[throwawaymsft]

I'm not sure I understand. Buffett has a strategy X, which has defeated strategy Y (buy a market index fund) 39/47 times.

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).

[lutusp]

You're missing the point. What is the probability that someone flipping a fair coin will flip 20 heads in an unbroken sequence? The answer is 2^-20 = about 9.5 * 10^-7.

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.

[Thrymr]

The question is, how many potential Warren Buffets were there in the pool to start with? You can't ask the question "what are the chances that this particular outcome would happen?" with a sample of one, you have to use the population it is drawn from. Otherwise it would be like saying "That's amazing! The lottery numbers today were 56 23 45 12 27 91! What are the chances!" Exactly the same as any other combination (very, very low). The trick is picking them in advance.

[zeckalpha]

While the probability of any individual defeating the market is 0.5 in any given year, the probability of someone from the pool of N investors getting beating the market 39/47 years is N * 0.5 ^ 47. (It's been a while since I've done probability, so correct me if I'm wrong.)

[lutusp]

> the probability of someone from the pool of N investors getting beating the market 39/47 years is N * 0.5 ^ 47.

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.

[magnusjonsson]

(47 choose 39) * 0.5 ^ 39 * 0.5^8 = 0.0000022, so that'd be about 1 in 500000 of all who traded for this long.