.78374178	2.923290834
2579	26.77844597	5.024669924
5132	26.77305592	5.003099986
3289	26.77144435	4.241762483
3840	26.76209129	4.988102783
3200	26.75621637	4.909861353
3160	26.75476947	3.502696248
492	26.75444672	2.378737397
3087	26.75397727	4.750005765
4007	26.7534338	4.472359899
2609	26.75216362	2.812043368
3197	26.73822988	3.489555553
3974	26.73614835	2.29437544
2373	26.72848631	4.606073047
5298	26.72181623	4.759095859
244	26.71997574	2.434557155
2062	26.71402469	3.381134747
2679	26.70818618	4.92097912
3737	26.70722871	4.694406783
4053	26.70634639	4.711244989
4213	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	4.721425886
3693	26.63287989	3.04613089
256	26.61872118	3.440247713
564	26.61446642	4.482348514
4514	26.61187106	3.630012581
3687	26.6110411	3.850752533
2944	26.60935766	3.206257831
4346	26.60209056	4.21091923
368	26.60004175	2.645172494
3537	26.5983709	3.135505472
5090	26.59782806	3.041699154
69	26.59763139	2.373898992
1143	26.59738532	3.266782595
3260	26.58972977	2.680962785
2532	26.58938267	4.779228216
1902	26.58850462	2.685506664
3322	26.58514649	2.412971109
1391	26.58400174	3.334718746
1251	26.58328725	3.402242187
176	26.58279334	2.049857269
3229	26.57970637	4.53703272
1503	26.57929467	3.572672791
3947	26.57885912	4.386647206
3843	26.57645274	3.063922875
2648	26.57598281	1.961334901
668	26.57535664	3.121461519
5124	26.57482088	3.043274732
1228	26.57313606	2.301085593
3770	26.57266847	3.257263347
488	26.57239973	2.123071087
548	26.57149383	1.977340005
2987	26.57081506	4.804216646
3489	26.57010615	3.698161133
1997	26.5690435	4.751209875
3618	26.5665499	2.369640313
2230	26.56469189	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	3.052714314
172	26.24839947	2.497935655
1690	26.24837381	4.78041901
4649	26.24323433	5.064579061
3059	26.23932458	3.449904559
4334	26.23911025	2.522299338
4230	26.23619474	5.224766906
3851	26.22911582	4.60867166
3743	26.22875829	4.889051009
604	26.22610608	2.69519888
3663	26.21401008	2.478653829
2993	26.21379976	4.169512723
2626	26.2112751	3.150349383
1501	26.21079805	2.655303631
5046	26.21002289	3.052815679
1787	26.20471087	4.712889397
4260	26.20305407	4.837627469
1405	26.20170696	4.34963873
2402	26.20064313	4.626073401
599	26.19684484	3.280733094
1706	26.19344299	3.404122366
2994	26.19151025	2.864445287
4505	26.18935954	3.540670688
4576	26.18893645	3.574562255
3668	26.18515619	2.957203321
4114	26.18279142	4.393037719
240	26.18116011	3.024836194
3061	26.17624311	3.38943116
3560	26.17309905	3.219754291
4156	26.16990076	4.270227703
3674	26.16978374	2.34680602
4063	26.15816355	2.433464744
2877	26.15815214	2.043660552
3527	26.15554784	4.742961837
4650	26.1537097	2.971449597
2085	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
4542	25.93218408	2.268942689
470	25.92900546	2.712770523
848	25.92858127	4.667055468
5299	25.92656074	3.336281888
3017	25.9264484	3.698140148
4464	25.92180028	2.768175565
61	25.92141899	2.296819806
2415	25.92068257	2.670833009
1569	25.90952041	4.208240308
3138	25.90810927	2.651098824
3861	25.90127159	4.812618119
4914	25.89795092	2.765773908
3294	25.89646384	5.0367673
280	25.89635151	2.416139724
3241	25.89501023	4.294856632
930	25.89292182	4.26501343
4568	25.88869622	3.274545025
3989	25.88591812	4.661304976
237	25.88168813	2.540944845
3542	25.88074749	3.235241647
3288	25.87907725	3.338059997
111	25.87734569	2.620246822
5136	25.87421649	3.233836853
1741	25.87037265	3.519553984
340	25.86990997	2.582688486
2848	25.86403163	2.690655936
4456	25.85881388	3.561056191
4247	25.85659721	4.230306483
3292	25.85590202	4.918602463
4352	25.8499675	4.971420091
3451	25.84979221	3.094023398
4048	25.84728806	2.267019922
204	25.84612418	2.517053417
1700	25.84127525	3.175144409
811	25.83803075	2.12468327
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	4.500585932
509	25.54527492	3.12314446
2909	25.54156456	4.668075495
1011	25.54069887	2.92962792
3461	25.54049723	2.408429052
4586	25.54009874	5.110525881
2632	25.53431784	4.734946682
2340	25.53370406	4.451863918
1695	25.53108432	4.254132937
3167	25.53047881	3.118857406
1737	25.52127245	4.508238166
1701	25.51975284	2.623468044
1195	25.51687843	4.811670092
2525	25.51541663	4.689395977
4004	25.51445947	3.018323443
5031	25.51333323	4.725898252
4490	25.51211312	4.642831294
171	25.50981405	3.360607851
4457	25.50693538	2.428362557
3880	25.50693169	3.238465311
2383	25.50315156	3.016170818
1899	25.49914579	3.030103074
2635	25.49893633	2.393166188
3324	25.49890784	4.070878561
2499	25.49797659	5.12070412
5276	25.49703342	4.800001084
2239	25.49331524	4.828035019
3684	25.48940875	3.292290666
4680	25.48939289	2.844312264
2980	25.48424865	2.176341854
2976	25.48328256	2.53049296
1719	25.47842295	3.647722572
293	25.4721076	2.352276952
108	25.47022506	3.558229018
5137	25.46616955	3.103568926
1429	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	25.37886633	2.410159052
1100	25.378469	2.288962532
3234	25.37804004	2.983542187
3793	25.37609307	4.63839743
4908	25.37565098	2.421141633
4014	25.37494531	4.670375908
4226	25.37454845	4.812482248
1551	25.37441359	4.244952042
686	25.36663015	3.690416809
2170	25.36634262	3.338661655
2512	25.3645518	3.397113917
4327	25.36294792	2.976102184
4012	25.36237554	5.029580492
4573	25.35857736	2.527534177
2444	25.35608656	3.23631681
2897	25.35454212	4.728974911
2199	25.35088002	3.47961028
2473	25.33994942	3.261003996
4332	25.33660887	4.96335051
5248	25.33606417	3.158157544
3238	25.33555991	2.097925259
3100	25.32833197	4.700940429
2673	25.3273103	3.001290433
291	25.32580941	3.310465304
5039	25.32145135	4.041817807
3548	25.32047822	2.527573441
4582	25.32046177	4.932474124
3659	25.31966047	4.868668136
122	25.31946069	3.638404347
4559	25.3189624	2.307153825
2080	25.31894942	2.816082278
3039	25.31483966	5.081277443
2936	25.3118763	3.669333472
3236	25.30941479	2.723351559
3602	25.30738924	2.145883001
709	25.30690616	3.156428673
3219	25.30567049	2.399956041
5053	25.30254219	2.29325552
5164	25.30131476	4.688192245
1846	25.29832584	3.377036114
2504	25.29488016	4.670289545
1160	25.29380764	3.425885914
3568	25.29261973	3.181554282
4567	25.29029893	4.541366246
5082	25.2902268	4.398354218
4023	25.28349664	4.060374707
3623	25.28284922	2.937444403
4232	25.28152901	4.208384721
2225	25.27972522	4.949354816
5048	25.27817212	2.826419106
3075	25.27407971	4.967746554
4171	25.26749566	2.991079168
4499	25.26749373	2.638582727
4376	25.26729379	3.059815272
1378	25.26686127	4.460640773
2729	25.26273859	2.495680489
4361	25.26244816	2.420830311
2411	25.2623798	2.308969889
5247	25.26080602	3.026012299
2185	25.25980363	4.46862356
353	25.25959175	2.78269167
3373	25.25931466	3.792342893
4382	25.25473672	3.210739303
4418	25.25135613	4.640494372
333	25.25114012	3.725479599
4069	25.24575324	2.657666584
1018	25.244359	3.255882957
3543	25.23747806	4.41785509
980	25.23155638	3.428655255
1751	25.23018315	4.446594733
1126	25.2301364	2.5089232
3204	25.22546874	4.97841685
4855	25.22512113	2.877373895
1038	25.22446844	3.178167514
3132	25.22032605	4.668640599
2549	25.21494944	4.731472717
4761	25.21251303	2.414999155
4501	25.21223891	4.797123487
103	25.20760538	2.710565465
5350	25.20539132	4.333647605
3669	25.20538476	3.215876794
3970	25.20414766	3.627800452
907	25.20203666	3.61664582
5337	25.20202196	5.128678294
3694	25.20133029	4.960540271
2713	25.20131476	3.057428729
568	25.19664388	4.465725168
1334	25.19551663	2.248974279
1225	25.19264188	3.355911045
5060	25.18989267	4.310328874
886	25.18884998	3.616793222
1973	25.18827727	3.129999405
3293	25.18688881	4.811952097
4947	25.18632377	4.688961028
5071	25.18529285	4.40186611
3172	25.17933559	4.62954264
1517	25.17703634	2.376820059
1802	25.17608205	4.666699871
3692	25.17570888	2.863014473
3785	25.16952585	5.002419729
4956	25.16662416	2.384322295
3336	25.16660017	4.492981566
271	25.16319025	3.555468804
4556	25.16151297	4.318558996
1148	25.16058706	3.615886422
4030	25.15642213	2.505343479
3487	25.15468817	4.495361168
1554	25.154376	4.416094199
296	25.15435409	3.279221305
2539	25.15294992	2.341062686
4632	25.15095485	4.811350302
5318	25.14882964	4.852799411
4604	25.14634451	4.094997253
1720	25.14198593	4.512110861
2484	25.14052161	4.245411324
5030	25.13972407	2.868671195
2429	25.13870567	3.441139078
4980	25.13798105	2.435154286
4779	25.13713319	2.406454595
4741	25.13682861	4.902253464
5179	25.13327246	3.17570646
1388	25.13218711	3.43402703
904	25.13150944	2.563426949
2412	25.13138842	2.377255003
3240	25.13073793	5.096147469
4031	25.13072758	4.36184208
4306	25.13059602	4.540920119
4083	25.13006336	5.064400225
3987	25.12979317	4.678831663
5115	25.12893641	4.685095078
3402	25.12739263	4.393712517
3019	25.12531303	3.565186401
919	25.12123321	4.68934242
3220	25.12106708	2.98013888
4735	25.11908159	3.583106763
5066	25.11559945	3.092524373
2960	25.11401276	2.343030711
4737	25.10890684	2.907482983
2399	25.10887666	3.413913069
4958	25.10713212	2.310375513
5056	25.10645053	4.071074373
3244	25.10234335	5.084083618
4035	25.09619831	2.307710873
1208	25.09155716	3.294906782
1801	25.09109277	3.321157904
2577	25.09099786	2.418712466
3006	25.08622353	4.302683791
4353	25.08561404	4.781901243
224	25.08462731	3.090629149
4143	25.08010373	3.399611526
1708	25.07369832	3.196929101
85	25.07311621	3.129663187
1482	25.07289558	3.329739522
4906	25.07009278	2.941301455
4957	25.06949535	4.767345844
4696	25.06818925	5.210150106
4183	25.06553692	3.478494651
292	25.06471765	3.47648627
4583	25.06111871	3.178239493
1288	25.0609267	3.440170342
1369	25.05628148	3.390386591
3754	25.05573478	4.544512423
335	25.0547191	4.988289365
3559	25.05318723	4.398362279
3996	25.05230927	4.550521357
1249	25.05061257	4.5384978
3777	25.04927297	4.774348605
3971	25.04918632	4.67452444
612	25.04893417	2.841204594
2861	25.04465461	5.012595447
102	25.03758286	2.280846026
5002	25.03728475	2.646009953
5093	25.03355754	2.704847405
4541	25.02786083	3.647734377
869	25.02766234	2.121771601
2874	25.0252236	4.672053091
1991	25.02462395	2.482068074
2554	25.02337734	3.094259726
3931	25.02083681	3.380067405
4597	25.01413231	5.121432361
4521	25.0111	3.142808467
3470	25.00798659	4.388831632
1339	25.00582165	3.32895109
1635	25.00448171	4.970753579
5201	25.00401204	3.052287542
4535	24.99827103	4.48854346
3458	24.9973129	3.017142044
5193	24.99613824	2.35791344
3853	24.99598212	5.022440425
956	24.9958687	2.215603208
5151	24.99494459	4.988368507
5185	24.99220705	4.031247239
1444	24.98886838	4.444968654
5150	24.98585759	3.40996498
4390	24.97880743	2.981973393
4616	24.97780461	4.42282269
4936	24.9777217	4.03407843
3787	24.97594345	2.984670363
4013	24.97532079	3.264286682
1769	24.97334658	4.738817452
5263	24.97234634	3.205351363
4805	24.96997993	4.899428471
4277	24.96938809	4.766965538
3410	24.96850416	3.310925634
5013	24.96704701	4.634155897
3566	24.96105625	3.357861131
1325	24.96099063	2.79508404
1622	24.95607772	2.862320993
815	24.95536643	2.402270319
3403	24.9553332	4.49516814
2172	24.95362146	3.578293045
5209	24.94970467	4.677768206
4082	24.94593403	3.108100088
2915	24.94480166	3.188544527
3070	24.93652533	2.261372977
2169	24.93371678	2.939242551
1977	24.93353537	4.761371852
4905	24.93247813	2.429263588
203	24.92304602	2.418964438
4594	24.91910275	4.803150124
1631	24.914352	4.330236545
4272	24.91340652	3.36001978
4943	24.91239934	4.041702624
5077	24.90955746	4.77927719
4997	24.90757019	3.117548133
1495	24.90109263	2.31058357
3137	24.89949234	3.538033305
375	24.89809691	3.673431849
3573	24.89768752	4.772170495
4181	24.89766479	5.172683519
3013	24.89030086	4.297537147
1684	24.88794322	2.984864212
5129	24.88310098	2.847600703
1537	24.87969525	4.325331972
3008	24.87792446	2.862856716
5188	24.87748886	3.096070235
3755	24.87676411	5.00464145
5133	24.8740483	4.696656253
4918	24.87086873	2.351753821
4758	24.86900266	2.870233222
4205	24.86740215	2.744231161
968	24.86722439	4.729212611
4472	24.85843949	4.890774485
702	24.8535846	3.620605353
5307	24.84766967	4.656797865
201	24.84450239	2.605940412
3067	24.84365423	3.467586628
4404	24.84181199	4.523679248
3499	24.84036361	3.175957752
3116	24.83494458	4.568778856
4348	24.83187526	4.274751498
2370	24.82721085	2.956515879
3223	24.82544369	3.329177356
4026	24.82276545	3.400793334
4483	24.82170915	3.068729642
5199	24.81894338	4.457804819
3027	24.81763969	4.576148606
421	24.81478708	4.899150434
2461	24.81381902	3.441331181
484	24.80356558	2.016718002
2556	24.80248828	4.805890867
4662	24.80209814	2.935243661
4907	24.80091103	4.169072018
2341	24.80080063	3.204444172
4229	24.80003855	5.097631741
3637	24.79940814	3.023060555
4769	24.79806827	4.730867119
5196	24.79461136	2.988590853
3247	24.79341439	4.569960647
3997	24.7882515	2.683641388
3301	24.78482526	2.635980697
3941	24.78336831	4.521707263
2543	24.78117495	2.675291213
2083	24.77935164	4.692913122
3547	24.77426142	2.628552095
2193	24.76933502	4.438965503
2496	24.76922639	3.499033233
1795	24.76874607	5.060522143
1351	24.76662485	3.22631336
5338	24.76648904	4.5600848
3859	24.76407619	4.469727271
3276	24.76369472	5.039896353
3251	24.76169742	4.287896429
4962	24.7589161	3.714478972
348	24.75465206	2.467443464
5200	24.75103473	4.93419181
2961	24.74954407	4.630826353
2559	24.74651499	2.245555343
3307	24.7461135	4.929059886
4169	24.74179169	3.60466435
2073	24.73764359	2.734103353
1209	24.7357406	3.484902467
4078	24.7342416	4.433346335
4772	24.73164742	3.238131737
3522	24.73138348	4.919240267
1515	24.73086011	2.727997423
1155	24.72816884	3.521062795
4065	24.72736738	4.891257456
3419	24.72523461	3.682855859
4132	24.72321169	3.018875777
4654	24.72016333	3.144929811
4810	24.71843834	3.08527887
2902	24.71092965	4.345658393
1644	24.7087656	4.556601725
4047	24.70721858	4.214943284
476	24.7066272	4.704155486
2240	24.70376111	4.68244458
885	24.70009998	3.009513172
1965	24.69966113	3.11550874
5135	24.69709973	4.814754456
1099	24.69036449	2.426487322
539	24.68648811	3.541178402
3545	24.68315214	4.550477809
698	24.68311158	3.505986617
4281	24.68309034	3.048697961
1072	24.68263046	3.401843736
4120	24.6784962	2.355138378
4119	24.67584313	4.579026527
2594	24.67342297	4.218955945
3136	24.6660738	4.739870043
2168	24.66596354	2.397865416
3705	24.66585136	4.33013099
1791	24.66553953	3.110649377
3497	24.66539823	4.291678134
4718	24.66454903	4.780020461
5069	24.66378667	2.940880511
45	24.66374005	2.722499659
2830	24.66282258	3.265360953
3473	24.66269089	3.491866861
4275	24.65807551	4.099169425
3607	24.652059	3.108258092
4131	24.65092099	2.320123189
5014	24.64654268	3.915320158
2876	24.64616896	3.513628657
4089	24.64396501	2.931371741
4780	24.64311063	4.636897952
4972	24.64294986	4.343494927
2640	24.64098829	3.490239969
423	24.63156539	2.844692422
2587	24.62929437	3.355325354
3616	24.62798492	2.688733403
3925	24.62417677	3.422483438
677	24.61968763	4.04491704
4209	24.61855675	5.028625498
4485	24.61758831	3.41608859
640	24.61655807	5.132738431
5268	24.61603128	4.673208409
3550	24.61298133	3.569444795
3781	24.61160338	2.956751892
1572	24.61097249	3.33721848
2771	24.60423448	2.419528367
3577	24.60203307	3.533800438
4562	24.60016204	4.117793273
4406	24.60000687	4.873742029
1954	24.59870672	4.863556155
3104	24.59656097	2.986829667
5257	24.59461216	4.391009211
5271	24.59431068	4.71850197
3053	24.59335715	5.301509992
4185	24.59278204	4.349058156
547	24.59253456	4.62213521
4731	24.5882433	4.726917069
4994	24.58724395	2.911882036
4775	24.5852788	4.715242819
4941	24.58285381	3.22548255
3701	24.58230033	4.394504727
1305	24.58123935	2.27361345
4500	24.57955149	2.820587137
1836	24.57824755	3.573163965
2643	24.57162088	3.347564772
1714	24.56930183	2.750844456
329	24.56552394	2.696709505
4959	24.56522649	4.533012589
4727	24.56509864	4.74753908
1561	24.5636833	4.454688325
5265	24.56222982	2.901623637
1748	24.56131296	4.821114848
4491	24.55622608	4.766102771
4398	24.55590033	2.842637897
4191	24.55311294	4.331386863
4931	24.55171028	4.491487692
1522	24.54849369	4.954217901
1566	24.54730077	4.224117487
1359	24.54711406	3.19830021
3707	24.54143234	3.086023114
3049	24.53959775	3.139165695
5207	24.53785577	5.00169339
4901	24.53225352	2.76620658
3690	24.52987671	5.096228223
5212	24.52079781	4.315594446
2789	24.51784104	3.563282037
3468	24.51539851	4.828663008
3175	24.51106043	2.564226935
4652	24.50923919	3.14305982
174	24.50617468	3.25444121
3574	24.5060246	2.549497173
2942	24.50562981	3.06732143
2638	24.49624186	4.359702629
2167	24.4924545	4.596658213
5163	24.48859892	3.145703292
498	24.48339841	5.063183537
2619	24.48140594	2.187822266
1716	24.47539935	3.495888288
1580	24.47283017	4.833488125
4475	24.47217979	3.193775961
3366	24.46880917	3.588707688
4331	24.46871339	4.456324068
3179	24.46804503	3.545345004
467	24.46799382	2.94499793
5109	24.46123724	5.089215383
3973	24.46110682	5.060098162
4673	24.4572171	4.718279277
4068	24.45402016	4.680754886
4469	24.45289386	3.385725597
1058	24.45170383	2.416320667
4589	24.44915526	3.522975275
1768	24.44866097	2.766945857
4716	24.44604139	3.249604559
1127	24.44537781	4.948121689
2010	24.44465032	3.434330298
4991	24.44286732	3.146676124
1168	24.44001114	2.898486651
3695	24.43504942	4.215957449
3405	24.43101225	4.494277569
4840	24.42846534	3.05596474
5155	24.42673823	3.243236774
5025	24.42636719	4.327562936
4322	24.42467862	3.442260719
3134	24.42289537	4.920709765
3654	24.42111587	3.122856371
766	24.41376599	2.608645343
4992	24.41310382	3.227102511
2856	24.41070855	4.544870754
4504	24.40985271	4.522811147
5142	24.40763997	3.263245773
5063	24.40191993	4.869262905
1793	24.40170515	4.874683368
708	24.40076072	2.452616677
2957	24.39967421	4.80558512
4401	24.3981972	4.747418753
3407	24.39685664	4.917200498
5186	24.39559044	4.70829375
3536	24.39538034	3.360555929
3635	24.39375205	4.809974793
4747	24.3913566	4.833660046
4695	24.38976297	4.880632306
2977	24.38783362	4.959380601
4006	24.386926	4.234501667
4768	24.38388011	3.104524083
2965	24.38191353	4.37917481
569	24.37934586	4.508345989
1972	24.37893206	4.478124305
226	24.37890503	3.052021579
5219	24.37742205	4.960470997
223	24.37737275	2.025043451
2048	24.37302725	3.089117677
4166	24.37216036	4.692096271
5336	24.37108354	5.062224083
4969	24.36884244	3.170792621
3673	24.36550156	3.184231469
3871	24.36472602	4.869474429
457	24.36281775	2.529186435
1013	24.36112521	4.920573819
4949	24.35748628	2.814251452
5224	24.35552295	2.921073943
4707	24.35293683	3.151937239
2542	24.35135759	3.067665125
4067	24.34824938	3.586000551
2421	24.34582027	3.76840402
4097	24.34299189	2.904907999
4115	24.34169546	3.941351918
5348	24.34084196	4.576700989
4986	24.34069528	5.060936688
3932	24.33510666	2.625500748
4099	24.33499339	4.721370983
4319	24.33381053	5.122171909
3815	24.33345419	4.764223633
120	24.32981159	2.616189837
5113	24.32725116	2.419129863
159	24.32710331	3.510022113
1912	24.32709403	3.744275388
281	24.32684362	3.618666072
3950	24.32166422	4.383719188
687	24.31867823	2.715317728
3096	24.31579037	3.026769296
1884	24.31453102	3.239922689
4645	24.31421886	3.120805697
2840	24.31314786	4.984450036
4001	24.30947018	3.345315475
4799	24.30794567	4.33186609
2197	24.30458763	3.306062101
5024	24.30030037	3.090223443
1546	24.29220321	4.627380193
692	24.29189858	3.329086193
3029	24.28997707	5.126058884
5198	24.28696006	3.246460436
3454	24.28499664	5.050057714
3940	24.27538121	3.577117504
1086	24.27294087	2.715862689
468	24.27168598	3.095424258
746	24.26984282	3.649066212
5253	24.26182527	4.648172545
4681	24.26141372	2.946859484
4292	24.26058039	4.341586273
3282	24.25959966	4.280241609
4206	24.25708951	3.358124747
4356	24.25592327	4.256710223
5050	24.25543644	3.022289248
4458	24.25115237	4.34311832
4219	24.25109297	5.104149228
3337	24.24922775	3.873906311
5038	24.2454318	4.879479531
4049	24.24442277	4.40157797
2604	24.24317531	2.344453793
4301	24.24223559	4.429378814
1576	24.24076487	4.829955126
662	24.24019553	3.372828506
5234	24.2391468	4.329166445
5045	24.23849386	4.721146581
4927	24.23098073	4.533730312
2441	24.22978655	4.488998803
4950	24.21545815	3.286750792
5214	24.21195053	3.061418745
4311	24.21117623	3.178509947
2832	24.21107393	2.888450339
5344	24.20868281	4.729823732
2002	24.2082718	2.411387193
3798	24.20759901	4.419292359
1661	24.20451847	3.425029677
1745	24.20234491	4.700095205
4618	24.19575801	4.823183614
2896	24.1952167	4.692180114
4051	24.19182464	2.986071867
4847	24.18854198	4.853063167
3600	24.18784939	5.125292708
5094	24.18340601	4.542766295
4243	24.18310357	4.929886989
1296	24.1827768	3.376945455
4380	24.18207298	2.969509725
5125	24.18043592	2.97941394
4981	24.18004119	5.079463277
4951	24.17885564	3.350214097
4638	24.17693321	4.574793198
4750	24.17477754	3.146545856
1607	24.17445238	4.496326219
4851	24.17159903	2.957520689
4922	24.16754474	3.996706068
847	24.15888064	3.114710782
4708	24.15550848	4.907462919
3988	24.15360408	3.731143238
3655	24.15185307	4.216099351
5320	24.15074845	3.152068544
4965	24.1495814	2.677463338
3872	24.14739951	4.743905719
4413	24.14179573	3.468820324
3297	24.14171425	4.94368251
3466	24.14012452	2.734822354
4754	24.13844412	4.290606166
3636	24.13555003	3.000741118
4160	24.13448888	3.30511474
4984	24.12731237	4.282209326
2335	24.12407982	4.691578388
3509	24.12325367	3.243931109
2882	24.12299503	4.48063056
3969	24.12146521	4.829838967
4154	24.12028498	4.423020592
4373	24.1192922	2.404982496
1493	24.11916117	3.242822074
4057	24.11817462	2.375288894
1721	24.1173607	3.436007804
867	24.11656102	4.97059375
3828	24.11400178	4.935434978
1	24.11360248	2.873176325
2591	24.11277689	3.08024946
5107	24.11077676	4.344819446
181	24.11069239	3.22529502
4546	24.10964667	3.062834677
2914	24.10927128	3.598615871
496	24.10639153	4.519116047
3521	24.10305606	4.410335838
3328	24.10216154	3.547262775
4607	24.10211884	4.763213477
5158	24.09833338	4.766668763
4821	24.09694947	4.739956051
5149	24.092464	4.157682555
4833	24.09225492	4.790483293
3201	24.09202699	3.445438053
2509	24.08979989	4.833100355
288	24.08659219	2.412024636
4932	24.08213232	4.175460592
1458	24.08048194	3.546914374
613	24.07782604	3.02256219
5304	24.07029963	4.316953441
3650	24.06358075	3.55342476
2242	24.06142714	4.694465094
2545	24.0606324	4.733612332
2220	24.05398804	3.541862749
4180	24.0521965	3.161358723
1662	24.04866035	2.591480752
4386	24.04451427	4.849334427
5195	24.04215851	4.504831684
157	24.04095354	3.047368065
3022	24.04019409	4.689619509
219	24.03638372	3.075767892
4719	24.03521135	3.099289054
5110	24.03455642	3.037138115
191	24.03365079	3.114949034
3748	24.03231977	4.835546127
3699	24.03229846	4.958829579
3992	24.03113292	4.033816359
4961	24.02642118	2.998438434
3315	24.02469433	4.512858124
5183	24.02428581	3.042677482
5065	24.020927	3.360002632
4715	24.02074945	3.049198052
894	24.02008508	3.192166809
4615	24.01215405	4.496330138
144	24.00978856	3.215666277
5213	24.00953983	2.955735071
3570	24.00901107	3.126427406
5255	24.00306119	2.962013282
3408	24.0000199	5.074710522
623	23.99785618	2.800010112
1649	23.99711594	3.407870085
2923	23.99127137	2.432544702
5229	23.98599514	3.126730139
2621	23.9830948	3.061010851
5034	23.97570696	4.673171224
2511	23.97465389	4.970910245
3161	23.97258103	2.60297558
5238	23.96966741	2.984693643
5126	23.96802746	4.690275017
3962	23.96317133	4.552300351
3647	23.96304887	4.350818958
611	23.96031537	3.748462716
229	23.96002079	2.703547402
5059	23.9574244	5.006144873
369	23.95643751	3.656723248
4140	23.95482202	4.227924187
4773	23.95308801	5.181295664
2424	23.9478651	3.151054095
2232	23.94434754	4.896534638
3581	23.94411918	4.95480311
4090	23.9422693	4.567665701
1785	23.94015975	3.568081251
2224	23.93940971	2.913482697
128	23.93402924	4.304081196
4121	23.93285518	4.54325108
4566	23.93280081	4.864234836
2855	23.9307956	4.857220987
5086	23.92972739	2.938138509
4128	23.92935415	3.150674017
2459	23.92593001	4.540300084
4543	23.92331343	3.427474281
3721	23.92084397	4.537417089
3398	23.91561306	3.022674604
571	23.91458079	3.378743743
4740	23.9143934	4.50611011
5323	23.91126481	4.836107124
4388	23.91011551	4.618880514
3829	23.90945724	4.692355975
4262	23.90843246	4.628546647
1849	23.90770525	4.804824697
4748	23.90691049	5.020335959
4508	23.89636068	3.188621814
2930	23.89474629	3.044736561
5203	23.88835472	3.306231852
4298	23.88513756	4.340543587
4235	23.88207356	5.194699649
2207	23.88134849	4.894259564
3846	23.877769	5.031962386
2028	23.87631328	3.583118726
2517	23.87564611	2.501927017
1590	23.87472304	4.909740422
4337	23.87275231	2.923191395
3058	23.87253856	4.783372595
4165	23.87145118	4.588764773
1847	23.86603971	4.547455891
5275	23.86250006	4.822306086
2147	23.86206523	2.412619085
1786	23.85842641	3.304568719
5047	23.85808193	4.150517857
3597	23.85622565	3.126693061
2079	23.85140346	3.101584147
5123	23.84928994	3.040902535
4474	23.84423925	3.114361646
441	23.84372095	3.660497146
4657	23.8419201	4.777588135
4072	23.84121488	4.57990011
4591	23.83938477	4.115965135
2358	23.83890579	3.36263705
5327	23.83308924	3.372313196
4929	23.83260861	3.437591634
2709	23.83030925	4.32438644
306	23.82964912	3.569289892
4237	23.82205067	2.929966629
4603	23.82195361	4.610632854
3495	23.82041063	5.004039373
418	23.81699544	2.652516786
313	23.81487923	3.11416096
5189	23.81109267	4.649851188
4579	23.8106977	3.32559921
4925	23.80873218	2.087862965
4744	23.80872571	4.83575594
265	23.79710724	2.770481002
4103	23.7954834	4.353548472
4730	23.7948509	5.056682711
4902	23.79180365	3.537643608
2161	23.79095836	4.492602658
4342	23.78539835	2.826307685
2347	23.78347489	4.223750059
4395	23.78152918	3.545382012
3506	23.77367989	3.32062052
2839	23.77021054	3.377376134
2867	23.76267675	4.629563534
4217	23.75614419	5.042124064
4835	23.75514246	3.120305806
4225	23.75279338	4.921497335
5140	23.74481711	4.049425372
3302	23.74442175	2.865593456
2458	23.74291487	2.984545814
3603	23.73854887	3.044928117
3530	23.73823364	3.333793746
2656	23.73750329	4.423192419
2216	23.73610459	4.999407691
2053	23.73545696	3.430899092
2833	23.73254689	4.83589645
2665	23.73243896	2.620989118
2115	23.7300609	4.439476954
4622	23.72304065	4.05414275
1672	23.7190603	3.177144367
3955	23.71867398	4.476761883
4452	23.71796223	4.683297715
2620	23.71765612	3.234743692
1818	23.71761404	4.816776524
4252	23.7167971	4.790458504
1287	23.70718403	2.80839529
4189	23.69992944	5.054483748
3959	23.69895353	2.815459813
3298	23.69749196	3.671114801
5283	23.69588502	4.827531651
3498	23.69080603	4.7762118
4734	23.68862203	4.41282355
2354	23.6881309	4.615923179
4794	23.68711125	4.987461784
5345	23.68525234	4.291519548
4529	23.68469284	4.539136058
2966	23.68386034	4.908620798
4841	23.67763712	5.136450932
1258	23.67622334	2.857536662
3493	23.67584418	4.549829528
4829	23.67427	4.568100754
3667	23.67400653	2.85131596
4330	23.67347619	3.424565168
2367	23.67315874	3.259212872
88	23.67129575	2.932386745
2926	23.67095304	3.015559977
2906	23.67065195	3.416987193
3016	23.66676903	4.642303569
4698	23.66218261	4.172821562
1946	23.66181737	4.996458351
5036	23.65717354	3.139822637
4852	23.65585263	4.404566838
4173	23.65489213	3.172141019
8	23.64736107	3.380187183
3704	23.64081368	4.651617028
647	23.63403656	3.485877614
116	23.63094568	3.301032368
2129	23.6299205	4.696155255
4248	23.62559337	4.717047774
4008	23.61757042	3.185772157
1076	23.61257363	2.985048355
5274	23.60191751	4.326416093
4977	23.60033697	3.264131373
1303	23.59855581	4.734455123
3661	23.59551074	4.548301001
1002	23.59374451	4.891402065
1827	23.59178512	4.664425807
2849	23.58867714	3.616395194
97	23.57234646	3.506474599
4993	23.56822537	4.906877125
4815	23.55626532	3.066349162
59	23.55414343	4.073516565
1506	23.55112449	2.404454123
5324	23.54901667	4.650034716
1512	23.54037805	4.478267237
5347	23.53929689	3.010677277
4392	23.53600418	3.097720008
4329	23.53567405	3.392503877
3026	23.53342178	4.768234916
3464	23.53235774	2.988746191
3331	23.53188754	4.718360823
4512	23.52838831	2.436563438
2647	23.52804619	4.906528599
3533	23.52335614	4.52848136
4628	23.52190111	3.000693584
2605	23.51769407	3.116074928
4108	23.51726528	5.168417034
5346	23.51698715	4.331540172
4938	23.49979955	4.085181876
4824	23.49618554	4.387439873
2489	23.49598897	3.207340604
3734	23.4935118	4.360860142
3567	23.49161925	4.679068511
5180	23.48884944	4.792780159
4572	23.48779806	2.90521693
3465	23.48680132	4.51209635
3835	23.48508523	4.936292187
3376	23.482648	4.103924546
4723	23.473961	4.653841266
4299	23.47120958	4.920213157
3152	23.46731392	4.408433711
5035	23.46553711	4.522000105
3072	23.46070881	4.755273318
841	23.46024868	3.523153696
4944	23.458463	2.701967699
3653	23.4529633	3.274372714
2515	23.45027603	4.917120848
945	23.4489162	3.885089034
3321	23.44836957	4.805106513
4746	23.44293703	4.829674407
4571	23.44136513	4.980249463
5296	23.44123904	4.159072814
1559	23.44067172	3.337737529
5240	23.43619888	4.577062126
4511	23.4360781	4.872367004
2359	23.43152875	3.476130005
3151	23.4285206	3.144841499
5176	23.42486371	4.365695159
1510	23.42022506	2.419949666
1939	23.41622352	2.81463051
1811	23.41515868	2.881886978
3480	23.41429346	3.21447752
554	23.41407856	4.341118897
2815	23.40927156	3.776455551
5076	23.4039033	2.611508046
2905	23.39702614	4.330984784
4641	23.39600644	4.527606104
3949	23.39147834	3.94520043
4289	23.38658306	4.299618741
3205	23.3851593	2.974919134
4791	23.38111497	4.47858247
3883	23.38020943	3.880383776
141	23.37685132	2.498610018
3586	23.37485252	2.958484777
3010	23.3729139	4.45006262
1094	23.37097154	3.535107641
5235	23.36826969	3.35020285
3173	23.36701127	3.484651428
3007	23.36694501	4.683564721
4079	23.36578603	4.810500086
1759	23.36210224	4.9064289
3397	23.35166836	4.405304417
1657	23.34889837	5.002806237
1124	23.3459107	3.259692648
5020	23.34366637	4.930018742
4665	23.34300595	4.735587104
216	23.34292666	2.377675793
3773	23.34179252	2.95365921
5316	23.34129385	3.834471385
321	23.3396341	2.79598003
957	23.33620556	2.869220063
2275	23.33155601	4.955535151
4005	23.33117937	4.563271759
4335	23.33054562	4.463345361
4098	23.32887165	4.610107192
865	23.32590981	2.57199816
101	23.32012669	4.275598257
4174	23.31833906	4.833485403
663	23.31674847	3.163337218
5243	23.31585392	4.371606025
5051	23.31503404	4.595335005
1247	23.31427882	3.159075451
3634	23.31218074	2.761674142
5220	23.30888427	3.06945883
4468	23.3050989	3.809050095
4480	23.30277154	4.706562568
1646	23.30243723	3.190832823
4955	23.30211007	4.771549839
3756	23.29763291	4.051733424
2721	23.2974599	5.045114621
3632	23.2971252	3.134580629
3753	23.29196183	4.848964002
4074	23.29147981	4.794756056
2487	23.28995273	4.272779588
5308	23.28877616	4.734623801
1332	23.28823568	4.690489568
3651	23.28768402	4.501201716
3267	23.28724501	4.662931502
4453	23.28649532	3.084382876
1699	23.28489924	3.289630413
4148	23.28409831	5.229049482
2022	23.27203845	3.511872891
4557	23.26943683	3.340078644
4212	23.26881565	3.455958032
3169	23.26466842	4.766189448
5295	23.26422625	2.441217676
2135	23.26412943	2.766970832
3290	23.26396669	4.809516046
5222	23.26244991	3.172452986
5000	23.25802678	3.225590648
4811	23.25690571	3.045458696
4507	23.25580707	3.084708635
1091	23.25376903	3.435991971
3181	23.25374647	4.490209444
3218	23.25060757	3.320190904
4818	23.24723622	5.003325021
3541	23.24615666	4.450378644
3554	23.2455797	4.387231142
2900	23.2444977	5.061375845
3139	23.23882813	4.905641901
2450	23.23740339	4.99496367
1468	23.23718518	4.37595292
2501	23.23153803	4.822272776
4784	23.22865037	4.900035197
2479	23.22527503	4.89962305
3453	23.22516331	4.549488914
2805	23.22412892	3.570412825
5291	23.22199181	3.299607715
4239	23.22089025	4.731977402
4940	23.22085176	3.011669761
5032	23.2089761	4.029553131
5239	23.20851807	2.599785039
4409	23.20634514	3.219696034
5033	23.19701399	3.928716
3272	23.19618514	4.711197067
5103	23.19591765	4.988031254
4152	23.19416373	4.41597827
2702	23.19150031	4.0090881
4537	23.19126267	4.560066486
4693	23.18603071	4.936582325
3953	23.18415116	4.677685882
3976	23.18330871	4.693507903
4122	23.17909106	3.31222608
4038	23.17610854	2.559298404
1831	23.17568586	3.342495377
5312	23.17242504	4.686182315
3256	23.16896604	2.453868181
3979	23.16524439	4.626303578
3728	23.16458793	4.507693978
2773	23.15954343	3.339428707
938	23.15459524	3.396158152
3037	23.15273523	4.994437302
2846	23.15167715	3.593618181
648	23.1482029	3.394358869
4506	23.14307277	4.777973569
3221	23.14235015	3.42215225
2825	23.13920232	4.911666367
1255	23.13853704	3.696987312
1642	23.13526505	3.588444485
4349	23.13363186	4.53720714
4525	23.13297819	3.149515168
1941	23.12104788	2.994463234
4749	23.12084104	5.095195939
3083	23.11930704	4.798942659
5301	23.1162141	4.418317135
4064	23.11393321	4.951552802
1547	23.11255561	3.649122151
2165	23.10973159	4.472274914
3034	23.10867293	4.901237138
3163	23.10809968	4.520866252
1370	23.10373339	3.015595689
4555	23.10143981	3.155743683
4075	23.09875427	4.872283993
4975	23.09697945	4.008136458
3280	23.09500223	2.853492785
4970	23.09401293	3.069323929
1450	23.09065842	4.261536937
3501	23.08899754	3.587414931
3619	23.08818206	3.107290642
2213	23.08234009	4.90205537
4933	23.08177596	3.193887226
527	23.07815668	2.651548857
2813	23.07538583	4.1803131
3011	23.07394566	3.382494392
3045	23.07066922	3.564408986
1778	23.05257846	2.844465704
3515	23.05106026	3.100832454
3849	23.04685796	4.521518627
4856	23.04556633	4.989758139
771	23.04138816	2.581229265
121	23.03235366	3.2584066
5041	23.03178165	3.263052606
4983	23.02884675	3.047284425
4704	23.02723814	4.372997403
5216	23.0156989	2.91762847
2136	23.01312396	4.447513481
2246	23.01103937	3.095306814
3184	23.00220542	3.836961361
3712	23.00195119	3.179889899
5325	22.99988143	4.869601801
3675	22.99953709	4.662884777
1944	22.99848075	4.893503062
2725	22.99478993	4.372762948
2483	22.9941463	3.678377191
1448	22.99263288	4.373957745
3719	22.99090164	3.190075114
3886	22.98763462	3.040317337
5074	22.98254674	4.884262495
3278	22.97707155	5.132258726
451	22.97553574	3.413584673
581	22.97416182	4.364726551
4545	22.97262004	4.581856173
4460	22.96894225	3.118831112
3216	22.96562998	4.02251198
2029	22.95768462	4.386843643
5310	22.95566406	2.59508432
4574	22.95062676	3.386240246
3455	22.94879534	4.69508368
3212	22.94861294	4.692036296
2600	22.9467135	2.785180408
3459	22.94499134	3.633574224
5314	22.94339025	3.006661184
4251	22.94324773	4.052152564
2333	22.94238194	3.51872052
4600	22.94099533	4.298965088
4192	22.94026519	4.304985569
2265	22.9393192	3.700813651
4314	22.93823268	4.387677075
2500	22.93693278	2.834758377
2988	22.93204652	4.891469656
5004	22.92065116	5.020256448
4280	22.91815427	4.475530236
4455	22.91630619	4.707778474
5311	22.91415121	4.321063176
4338	22.91388894	4.87290849
2344	22.91085571	5.173327169
4492	22.9079349	4.572703902
151	22.90433433	2.867505429
4145	22.90013167	4.23931798
3457	22.89685069	4.476104961
2963	22.89682013	4.547231854
4682	22.89580109	3.019942263
2186	22.89447479	4.925388436
5040	22.89396512	4.751509902
4293	22.89240913	4.735854872
3250	22.89107844	3.36233001
617	22.88651874	4.979182056
5080	22.88613367	3.018480544
3028	22.88482548	4.622528543
1781	22.88365474	3.556363517
1398	22.86668968	3.393810294
5232	22.86430886	4.799800149
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

Python 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('	')
	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

Accepts a filename as an argument. The file should be a tab delimited file of red1 red2 red3 blue1 blue2 blue3 redscore bluescore

14

Very interesting results, thanks for reviving this!

15

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/introducing-nfl-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_Football_Elo_Ratings#Basic_calculation_principles 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.

16

Would you please post a ZIP of your input data file?

17

It’s the same one I PMed you a couple weeks ago, but sure.

https://dl.dropboxusercontent.com/u/5193107/scores.zip

You’ll need to install the trueskill package (‘pip install trueskill’) to use it.

18

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/5193107/Elo%20Trueskill.xlsx

19

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?

20

No, I guess I should have used a better word than “predict”. More like “postdict”. I went into it “knowing” an Elo/TrueSkill rating and tested against the data that was used to calculate it. Of course we won’t have all the data to calculate the final Elo ratings during the season. My next step is to calculate all the ratings as if it is just before championships and then see how each does with “predicting” championship matches. My SWAG is that the success rate in predictions using the “postdicted” matches is a ceiling for how good we can hope for the predictions to be.