Are Winrates Normally Distributed?

[sthief09]

BIG thanks to Justin A for coming to me about this. He was the one who first noticed it and most of this was his idea. I had some free time last month on my flight to Vegas so I did most of the tedious Excel stuff.

Also, Barron, I know this doesn't have anything to do with high stakes poker, but I feel that it is an interesting topic that many posters will be interested in. If you don't agree, please move it to MHHUSH.

I am not a statistician but based on my not-quite-intermediate understanding of statistics, this is what I've come up with.

Methodology: I took a database of about 150k hands at one limit. I took these hands and put them into Excel. I chopped them up into blocks of hands (in chronological order) and plotted them in a histogram.

Theory: BB/100 is the average BB you will win every 100 hands. If you've played a large enough sample of hands (technically 50 samples should be enough, so 5,000 hands), the sample should behave normally and form the shape of a bell curve.

Results: The following graphs are of BB/25, BB/50, BB/100, etc. Notice that they are skewed toward the low end. This would suggest that winrates are not normally distributed, which would mean you are more likely to run good but the bad runs will be worse. I don't remember the exactly mean but figure it's somewhere between 2 and 2.5 BB/100. for BB/10 it would be between 20 and 25, etc.

Can someone with a better understanding of statistics explain this?