Investing being random chance doesn't mean everyone will do about average. It means that some people will make quite a bit of money and some people will lose quite a bit of money. It just happens that Warren Buffet is an outlier.
We can say any return in strategy X is
1) Due to random chance (i.e., it defeated the market 39 times "randomly") 2) Not due to random chance, and there is an inherent advantage
I'm saying the probability of 1) is sufficiently low so as to believe 2).
Next question. How many people need to be flipping coins for one of them to have a better than even chance to flip 20 heads in a row? Answer: about 3/4 million.
Next question. How many investors are there in the world? Answer: many more than 3/4 million.
Next question. If someone among millions of investors makes 20 successful market picks in an unbroken sequence, what's the probability that he will attribute that outcome to blind chance, and what is the probability he will start selling a book titled "Secrets of the Winners" on late night TV?
My point? When confronted by an unexplained occurrence, it's wise to consider the possibility that it's a random outcome. This is called the "null hypothesis" and it's the first possibility a scientist considers.
No, that's wrong. If the original performance had been an unbroken sequence of successful years, say, 39, it would be possible to apply the binomial theorem to it, but the binomial theorem would need to be applied both to the original probability and to the calculation of how many investors would be needed to create a better-than-even prospect of that outcome.
But the 39 successful years were randomly distributed among years where the performance wasn't better than market indices, which makes the probability much higher for it being explainable by chance -- how much higher depends on the actual pattern, which I wasn't able to find.