paper: How Accurate is OPR?

Thread created automatically to discuss a document in CD-Media.

How Accurate is OPR?
by: brennonbrimhall

By taking Team 20’s scouting data and comparing it to OPRs, we are able to quantify how accurate OPR really was for 2013.

By taking Team 20’s scouting data and comparing it to OPRs, we are able to quantify how accurate OPR really was for 2013. The results are very informative, and it is concluded that OPR should not be used to predict a team’s scoring output at an event in lieu of real scouting.

How Accurate is OPR.pdf (438 KB)
Dataset.xlsx (14.3 KB)

How did you validate the accuracy of your scouting data? Why did you choose to use percent error, rather then absolute error?

A few more things that would be interesting to look at:

Do the results change if you only look at the top 24 or 30 teams at an event (the teams you would be considering when forming a pick list)?
Is there an OPR at which it becomes more accurate? Looking at chart 13, OPRs above 15 seem much better then those below 15 (obviously game dependent).
Can you quantify the percent chance that Team A is better then Team B, given a specific OPR difference (IE, Team A has an OPR that is 1 higher then Team B, and has a 55% chance of being better then Team B, but Team C has an OPR that is 10 higher then Team B, and has a 90% chance of being better then Team B.
Does the percent error histogram still look normal if you discard the outliers and put more bins between -100% and +200%?

These are all good things to think about. Particularly, you may want to reconsider your use of percent error as opposed to absolute error. I’m estimating here, but it looks like absolute error would’ve been pretty consistent regardless of true scoring. Take a look at the correlation of those; I’d bet very little of the variation in absolute error is explained by variation in true scoring average.

If there were such a correlation, you would have noticed it in the residual plot for your OPR-True Average linear regression. I didn’t notice a residual plot in your pdf; they are essential for determining if your model is a good fit for the data.

Merry Christmas!

At our events, we scouted collaboratively with other teams. Accuracy actually became a prime concern of ours, so we had every entry into our scouting database checked over by our head scout before entry (who had been watching each match as a whole immediately before validating). Additionally, we recorded matches for further verification. There were a few instances I can recall where errors were detected in entries, and we used our footage to re-scout that robot for that match.

This was an attempt to make the results of our paper more applicable to other events in the 2013 season. Archimedes, for instance, is hardly indicative of the average regional or district event, and yet it forms more than half of our data (51%, to be precise; out of 196 event/team combinations sampled, 100 were from Archimedes).

Let me get back to you on answering your questions backed up with relevant diagrams and calculations. I’d also like to look at posting our dataset too. However, here are my suspicions:

  • If you see my response Basel A’s question below, sampling only the top 30 or so teams from each of our competitions should decrease the percent error, which would change the percent/tolerance table for the better. OPR should become more accurate.

  • I have no idea. Really intriguing question, though.

  • Since we do have the averages and standard deviations for each team, you could let Team A and B be represented by a variable with mu equal to their Average Score and sigma equal to the Standard Deviation in their score. If you subtract the two means and add the two variances, you should be able to find the number you’re looking for by integrating from -infinity to 0 and 0 to infinity. We used this method to predict match outcomes, but it was not very accurate. I don’t know of a simple way to extend that to OPR, though.

  • I’ll get back to you.

If you look at the scatterplot on slide 9 and compare the least squares line to the scatterplot, you’ll see that absolute error decreases as Average Points Scored increases (I did have a residuals plot in here previously, but it looks like I accidentally removed it before I posted it). The percent error decreasing as Average Points Scored is not simply a function of the denominator for the percent error calculation increasing.

I did do a residual plot, and include it previously; it must have been accidentally removed during my revising. I’ll make sure to fix that to back up my previous claim (see answer to previous question).

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)


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1912	1243.02329641761
4256	1243.1234425866
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177	1298.14851750709
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1259	1304.77083337882
2016	1304.77158226126
1701	1304.83106217299
123	1305.20985295384
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2252	1306.8811312566
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3007	1314.60424771957
3489	1316.05914294719
219	1316.84892325961
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3280	1319.40981878176
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704	1322.97338577469
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3061	1324.16313579247
358	1324.96469417498
3663	1325.6914970453
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2984	1330.062750106
3266	1330.18335392097
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2013	1330.84744303641
1741	1332.58586901939
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1403	1333.46915170123
4342	1333.66717196389
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2468	1335.09054388138
3812	1335.10945140519
233	1335.79225254598
2907	1335.93118048485
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4343	1339.1218049285
1405	1339.39538636078
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3970	1341.53799141712
1899	1342.07440562702
694	1342.24865606202
696	1342.50799159151
1592	1343.02460823041
2630	1343.85709190931
3387	1343.94322367349
2974	1345.01714621647
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2137	1350.36641022242
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3512	1351.65247238273
2486	1352.20749851983
2415	1353.20112007504
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27	1354.12762753658
4334	1354.66774259513
3802	1354.98512900048
1388	1355.01309380782
3171	1356.52080593583
2403	1356.69293625798
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1503	1357.87609089489
3309	1358.07046362637
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2614	1361.37019850202
1662	1364.2228618304
4158	1364.51023895093
3593	1364.62312113595
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2619	1371.64916209155
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3641	1373.79958395696
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128	1374.45712116104
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3467	1379.54358188031
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2791	1382.09428901178
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2638	1396.62681692185
155	1399.22392827322
1732	1400.31444752705
1625	1402.01624571653
2443	1403.01972826776
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2168	1404.41889197264
1939	1405.96727989276
303	1406.16077030994
3284	1406.6318958928
193	1406.77092695414
1421	1407.41709440476
111	1408.88959428744
955	1409.03965448902
4265	1409.9440029336
2851	1413.39692792868
192	1417.5072147051
103	1417.85861528435
3173	1418.08718577889
2826	1421.62238697863
2130	1422.00380603616
967	1423.83644700277
3824	1424.4877607948
293	1424.65111902078
3847	1428.17346094668
3990	1428.71918123344
222	1429.32173263643
624	1429.93955210178
329	1433.19542652553
2000	1433.42748392377
435	1435.72257537983
573	1435.76564950198
1676	1436.66179872081
2145	1438.26225072112
1918	1438.35183688243
3414	1441.73203874618
2512	1443.91869270898
360	1444.28343940142
2052	1445.68913015397
3928	1446.03315620176
125	1448.82568950045
3015	1450.51613073011
225	1453.00217390966
379	1453.75327305984
234	1455.65184105526
3539	1455.78157632052
3245	1459.87672441115
79	1464.71268563065
3314	1465.75815012018
2959	1467.68723662095
316	1470.69220506702
525	1471.31100927972
2648	1473.77307045129
1806	1477.55496241367
1519	1481.06920018518
948	1483.54675958234
987	1484.17839583617
2485	1484.49503422745
254	1485.66484858734
973	1485.94027814882
2729	1491.57552945501
2054	1508.534964774
701	1510.12548469239
1538	1510.20015629137
610	1516.28684596015
2169	1518.27635745321
148	1519.20474272572
1717	1523.36578325197
1983	1540.37859616682
245	1541.67918480531
862	1541.69744273021
1334	1549.90012172128
20	1556.33980046564
2590	1563.59789520569
868	1565.15790036299
67	1587.83178342892
1718	1602.55543781965
11	1625.84868762694
118	1655.58062776287
1114	1659.4593538914
33	1663.08681001952
359	1693.81098547929
1986	1696.82704216305
1477	1699.43206031541
2056	1709.75985745116
469	1860.09151515805

Sorted by Team #:


1	1222.5778695651
4	1216.73156523205
8	1148.55669846065
11	1625.84868762694
16	1245.52529618795
20	1556.33980046564
21	1184.91278746326
23	1184.34130858306
25	1215.13711302163
27	1354.12762753658
28	1257.56169785021
31	1163.19418908257
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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)

I’ve added the dataset used for these calculations to the paper. Feel free to use it to do any more analysis that you’d like.

Now, to answer specific questions:

Yes. By selecting the top 30 teams (in terms of Average Score), the least squares line becomes


y = 1.0486x - 0.7729

with an R^2 of 87.32%. The model actually moves further away away from the line we’re expecting (y = x) when compared with the overall combined model, though it has a much higher R^2 value (a change of 7.02%).

In terms of the percent error model, the new mu is 1.11% with a sigma of 45.10%. The new table for the probability a team will fall within a given percent error is as follows:


10%	17.543%
20%	34.248%
30%	49.396%
40%	62.475%
50%	73.230%
60%	81.649%
70%	87.927%
80%	92.383%
90%	95.396%
100%	97.336%
110%	98.525%
120%	99.219%
130%	99.605%
140%	99.809%
150%	99.912%
160%	99.961%
170%	99.984%
180%	99.993%
190%	99.997%
200%	99.999%

Here’s a table of the different averages and standard deviations for OPRs greater than or equal to the OPR listed. I see large increases in standard deviation from 10 to 20 (as you observed), and from 30 to 40.


OPR	mu	sigma
80	6.88%	15.60%
70	13.02%	13.92%
60	12.57%	21.20%
50	18.15%	25.74%
40	20.00%	25.31%
30	23.33%	55.35%
20	20.56%	51.77%
10	24.36%	92.58%
0	20.76%	100.66%
-10	3.08%	131.97%

This table has the mu and sigma for all teams within the OPR bin.


OPR	mu	sigma
80	6.88%	13.51%
70	17.12%	11.27%
60	12.12%	26.05%
50	26.12%	29.06%
40	24.18%	23.79%
30	28.43%	81.58%
20	13.57%	40.66%
10	36.60%	165.01%
0	4.63%	129.47%
-10	-287.83%	216.42%

Let Team A be represented by a Normal model with mu OPR, and sigma equal to the sigma in the table above multiplied by the team’s OPR. Follow the same pattern for Team B. Subtract the two normal models (subtract the two averages; A-B, and add the variances to find the new sigma). Integrate underneath this curve from 0 to infinity to find the probability A would score more than B.

This is a method to approximate a prediction strategy I detailed in this post: http://www.chiefdelphi.com/forums/showpost.php?p=1277423&postcount=1

Yes. https://drive.google.com/file/d/0B4tDHZQW_UvVNzA4bEFDeHRHWlk/edit?usp=sharing

We’re not creating a model for the data we have, which is why I removed it; this wasn’t about creating a regression that was supposed to model the data. Instead, this was about checking one of the properties of OPR: ideally, it should have a 100% correlation with True Average score, with an intercept of 0 and slope of 1.

That being said, here’s links to the residual plots:

As a function of OPR:
https://drive.google.com/file/d/0B4tDHZQW_UvVWmJvMExoWDYwUnc/edit?usp=sharing

As a function of True Average Score:
https://drive.google.com/file/d/0B4tDHZQW_UvVX2x6QU44dmxQT3c/edit?usp=sharing

Elo predictions of matches on Saturday, based on the previous day’s matches for Archimedes were around 65-80% accurate, if memory serves.

It was more accurate than the method we used where a team was represented by a normal model with mu equal to true mu and sigma equal to true sigma, and integrating underneath to find the chance for each alliance to win. See thread here: http://www.chiefdelphi.com/forums/showpost.php?p=1277423&postcount=1

How hard would it be to add the team number and event to the dataset?

Not hard at all.

I removed team numbers and events intentionally for team anonymity/confidentiality concerns. None of the teams used in the study granted any sort of permission for having statistics published about them on Chief Delphi, and it’s not like True Average Score can be derived from other, public sources information. It was kind of like publishing the FRC equivalent of how much someone weighs without prior permission. It just didn’t feel right.