Quote:
Originally Posted by Josem
BF,
You make a fair point, although I suspect any such visual effect will be pretty marginal, since those areas are already very dense.
That said, of the 870 plotted points, 710 - the vast majority - are of under 7,000 hands, and 334 are between 2,500 and 3,500 hands.
If we reduce the sample size to the 334 players with 2,500 to 3,500 hands recorded, the mean bb/100 becomes .52 and the standard deviation is 17.12 - leaving the alleged cheater out at almost 9 standard deviations above the mean.
9 standard deviations is something in the order of 1 in 1,000,000,000,000,000,000 - or winning three consecutive 1-in-a-million events.
Of course, if anyone has any hand histories to help improve the sample size, feel free to email them to me at michael@michaeljosem.com
edit:
p.s. i understand that there are another 5k hands with the alleged cheater winning at the same rate. this would suggest that it is reasonable to include all the players that i have data for.
Josem, the graph is a good idea but it is extremely misleading, and it would be premature for people to start throwing around numbers like nine or ten standard deviations above the mean.
This scatterplot doesn't mean anything for (at least) two reasons. First, there are few samples with very high VPIPs like NioNio. These will have by far the most widely varying results that are much less likely for the cluster of sane, "normal" players. Second, there's an enormous selection bias at work: if this guy wasn't cheating he was the maniac who got struck by lightning; no one makes threads like this when the crazies lose.
I'm sorry to dump on your graph but drawing meaningful statistical conclusions about this player's luck is very tricky and needs to be done by someone well-versed in this kind of analysis. (I certainly don't feel I have the background to do this.)
My ideas for improving the scatterplot would be as follows.
-First, get every hand possible on NioNio.
-Obtain a (large) sample of data on players with vaguely similar styles, VPIP, aggression, etc. at similar stakes to get an idea of their lossrates and standard deviations. This will give you a poor approximation of the sample pool from which this guy would have been drawn were he not cheating.
-Simulate a bunch of 3k hand random walks using the average maniac lossrate and NioNio's observed standard deviation. These represent NioNios in alternate universes, so to speak.
-Now scatterplot and observe how much of an outlier NioNio is.
Ideally, you would repeat this for a range of lossrates to see how robust the conclusions are. The likelihood of extreme results may be extremely sensitive to small changes in parameters.
This is just a start and I'm sure people with better stat and programming backgrounds would be able to do better.