Round 3

Since it's the weekend, it's sports time.  First up, my picks for this round of things:

One that I was doomed to get wrong.

And the other doomed one.  But a new mistake!

Texas A&M:

29.687500       14.062500       3.125000                3       6       3       Texas A&M

28.125000       18.750000       21.875000               3       8       2       Oklahoma

First up, I think my analysis notes have been wrong on the previous posts.  The file I'm pulling these numbers from is in 2016/2015/2014/group/game/rank/name format, not 2014/2015/2016 format.  This changes the analysis for some of my previous mistakes, but I'm too lazy to go correct those.  In any case, using this new, correct information, it looks like I thought (from the 2016 ratings) that Texas A&M should be slightly better than Oklahoma.  Folding in previous years could have potentially altered that choice.

I was thinking a bit about adding some score-based information in as well.  The idea being that each team scores a given median number of points across all their games, and have a given median number of points scored against them.  By comparing how well a given score ranks in all their games, and against their opponent's, it should be possible to construct offense and defense ratings.  This might be useful to say, "Team X is generally better, but they only are a +1 in offense, and they're playing a +4 defense, so they might not win."  The other benefit would be to add two new metrics, which could then be used across the full multi-year dual-gender score set to determine which relative weights each should be assigned to a more complete prediction model.

I think the first step that I should do, though, is to dump all of that data into a database, instead of using horrible fixed-width formatted files to manage things.  That's largely a consequence of not really caring a lot about the project.

In any case, here's the comparison table for round three:

#Bracket	N_R1	PP_R1	Nwrong_R1	P_R1	S_R1	N_R2	PP_R2	Nwrong_R1	P_R2	S_R2
Mine	32	1	6	26	.995	16	2	4	50	.998
Heart-of-the-cards	32	1	10	22	.656	16	2	8	38	.320
Julie	32	1	10	22	.656	16	2	6	42	.738
BHO	32	1	9	23	.823	16	2	6	43	.820
538	32	1	8	24	.928	16	2	7	42	.738
Rank	32	1	13	19	.129	16	2	6	39	.424
#Bracket	N_R3	PP_R3	Nwrong_R3	P_R3	S_R3	N_R4	PP_R4	Nwrong_R4	P_R4	S_R4
Mine	8	4	3	70	.998903	4	8
Heart-of-the-cards	8	4	6	46	.044	4	8
Julie	8	4	4	58	.610	4	8
BHO	8	4	4	59	.674	4	8
538	8	4	2	66	.955	4	8
Rank	8	4	2	63	.875	4	8

This now has the added columns of S_RX.   These are my simulated CDF values based on the Yahoo selection pick fractions given for each team.  This is another piece of kind-of garbage code that I threw together earlier in the week.  I think it's doing everything correctly, but I don't see any simulated results that get a total score above 83, and yahoo does list some in their leader list.  Maybe 1e6 simulations isn't sufficient to fully probe things?  Maybe I'm truncating or rounding something odd?  The main idea behind this calculation is to see how well a given set of picks should rank.

Plots for individual rounds and the total after three.  In general, the mean drops (because past mistakes have continuing consequences) and the variance increases (because there's the 2^N point scaling thing and because the number of individual games is falling as well).