Question about Winrate

[Lmn55d]

Ok, if I have a winrate of 1.42BB/100 after 4000 hands, what would you guys say is the range of my true winrate. Like, is it possible that I'm a 3BB/100 player and just have a sample size that is too small?

[uuDevil]

You have to provide your standard deviation as well. But this is such a small sample I'd guess the answer is easily yes.

[pzhon]

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You have to provide your standard deviation as well. But this is such a small sample I'd guess the answer is easily yes.

[/ QUOTE ]
The standard deviation changes from player to player and game to game, but usually not by a huge amount.

Let's assume the standard deviation in 100 hands is 15. In 40x100 hands, the standard deviation of the win rate should be about 15/sqrt(40)~2.4. After 4000 hands, your true strength is very likely to be within 2 standard deviations, 1.4+-4.7 BB/100. That's not a very tight estimate. It is hard to conclude anything from only 4000 hands.

[jason1990]

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The standard deviation changes from player to player and game to game, but usually not by a huge amount.

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If we're talking about "good" players, I would probably agree. But a weak-tight player, or a LAG, or perhaps anyone with a true winrate that is negative, could likely have a standard deviation that differs significantly from the "norm".

I just wanted to mention this because the OP might be trying to decide if he's a "good" player. And, it seems to me, the assumption of a 15BB/100 SD presupposes this fact to some degree.

[Lmn55d]

how do I find out my standard deviation?

[uuDevil]

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how do I find out my standard deviation?

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If you have PokerTracker, it's under
"Session Notes" tab -> "More Detail..." button

[Lmn55d]

ah cool. So say I know my current winrate after a small sample size of hands and my standard deviation. How can I find out the range of my true winrate?

[ode]

How much is large enough sample size to draw a conclusion on if you are or aren't a winning player at a certain limit (on let's say 97% certainty).

Is it 50k+ hands, 100k+ hands?

I currently have 29,138 hands of $2/4, BB/100 of 3.52, SD/100 of 15.2394.

I'm pretty certain I'm a winner, since I've been playing and winning for quite a long time. Those are just since I recently started logging with PT.

But so, how much is enough when speaking of sample size?

/ode

[uuDevil]

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ah cool. So say I know my current winrate after a small sample size of hands and my standard deviation. How can I find out the range of my true winrate?

[/ QUOTE ]

pzhon showed the idea above.

The interval

WR +/- 2*SE

will include your true win rate with 95.4% confidence, where SE= SD/sqrt(N), SD and WR are in BB/100, and N= #hands (in hundreds)

The factor 2 can be varied depending on the desired confidence:

1 -> 68% confidence
1.96 -> 95% confidence
3 -> 99.7% confidence

The greater the desired confidence, the wider the interval.

[uuDevil]

[ QUOTE ]
How much is large enough sample size to draw a conclusion on if you are or aren't a winning player at a certain limit (on let's say 97% certainty).

Is it 50k+ hands, 100k+ hands?


[/ QUOTE ]

Whether or not you are a winning player depends on WR, SD, and N (#hands). Calculate the quantity

WR/(SD/sqrt(N))

This is the distance from breakeven in # of SD. For >= 97% confidence, this quantity >= 2.17.

[ QUOTE ]

I currently have 29,138 hands of $2/4, BB/100 of 3.52, SD/100 of 15.2394.

I'm pretty certain I'm a winner, since I've been playing and winning for quite a long time. Those are just since I recently started logging with PT.

But so, how much is enough when speaking of sample size?



[/ QUOTE ]

It's relative, but 3.52/(15.2/sqrt(291))=3.95 so you can be better than 99.9% confident you are a winning player.

[Lmn55d]

thanks dawg, thats pretty interesting. One last question...how exactly should you go about selecting a level of confidence? Why would one choose 68% rather than 99% or example?

[uuDevil]

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...how exactly should you go about selecting a level of confidence?

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It depends how big a lie you want to tell. /images/graemlins/smirk.gif

I'm not a statistician, so don't take this as gospel: It's somewhat subjective, and often dictated by convention. 50% and 95% are the most common levels I've seen. If you choose a very high level, it may make the interval ridiculously wide, e.g. "I have 99% confidence that I win between -4 BB and +5 BB/100". If you choose a very low level, you may narrow the range but still sound silly, e.g. "I have 1% confidence that I win between 3.0 and 3.1 BB/100."

[SparkyDog]

Is there an easy way to graph the upper and lower bounds of a winrate at various confidence intervals?

[uuDevil]

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Is there an easy way to graph the upper and lower bounds of a winrate at various confidence intervals?

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The simplest way I know is to use Excel or other spreadsheet. It would look something like this: link. (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1213573&page=&view=&s b=5&o=&vc=1)

[Lmn55d]

one more thing, what does SE stand for in that equation? Standard something?

[uuDevil]

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one more thing, what does SE stand for in that equation? Standard something?

[/ QUOTE ]

Standard Error (http://mathworld.wolfram.com/StandardError.html)