[wgardner]

Originally Posted by Ether

[A] and [b] CSV files for all 117 events in 2015 (9878 qual matches, 2872 teams) can be found at the link below at or near the bottom of the attachments list

http://www.chiefdelphi.com/media/papers/3132

Thanks for the awesome data, Ether!

Here are the results for the Waterloo tournament:

mpt = matches per team (so the last row is for the whole tournament and earlier rows are for the tournament through 4 matches per team, through 5, etc.)

varM = variance of the match scores

stdevM = standard deviation of the match scores

varR and stdevR are the same for the match prediction residual
so varR/varM is the fraction of the match variance that can't be predicted by the OPR linear prediction model.

/sqrt(mpt) = the standard deviation of the OPRs we would have if we were simply averaging a teams match score to estimate their OPR, which is just stdevR/sqrt(mpt)

StdErrO = the standard error of the OPRs using my complicated model derivation.

stdevO = the standard deviation of the StdErrO values taken across all teams, which is big if some teams have more standard error on their OPR values than other teams do.

mpt	varM	stdevM	varR	stdevR	/sqrt(mpt) StdErrO stdevO
4	3912.31	 62.55	206.90	 14.38	  7.19	 12.22	  1.60	
5	4263.97	 65.30	290.28	 17.04	  7.62	 10.44	  0.71	
6	3818.40	 61.79	346.49	 18.61	  7.60	  9.44	  0.43	
7	3611.50	 60.10	379.83	 19.49	  7.37	  8.64	  0.30	
8	3617.25	 60.14	429.42	 20.72	  7.33	  8.28	  0.17	
9	3592.06	 59.93	469.44	 21.67	  7.22	  8.00	  0.11	
10	3623.44	 60.20	539.33	 23.22	  7.34	  8.01	  0.10	
11	3530.91	 59.42	548.08	 23.41	  7.06	  7.58	  0.08	
12	3440.36	 58.65	578.65	 24.06	  6.94	  7.38	  0.07	
13	3356.17	 57.93	645.25	 25.40	  7.05	  7.42	  0.06

And for comparison, here's the same data for the Archimedes division results:

mpt	varM	stdevM	varR	stdevR	/sqrt(mpt) StdErrO stdevO
4	1989.58	 44.60	389.80	 19.74	  9.87	 16.51	  1.28	
5	2000.09	 44.72	714.81	 26.74	 11.96	 16.31	  0.57	
6	2157.47	 46.45	863.88	 29.39	 12.00	 15.17	  0.37	
7	2225.99	 47.18	916.16	 30.27	 11.44	 13.64	  0.29	
8	2204.03	 46.95	985.63	 31.39	 11.10	 12.77	  0.24	
9	2235.14	 47.28	1053.26	 32.45	 10.82	 12.21	  0.10	
10	2209.46	 47.00	1056.14	 32.50	 10.28	 11.37	  0.12

The OPR seems to do a much better job of predicting the match results in the Waterloo tournament (removing 80% of the match variance vs. 50% in Archmedes), and the standard deviation of the OPR estimates themselves is less (7.42 in Waterloo vs. 11.37 in Archimedes).