Coefficient of Variation

[RacersEdge]

What kind of ranges are people seeing for a COV for their play? (COV = standard deviation of winnings per time period/average winning rate per time period). Is there also a theoretical number/range out there for COV?

[Chris Villalobos]

I've heard that for a good HE player the COV per hour is around 12. My personal online results for 5/10 are 7, but I get to play many more hands per hour on-line than in a live game. Therefore, my Standard Deviation should be lower and my win rate should be higher than if the same game was played in a card room. Though it may also be showing me that I'm not aggressive enough.

Chris V

[RacersEdge]

12?? Really? I guessed it would be high - but not that high.

So let's see - if you average 2 BB/hour, and your COV is 12, you SD is 24 BB. So a 1 SD shift would be 26 BB. That seems very high.

What about distribution on the hourly win rate? I'm sure sure someone has plotted this out either empirically or actually. I'm guessing definintely not normal - exponential or maybe a bimodal looking histogram.

[Drummer]

StatKing software defines Coefficient of Variation as (Hourly Win Rate / Hourly Standard Deviation). It also quotes Mason as saying in "Gambling Theory and other Topics" that in many poker games an expert can maintain a CoV of around 0.1, and in Holdem an expert's CoV may even be as high as 0.15.

[Bozeman]

EV of 2BB/50 hands is big, only doable in soft games, and unless it is a very weak tight game, your SD will be high. Getting less than ~10 BB/sqrt(50 hands) for SD may be possible, but it is unlikely and will probably negatively affect your win rate. In online games where you can play many more hands per hour, then CoV (SD/EV) will go down. CoV is not a great metric, because it is not unitless (it has units of sqrt(time)), so it is not scale invariant. Thus use of it is contingent upon specification of units.

Craig

[Chris Villalobos]

Unless you play in a very easy game you should not be able to hold on to a 2BB per hour win rate in the long run. If you are doing that well, then you probably should get into a bigger game because you are waisting your talents.

A more realistic win rate would be 1BB per hour. This takes around a thousand hours of play to dial in though. On one on-line 5/10 HE game my win rate has a 95% chance of being anywhere between $6 to 37$ per hour and that is with around 400hrs play.

In reality, the my mean is proabaly less and my STD is more because my data is a bit old and the games have gotten tougher. My point is that you will need at least a year's worth of data to get some good statistics and then you might have to adjust those numbers to reflect how much the game and your skills have changed through time.

If you take many random samples of any distribution the "central limit theorem" will take effect, and you will see a normal distribution so Z scores will work.

Chris V

[RacersEdge]

The CLT says normality of the sampled data no matter what the underlying data distribution. The more non-symmetric, the more points needed to get a normal looking curve. I'm calling the hourly rate the "raw data". I was interested in that distribution. I don't think even 40 hands / hr makes it normal.

[Zeno]

The coefficient of variation is a measure of relative dispersion and is used more to measure the variability or diversity between two different data sets. In relation to poker it would have more validity if used for comparison between different games to calculate a ‘dispersion value’ for a comparasion - say between 20/40 holdem and 20/40 stud. I don’t see that it has much value beyond the usual calculated STD within a single data set for a particular game unless, perhaps, you have a tremendous amount of data. Further, how would you apply the number derived, would the value really have a meaningful application to your game? Am I wrong in any of the above assumptions? If so, please explain. Thanks.

-Zeno

[Chris Villalobos]

Well, I have actually made a histogram of my win rate per hour for over a hundred samples just to see if it was normal. It was pretty normal though it did have some flyers out at the end of the positive side. I have a bad habit of staying too long when losing and jumping out of a game after a big win so my sampling has some problems. That being said, the histogram definately wasn't bi-modal. So I don't think we have to move away from Z scores. I just use 3 standard deviations on everything. I haven't got ruined yet (knock on wood).

Chris Villalobos