DERB

[elindauer]

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With an SD of 30BB/100 hands ... interval is 2.8BB/100 at a 99.7% confidence... So the math tells us that he is likely a winner... it'll take more than some bad beat stories and a few hand histories before I'll write DERB of as a fluke.

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Hi rigolleto,

Your math is off here, but it's subtle why it's wrong. The problem is the way you've selected the "random variable" to analyze.

Basically, there are hundreds, maybe thousands of guys with stats like DERB. All of these random variables have been sampled over and over, and then the very best performing one has been chosen and singled out. There is a huge selection bias here, so that it is extremely likely that DERB is in fact way on the high side of the variance. Since the confidence interval calculation you are making assumes it's equally likely he is on the high side as on the low side, it's invalid.

To give you a clearer picture, imagine you flipped a large number of pennies ten thousand times each. You record the results. Then you pick out the penny that came up heads most often and run a confidence interval analysis on it. You'll find that this analysis suggests it's extremely likely that this penny comes up heads more often than tails. Maybe it'll suggest that this penny is 99.7% likely to be weighted toward heads, to not be a fair coin. Obviously, this is not the case.

To make another analogy, it would be like taking any random bad player, and then throwing out 10% of the hands in which he did the worst. Oh look, he's a huge winner now. Yeah, of course.

In light of this, anecdotal evidence suggesting that DERB is bad is all you should need to be confident he is not a winner and is simply the luckiest player at party. This sounds unlikely until you remember how we chose this guy... we searched the database for the most ridiculous stats / win combination. Of course, this is likely to correspond to the luckiest guy.

To get a better idea of how DERB's true win rate, lump all the players with similar stats to his together and run a confidence interval analysis on the results. To get an even better idea, track his NEXT 100,000 hands or whatever, now that you've singled him out and do a confidence interval analysis on those hands. That's his true win rate.


Good luck.
Eric