I'm unfortunately not as well versed as I'd like to be on statistics, but this comment made me think of something I read... I believe it was in the book "Fooled By Randomness" by Nassim Taleb (I could be wrong since I read quite a number of books on this subject), where he states that someone like Warren Buffet is still statistically possible within the realm of chance given how many managers there are. Now of course Buffet does seem to use good methedology (buy low, sell high,etc), but it still struck me as interesting that you can often make data say what you want.
Now I'm not sure if a day trader, given that he puts on thousands of trades within a year could be so lucky over the long run (Buffet for example puts on many less trades), so I'm sure there is a certain number of trades beyond which it would be possible to still be a winner less than 0.00001% of the time if by chance and not an edge, even with the huge number of day traders out there, but this idea of the statistical nature jumped into my head when I read your comment.