How much does this screw up my SD calculations?

[fimbulwinter]

since becoming a live player, i've kept records of my live play by $/hour rather than by BB/100. when i enter the data and do my analysis of hourly rate, SD etc. i just use the mean from the day in terms of hourly rate.

like say for example i play 8 hours and lose $400; i would enter (-50, -50, -50, -50, -50, -50, -50, -50) into excel as the data points for that day instead of (70, -25, -125, 30 etc.) as it probably actually happened at the casino.

I realize this doesn't affect my mean, but it must skew my standard deviation, right? or maybe it doesnt when taken in the context of many sessions reported this same way? any way to counteract/account for this? Do live players who do this keep a notepad and take record of their stacks every hour?

FWIW right now i have maybe 300 hours of live play on the books with most sessions lasting 8 or more hours, but a smattering of smaller ones.

thanks to those who are good at math,

fim

[gaming_mouse]

if your units are BB/hr, then you should use the actual hourly data points to calculate your SD.

i believe your method would eventually converge to the correct SD, but the convergence would be much slower than if you use the actual hourly data points. that is, your estimates won't be as good for the same amount of data.

gm

[Lexander]

Your SD calculations will be assuming independence, when in fact your data is highly correlated. Correlated data has higher variance than uncorrelated data. So, without thinking too hard about the math, my immediate thought is that your sample variance (used to calculated your standard error and estimate your standard deviation) will be too low.

- Lex

[uuDevil]

There's no need to track hourly results if you do it this way:

Mason's SD Essay (http://www.twoplustwo.com/mmessay8.html)

[fimbulwinter]

awesome, kick ass

fim

[gaming_mouse]

[ QUOTE ]
There's no need to track hourly results if you do it this way:

Mason's SD Essay (http://www.twoplustwo.com/mmessay8.html)

[/ QUOTE ]

Your estimates will still not be as accurate as they would be if you used hourly data.

[fimbulwinter]

i assume this gives the upper bound of your likely SD then?

[Siegmund]

No, not an upper bound; a best guess at it. (See defition of Maximum Likelihood Estimate for what exactly is meant by "best guess" here.) But the more information you have, the more precisely you can estimate something. If you keep track of your fluctuations hour by hour you know more about your SD than if you only keep track of the end-of-session total. (At one extreme, if you only knew your starting and ending bankroll, you'd know nothing at all about your SD; at the other, if you kept track of the result of every hand you'd know it very well.)

You don't see people talk about the precision of their variance estimates much - the formulas to calculate the uncertainty in your estimated variance are not pretty, and the uncertainty is often high - but there are better and worse ways of doing it.