ITH Poker Forum

[darvon]

OK. Let me see if I can explain. The word Normal is being used two ways here.

All of these "curves" of data are called probability density functions (PDFs).

"Normalizing" a curve is just dividing the value (i.e. adjusting the height of the curve) to get the total area under the curve to equal 1.


There are a whole bunch of mathematically defined PDFs, such as a Binomial Distribution, a Poisson Distribution, and a Standard Normal Distribution. Each have a different shape..


When we say that "68% of events fall within one SD of the mean, 95% within 2 SD", we are ACTUALLY saying is "68% of events fall within one SD of the mean, assuming that the data follows a Standard Normal distribution". Different shaped curves will NOT follow the 68%, 95%, 99% rule.


For a set of discrete table of data (not a continuous curve) the SD is DEFINED as

sqrt ( sum( (x-mean)**2) / (N-1) )

where N is the number of datum and mean is the average of all the data, summing over all x data.

In words, take the the difference between each data pt and the mean, square it, divide by N-1, and then take the square root.


This is what PT does.


The question is then what does the SD tell us about our results? If we assume that our winrate follows a Standard Normal curve, then we get the 68%, 95%, etx rule of thumb and we can start to use it for analysis and comparison with other players.


It is VERY possible to have PDFs which are NOT a Standard Normal Distribution. But until you nail down, (or assume) the shape of the curve, the SD doesn't tell you much.

Imagine a coin that has -1 on one side and +1 on the other. We flip it 100 times and get 50x-1 and 50x+1. The mean is 0. The SD is sqrt(100/99) or a little over 1. notice that 100% of our results are within 1SD, not just 68%.

Now imagine a 4-side dice. The sides have values: -10,-1,1,10. Again we roll 100 times and get a 25/25/25/25 distribution. Our SD is 7.14 but 1 SD only contains 50% of our results.

So we just assume win rate to be Standard Normal and then we can start to use the SD from PT.

[LdyLukAA]

In the book Poker for Dummies (I hate that name by the way )

Lou Kieiger (sp) gives a great explanation of SD by using temperatures.

From memory (and at work...no book)
If is the temp is 90 on Monday
75 on Tuesday
60 on Wed
85 on Thursday
65 on Friday

He says total this up and get your average of 75.....

So on the day the temp hit 90 you are 15 degress above the average..

Edit: Ok..I looked at the book last night and saw that what that +15 degrees is the VARIANCE....now you have to do some things with the variance to get the standard diviation.

Buy his book.....I STILL can't find my SD on Poker Tracker.....Anyone?

So your SD is 15.....

At least I think that's what he said.

Now, how to find my SD on Poker Tracker...still looking.

[Harte3]

Session Notes Tab and then "More Details" button is where SD is found.

All the detailed explanations on SD are fine for those not arithmetic challenged like me soooo.....what does this mean to me?

Standard Deviation/Hour 16.6--13.3. Simple interpretation?

Standard Deviation/100 Hands 21.6--16.9. Same question here.

And is there any "Target" or desirable deviation?

[Harte3]

Session Notes Tab and then "More Details" button is where SD is found.

All the detailed explanations on SD are fine for those not arithmetic challenged like me soooo.....what does this mean to me?

Standard Deviation/Hour 16.6--13.3. Simple interpretation?

Standard Deviation/100 Hands 21.6--16.9. Same question here.

And is there any "Target" or desirable deviation?

[Ben Coates]

Standard Deviation is the measure of how far you can stray from your average win rate. For example, if you win at 2bb/100 and have a st. dev. of 12bb/100 hands, then you have a 68% chance of finishing -10bb to +14bb every 100 hands. I prefer to use 2 standard deviations as it gives a 98% chance or confidence level. So for the same example winning at 2bb/100 you have a 98% chance of finishing -22bb to +26bb every 100 hands.
Hope that was clear.

[PauliF]

first why are you responding to a 6 year old thread?

second 2 standard deviations around the mean is a 95.4% confidence interval actually

hope that is clear