Standard deviation

knife420 · #1 01-10-2006, 05:24 AM

ive looked at quite a few post and continue to hear the term standard deviation, but im still not smart enough to really understand the concept, is it just the average swing one will sustain compared against average win rate or am i compleatly wrong here, please help the slow learner out thanks

DrVanNostrin · #2 01-10-2006, 08:48 AM

Standard deviation is basically the amount off your average you are on average.

The formula is as follows:

SD = {summation over y}[((x-y)^2)/(n-1)]^1/2]
-x is your average or mean
-y a complete set of individual values
-n is the number of individual values in your set

The formula looks far more complicated than it really is. It's necessary to square and then square root to get rid of negitives. If you didn't do that you would get zero everytime. '(n-1)' is used instead on 'n' to ensure that there are at least two numbers in the set.

AaronBrown · #3 01-10-2006, 10:11 AM

If you won or lost exactly the same amount every hand, your standard deviation would be zero. If your wins and losses fluctuated wildly, your standard deviation will be large.

DrVanNostrin gave you the mathematical formula for computing standard deviation. A somewhat simpler formula that is sometimes used instead of standard deviation is mean absolute deviation. If your average win rate is 2 BB/hour, the mean absolute deviation is the average amount your win rate deviates from 2 BB/hour. So if your results are +3, -4, +7; your average win rate is (3-4+7)/3 = 6/3 = 2. In the first hour you were 1 away from the mean, in the second hour you were 6, and in the third hour you were 5. (1+6+5)/3 = 12/3 = 4. So your mean absolute deviation is 4. This tells you what kinds of swings to expect; a result of -2 or +6 is the expected amount away from your mean. Anything outside that range is a larger swing than average, anything inside that range is smaller.

Standard deviation just squares the deviations before averaging them, then takes the square root of the result. In the example above (1^2+6^2+5^2)/3 = (1+36+25)/3 = 62/3 = 20.67. The square root of 20.67 is 4.55. So the standard deviation is a little different from the mean absolute deviation, but it's a similar idea.

There are two uses of standard deviation. First, it helps you decide how much to trust the average win rate. If you play for 100 hours with a win rate of 2 BB/hour and a standard deviation of 10 BB/hour, you're more confident that you are really a positive EV player than if your standard deviation were 40 BB/hour. In the second case, there's more chance that your win rate was due to luck. Standard deviation allows an exact calculation of that. It relies on some dubious assumptions, but the calculation works pretty well anyway.

The second use for standard deviation is predicting future results. The larger your standard deviation, the larger your expected swings (both good swings and bad ones). A high standard deviation player needs a larger bankroll than a low standard deviation player.

It's a pretty good rule that 2/3's of your results will be within one standard deviation of the mean, and 19/20 will be within two standard deviations.

Nut4Dawgs · #4 01-10-2006, 06:10 PM

OP: please forgive a mini-hijacking here...

Aaron, have you ever considered writing a book about poker math? I'm dead serious. Not to knock DVN's reply - as I was reading it I was thinking how confusing that would look to someone without a clue as to math formulae.

Then you, in your usual way, come along and break it down in a much simpler form. Simpler, but not quite on a "Dummies" level. And that's the level I think that would sell.

Think about it.

efficacy · #5 01-10-2006, 06:22 PM

I just created a blog article that talks about bankroll management and standard deviation. It doesn't go into detail about how to calculate it, but it does explain what it means. bankroll management

AaronBrown · #6 01-10-2006, 10:23 PM

Thanks for the kind words. You might like Wizard of Odds. I have no connection with him, I don't know him personally, but he does an excellent job of explaining and computing odds. I would be hard pressed to write a better book than his site.

I hope no one thinks I put you up to your post, but since you make a direct suggestion, I feel justified in saying I do have a book coming out in March, The Poker Face of Wall Street. It has some math, some poker, some finance and a bunch of other stuff.

Nut4Dawgs · #7 01-11-2006, 04:38 PM

Once again, the qualifications/level of expertise/success, etc., etc., etc., of someone on this board impress me. I should be getting used to it, but it continues to amaze me.

Thanks for the link to Wiz. A very brief look-see was informative.

LOL at putting me up to anything! The fact that you're an author did not surprise me. I'm looking forward to the March release.

Anecdote: One of my corporate lives (early 70's) involved monthly, week-long meetings in Manhattan. My knowledge of the market was minimal but go find someone in NYC who's not a "player!" and talking about it. The more I learned about the Street, the more I became convinced it had to be the world's largest/greatest legal crap shoot. Waaaaay to big a game for my tight azz. Love the city, though. (1 week at a time)

Again, thanks, and continued success to you.

Mathemagician · #8 01-11-2006, 05:42 PM

[ QUOTE ]
I hope no one thinks I put you up to your post, but since you make a direct suggestion, I feel justified in saying I do have a book coming out in March, The Poker Face of Wall Street. It has some math, some poker, some finance and a bunch of other stuff.

[/ QUOTE ]Looks like a great read, especially for a math geek, CTA, and avid poker player such as myself. Pre-ordered from Amazon a few moments ago...

Looking forward to it!
M