Of course there is a rigorous way to prove that with larger sample sizes the sample statistic converges to the population statistic, if you pick the mean then the average value of a sample set will converge to its expected value over larger and larger sample sizes. Take a look at the concept of the law of large numbers: http://en.wikipedia.org/wiki/Law_of_large_numbers

The proof is on the same page and directly relates to your problem.

By the way, I concur with Nassim Taleb on this one (though I disagree with his style of trading and some of his opinions on options trading). George Soros has proven many more times than Buffet that his investment and trading skills are highly skilled and that his returns were not the outcome by mere luck. Its that most people only know about his BOE play but hardly anything else. Buffet in turn has done a lot bigger deals but fewer in between, simply because his investment style is much more longer term oriented than Soros's.