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Effect of varying the parameters
Posted By: Timothy Chow
Date: Wednesday, 9 April 2014, at 2:55 p.m.
In Response To: Probability that a 6.0 player can join Mochy's 4.0 club (Timothy Chow)
To get a sense for how robust the estimate of 1% is, I looked at increasing the variance.
k theta prob(PR<1) prob(PR<4) prob(PR>10) prob(Mochy's club)
3 2 1.4% 32.3% 12.5% 2.2%
2 3 4.5% 38.5% 15.5% 5.2%
The second of the lines in the above table looks like more variance than I would expect, particularly at the low end (though that's also probably the regime where the gammadistribution model is the least believable), but the first line still seems plausible. So I'd feel pretty confident stating that the probability that a 6.0 player can join Mochy's 4.0 club on the first try is less than 5%, but could believe that it's as high as 2%.

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