Standard Deviation usefulness?

[EGO]

I'm trying to figure out what my "average" swings are, and have found my standard deviation both per hour, and per hundred hands in PokerTracker. I'm wondering how to use this number.

From what I understand, it basically represents the amount of "swinginess" (for lack of a better phrase) I can expect with my play. My SD/100 hands is 10.8739 big bets. Am I right in concluding that I can expect up or down swings of 3x this number?

Is SD useful for anything else?

Thanks in advance.

[BruceZ]

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I'm trying to figure out what my "average" swings are, and have found my standard deviation both per hour, and per hundred hands in PokerTracker. I'm wondering how to use this number.

From what I understand, it basically represents the amount of "swinginess" (for lack of a better phrase) I can expect with my play. My SD/100 hands is 10.8739 big bets. Am I right in concluding that I can expect up or down swings of 3x this number?

[/ QUOTE ]

Your average swing will be 0.8 times your standard deviation. The 0.8 comes from sqrt(2/pi), which comes from the doing the integral in this post. Also, your median swing will be 0.69 times your standard deviation. This is the swing that you will exceed 50% of the time. You will be within 1 SD of your average 68% of the time, within 2 SD about 95% of the time, and within 3 SD about 99.7% of the time. In general, you can convert any number of standard deviations S into a probability by using the Excel function =2*NORMSDIST(S)-1. You can convert a probability p into a number of standard deviations using =NORMSINV(0.5*p+0.5). There is no maximum swing for a normal distribution; larger values just become increasingly more unlikely.


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Is SD useful for anything else?

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They can be used to determine how long it will take to have a certain probability of being ahead. Convert the probability you want into a number of standard deviations S, for example by using the Excel function =NORMSINV(p), and then it will take 100*(S*sigma/u)^2 hands to have a probability p of breaking even, where sigma is your SD for 100 hands, and u is your win rate for 100 hands. For S=1, this number of hands will give you about an 84% chance of breaking even.

You can also use SD to determine your bankroll requirement and risk of ruin using the information in the links below.

Bankroll Formulas

Derivation of bankroll formulas

Online calculators for bankroll and risk of ruin

[EGO]

My head 'sploded all over the place.

Thanks! [img]/images/graemlins/grin.gif[/img]

[demon102]

wow my heads hurts from reading this