post or article explaining "confidence"

[jaydoggie]

Is there a good post, or article I can read somewhere about confidence, as it's referred to in Aleo's spreadsheet. Also, something that might explain standard deviation a little. My SD/tourney is $8.77. Total SD $83.22. I play $5+.50 on 'stars. Is this good or poor?

[AleoMagus]

Ok, here goes...

...

Standard deviation in SNG poker is equal to

SQRT((F1)(p1^2)+(F2)(p2^2)+(F3)(p3^2)+(Fn)(pn^2)+( W^2))

where,
F1= probability of finishing 1st
F2= probability of finishing 2nd
F3= proabability of finishing 3rd
Fn= probability of finishing nth

(note: all OTM finishes may be combined as one probability for ease of calculation)

p1= Net profit for 1st
p2= net profit for 2nd
p3= Net profit for 3rd
pn= Net profit(loss) for nth

W= win(loss) rate in net $/tourney

....

Total SD after n tourneys equals SD*SQRT(n)

...

Usually, better players will have a higher SD, but in SNG poker this is not that large a difference. After a moderate sample, almost all SNG players will have a comparable SD despite their actual results. This is not theoretically true in the sense that if you almost always won, your SD would be very small, but in practice, it is true. DOn't worry too much about SD. It is mostly useful for other calculations (like confidence and projected earning).

...

As the # of SNGs played increases, a player's confidence in the statistical accuracy of their results will increase. As such, it is possible to derive a confidence interval based upon the accuracy of results desired. For example, if a player finds that fter a given number of tourneys, they are making a profit of $10/tourney with all tourneys having a $33 but-in, they can say with a derivable degree of confidence that this is accurate to +/- $1 per tourney, +/- $5 per tourney, or any other value for which they want to calculate confidence.

This is done as follows:

Z=(x(SQRT(n))/SD

where,
x=+/- $x degree of confidence desired
SD= Standard deviation per tourney
n= total number of tourneys in the sample

This Z value is then converted on a normal distribution table (or converted automatically as in my excel spreadsheet) to find an associated A value.

Normal Disribution table (http://www.math.unb.ca/~knight/utility/NormTble.htm)

So,

% confidence = 100(2A-1)

...

Winning confidence is slightly different, as it not only calculates your confidence in your profit per tourney +/- profit per tourney ($0 to 2x your usual profit), but also every other positive profit value possible.

This means that winning confidence is calculated by doing the usual confidence calculation on +/- W per tourney, where W=your actual win rate, THEN we take that confidence
and add (1-that confidence/2). This factors in all the other positive profit possiblities. Some of you will notice that on a lot of the older spreadsheets, we were not calculating a 'true' winning confidence, but rather only profit +/- profit. The new spreadsheet is correct.

...

These confidence calculations assume that SNG tourney results obey a normal distribution. Some have speculated that this might not be true (including myself) but tallstack and I recently showed in another thread that the normal distribution is, in fact, a very good approximation.

QED (http://forumserver.twoplustwo.com/showflat.php?Cat=&Board=singletable&Number=1241103 &Forum=,,,All_Forums,,,&Words=&Searchpage=2&Limit= 25&Main=1241103&Search=true&where=&Name=5278&dater ange=&newerval=&newertype=&olderval=&oldertype=&bo dyprev=#Post1241103)

...

Phew. That's a lot of explaining in a short amount of time, so I'll stop here so you can ask if you want anything clarified. Also, if any others who know could double check my numbers as I wrote most of them on the fly and they may have errors.

Hope this helps

Regards
Brad S