Does anyone have the math skills to isolate the variable, a.

[VivaLaViking]

A power series. If you entered a number of poker tournaments with a variable number of entrants you may ask yourself, "How often do I finish in the upper quarter". You would probably normaize your finish by simply taking the percent of the place finished over the number of entrants.

Probability, p, of finishing in the top x percent, x, is p = x ^ a (eg Prob finishing in the top ½ is p = ½ ^ a).



For N trials, the data points of the percent finishes are used to find c with the data points d1 to dN.


ln(d1 * d2 * … dN)
------------------ = c
. . . . N

Then we can find a.


ln(a)
------ = c
(1 - a)