[elindauer]

Hi rigolleto,

Justin is right on here. Think more about what he's saying. I'll explain where your logic is off below.

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We're doing the same here with DERB. His stats were chosen because of the bizarre results, therefore we cannot use confidence intervals to figure out whether or not he is a winning player. I hope all that made sense.

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I have to disagree. Your objection would be true if we had say 1,000,000 hands with DERB and picked a 100K series out of them because this series was bizarre. But the fact that we chose to isolate all the hands where DERB was at the table doesn't bias HIS stats.

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You're right that we haven't biased DERB's stats, but we are biased in selecting DERB to begin with. If DERB were a losing player, the way so many players who play like him are losers, than we wouldn't be talking about him. He is only interesting because his results are so good. This is why and how he was chosen. It's not like we said, let's pull out a random guy with 30/18 stats and analyze his play... oh look, DERB. No, it's, let's look for a statistical anomaly among the thousands of players I've tracked... hey, check out this guy!

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You analogy is flawed because you are assuming that each player can be represented by the same coin. A more true analogy is to make 1000 cointosses with 1000 coins and the result is say 500,152/499,848. You record all tosses and what coin they where made with. Now you isolate your sample to a specific coin and find that the result for this coin is 611/389. You now have good reason to suspect that this particular coin is different from the others because the 1000 tosses with this coin can statistically be treated as a seperate event.

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This is only true if you choose the coin randomly. If you choose the coin precisely because it's the one with the most skewed stats, then you've biased the game and confidence intervals don't apply.

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Let me try my own analogy: let say we randomly sample 4000 people and ask them who they would vote for as president Andyfox or Ed Miller and the result came back 50/50. Now we pick a subset, say ages 18-30, and for this subset the result is 30/70. Just because we picked a subset it doesn't mean that the sample is not random anymore; it is a random sample within the universe of 18-30 year olds. Just as hands with DERB in them is a random sample within the universe of hands DERB participated in.

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Again, your reasoning is accurate if you chose 18-30 randomly, and not because the results in that age group were abnormal.

Finally, let's say you flip 1 coin lots of times. You expect that a confidence interval will have 50/50 as well within the expected value for the coin. However, if you repeat the experiment many many times, eventually you are going to find a coin that comes up 5 standard deviations out. This isn't surprising, it's expected, and it doesn't make it 98% likely that the one lucky coin is biased. It's just a function of the large number of random variables. To get a feel for how likely it is that we would find someone so many standard devs out, we need to find out how many players are in the database that this guy was taken from. I bet the answer is... LOTS.

Good luck.
Eric

PS. It's also interesting to note that the average player with a decent number of hands in a database like this is going to be on the high side of the variance. You don't see guys with DERB's stats that are monster losers simply because a losing player that goes on a big downswing is likely to just quit. So guys with small numbers of hands will tend to be on the low side of the variance, while guys with large numbers of hands will be on the high side. Does that means playing lots of hands makes you lucky? No. It's just a biased sample.