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BGonline.org Forums
Bob Koca, ask not for whom the bell tolls
Posted By: Bill Phipps
Date: Thursday, 28 June 2012, at 12:56 a.m.
I know there are several good statistician/mathematicians on this board. I would like to walk through how I am thinking about the Stick cheating accusation and have you tell me where I may be making mistakes and how to correct them.
My goal is to take what I can remember from basic stats, and approximate what PR range Stick’s result likely falls within.
We know from Iancho’s numbers that Stick’s last 50 matches were played with a 2.3 PR.
I checked my own last 50, 7 point matches. My PR was 3.8 with a standard deviation of 1.21. If memory serves, that makes the standard deviation of the sample 1.21/(sqrt of 50) or .17. Meaning, I can be 95% confident that my true PR is somewhere between 3.46 and 4.14
I then checked on MCG’s last 25, 7 point matches. His PR was 3.25 with a standard deviation of 1.25. Making us 95% confident that his true PR is between 2.75 and 3.5 - This result seems compatible with the result on my own data.
If I ignore that a lower PR likely comes with a lower Standard Deviation, and assume that Stick’s 2.3 has a Standard Deviation similar to my own, that would make us 95% certain that his true PR is somewhere between 1.96 – 2.64.
How accurate is this estimation likely to be? How does the fact that the distribution is lognormal effect the standard deviation? Is the assumption that the standard deviation of his individual matches would be similar to my own wildly off?
Where I am headed with this to show what the odds are that Stick is really a 3.0 player who had a lucky run and posted a 2.3. I have been under the belief that there is very little chance of this happening Does anyone disagree?
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