Perhaps it's just me, but if the correct method is giving you a different answer than you expected, maybe your expectation is wrong.
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Perhaps it's just me, but if the correct method is giving you a different answer than you expected, maybe your expectation is wrong.
I just realized (and correct me if I'm wrong here Tom)...
Back to the whole regression to the mean discussion...
The error variance found in that methodology using the binomial distribution needs to be unweighted. I usually calculate weighted standard deviations, but the expected error (with an average playing time found in that inverted way you showed above) assumes no weighting.
When I calculated the average PA with the 1/SUM(n/X) method I got 11-ish...and an error variance in OBP of roughly 0.02...which is a standard deviation of 0.141 which is the standard deviation you'd expect if you didn't weight it by PT and therefore the guy with 1 PA is just as significant as the guy with 750. The observed weighted standard deviation was 0.065 which is WAY lower than 0.141 which wouldn't happen if the weighted standard deviation naturally screened out some of the variance caused by small samples getting into the distribution.