It's a completely different matter.
As far as I know analysts are doing their analysis when pricing stocks.
They may not be so good or discount all the factors, but analysing the products of some companies, their revenues, returns and other parameters seems extremely different than flipping coins to me.
So your analysis has no whatsoever basis given that you are comparing a completely random outcome of some well known physical action to a chaotic system (the market) in which at least the basics influence factors on his constituents are well understood.
Or are you suggesting for example that warren buffet is just being lucky for endless decades and you and everyone else know at least how to equate his performance?
If is that what you think then please, I would be rather amused to see your performance as an investor compared to him in the course of several decades.
Well, see, that's the whole deal, investigating _how_ different it is than flipping coins. That's the whole question, really. Starting with the assumption that they _must_ be doing better than chance is not the right place to start in order to analyze if they are or not.
Most statistical analysis is about trying to distinguish meaningful results (implying a repeatable correlation of some kind that means something), from random chance with no meaning. The whole point is you _don't_ start out knowing if the thing you are investigating is random chance or not, if you did, you wouldn't need to analyze it. That's what statistical analysis is for. In part because we humans are really really good at finding patterns and assuming a meaningful correlation when in fact it's just random chance.
The coin example is useful because we all know (or define for the sake of the discussion) that it must be random chance, so any analysis that appeared to say it wasn't is probably in error. And using the same sort of analysis on something where you don't know how much of the effect is due to random chance--is not going to answer the question.
I mention him because apparently for the parent message he is only a coin thrower and he will give us only insights on the percentage of people that can get 10 heads in a row.
If someone tried to use Buffet as an example of market beating but did zero statistical analysis to determine how likely it is to be actual skill they would also deserve to be dismissed.