Quote:
Originally Posted by IsaacAsimov
Now what if the top 100 winners are all winning at 8bb/100 and have played between 100-170k hands? Is that "absolutely meaningless"?
The math shows that this would be more than meaningless, assuming there are at least 5,000 regs. It would be meaningful if, for example, there were 1,000 regs or less. Here is the math:
Let's take a player whose "true winrate" is 0bb/100, that is breakeven. What are the chances for him being a 4 ptbb/100 winner over 160k hands?
Assume a usual standard deviation, for PLO, of 80ptbb/100. This translates into a standard deviation of 3200ptbb over 160k hands. (To get this, we compute 80*sqrt(160000/100).)
A winrate of 4ptbb/100 translates into 6400ptbb over 160k hands. So two standard deviations.
The chance of a random variable to be at least two standard deviations above its mean is around 2.2%. (This assumes the random variable is normal, but you'll get similar results for other well-behaved random variables, and besides, the winrate over a large number of hands should be approximately random due to the law of large numbers.)
Therefore, if we know that the number of regs is at least 5,000, then it wouldn't at all be surprising if the luckiest 100 of them are winning at least 4ptbb/100 over 160k hands. If the number of regs is, say, 500, then the existence of a hundred players winning at 4ptbb/100 over 160k hands would indeed be surprising.
If you give me relevant numbers to check I can do similar analysis for them.
Edit: by the way, it appears to me like there are few people involved in the discussions here with solid professional background in statistics (I mean Masters-level or higher). No offense meant: obviously this is something one has to learn. I think such background is really important for the purpose of discussions with pokerstars, as well as to understand for ourselves what the data actually means. I think the topic needs a dedicated statistician. But if no one steps up, I have some relevant background (Ph.D. in math) and would love to lend a hand. I'll be available in this thread and in PMs, and when the player reps get selected for the pokerstars meeting, I'll contact them directly to ask if they want some one-on-one discussions about statistics of poker vis-a-vis rake. My offer is standing to just about anyone interested.
Last edited by eldodo42; 03-29-2013 at 06:12 PM.