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BGonline.org Forums
Playing Under a 2.0 in the Near Future
Posted By: Timothy Chow In Response To: Playing Under a 2.0 in the Near Future (Stick)
Date: Wednesday, 20 February 2013, at 6:36 p.m.
Stick wrote:
Unfortunately I know thanks to things like trying to belittle MCG's accomplishment of playing a 1 PR that normally doing that raises one's PR.
No, this is a mathematical fallacy that is worth explaining. I have done so here before but I'll try again.
What happened in the MCG case was this. A bunch of PR's were produced from the tournament. As a community, we focused our attention on the lowest PR because of its human interest.
Even if "strong" and "weak" analyses are equally likely to come out higher/lower, if you analyze a bunch of matches on one setting, and then pick the lowest one, and re-analyze on the other setting, then the re-analysis is likely to yield a higher number. Roughly speaking, the act of selecting the lowest PR biases you towards matches whose PR's have been lowballed (for purely random reasons) by your initial analysis method.
To put it another way, if for some strange reason you decided to roll out all the matches first, and then picked the lowest one, and then re-analyzed it on a weaker setting, you would similarly find that the weaker analysis setting would tend to be higher than the rollout analysis.
This phenomenon is known as regression toward the mean or the "sophomore slump."
Having said that, I agree that of course you will certainly do better if you only pick the largest errors for rollout than if you roll out everything, because then you won't be penalized for the errors that the full rollout would detect but that the low analysis setting doesn't. So it is certainly in your interest to use such a selective rollout method, but not quite for the reason you state above.
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