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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 gamma-distribution 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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