[jubeirm]

I've been keeping records of my play for a while and computing a "simple" (see below) standard deviation (StdDev). I have also been downloading my playing history and realize that through this I can probably get some much better information about my volatility. What is the difference between the "simple", weighted, and theoretical limit StdDev that I discuss below? What is "best" in a theoretical sense and what is best for our purposes as poker players? Why?

First lets assume I have the following 5 sessions in my logs. Notice that I have most sessions between 1-2 hours and 2 sessions on the extremes (30 min and 5 hours).

Session 1: +30$ for 1:00 hr = +30.00 $/hr
Session 2: -23$ for 1:30 hr = -15.33 $/hr
Session 3: +12$ for 5:00 hr = + 2.50 $/hr
Session 4: +15$ for 2:15 hr = + 6.67 $/hr
Session 5: -17$ for 0:30 hr = -34.00 $/hr

Now what I am calling a "simple" StdDev is the usual sum of squared differences between the average and each observation. For example, for the above sessions StdDev = 24.08 $/hr

A weighted StdDev would give more weight to a longer session (e.g. Session 3) and less weight to a short session (e.g. Session 5). So for the above the average is -2.03 $/hr and the weighted StdDev

Var = Sum{i=1 to 5} [w_i * (x_i - xavg)^2] / (n-1) =
[1*(30 + 2.03)^2 + 1.5*(-25.33 + 2.03) + 5*(2.50 + 2.03)
+ 2.25*(6.67 + 2.03) + 0.5*(-34.00 + 2.03)^2] / 4 = 518.12

StdDev = sqrt(Var) = 22.76

Lastly, one could take this as far as physically possible by considering each win/loss and the time between them. For example, if I pull down a big pot ($60) after 5 minutes, fold for 20 minutes, and then lose a large pot ($47) I will have two observations and weights:

w1 = 5/60, ob1 = 60/w1 = 720
w2 = 20/60, ob2 = -47/w2 = -141

Then I can compute a weighted StdDev over all my observations (i.e. wins and losses) for all sessions. The trouble I am having is how do I interpret the results. I'm not sure what the difference between the three is and how to determine which result I should prefer. Any ideas?

Note: In all the above I used the formula for Sample StdDev. Also, all the above can just as easily be applied to BB/hr, $/100, BB/100, etc.