In four of the last five calendar years, [Warren Buffett] has underperformed his own benchmark, the S.&P. 500 with dividends, often by significant margins. (In 2011, his return of 4.6 percent beat the benchmark by 2.6 percentage points.) In addition, data provided by Morningstar shows that he underperformed the average stock mutual fund investor in four of the five years.)

By contrast, in the previous decades, he had underperformed the S.&P. only six times.

Mr. Mehta said his calculations showed that given such a long period of outperformance, there is only a 3 percent chance that the recent stretch of underperformance was a matter of bad luck.[emphasis added]

You don’t need to know anything about finance, Warren Buffett, or Mr. Mehta’s calculations to be able to sniff this out as total nonsense. How? Because there is absolutely no way that this writer for the NY Times, or any other mortal, could know the *a priori *probability that some force other than luck has started affecting Warren Buffett’s work roughly 5 yrs ago, in such a way that would cause his performance to change in the way that it has. And you’d have to know this in order to make the quoted claim.

More simply: in many cases you can be almost certain that a statement is bogus when it takes the form “based on this evidence, there is an x% probability that some force other than luck is involved.” The exceptions are cases where, prior to seeing the new evidence, you would have been able to say a) what the probability of some cause other than luck being involved (this is often very difficult) and b) what the probability of observing the new evidence would be, given that cause.

Very interesting comment. Most of these NYT people are idiots.

If erroneous math-related info is getting into the NYT, it’s sort of your fault. One of the main jobs of this blog has been to keep the NYT line, but you stopped cracking the whip for a couple of years. What did you expect would happen?

I think the claim is that under the assumption that nothing else has changed (i.e. warren is making his performance goals with the same probability as before) That the chance of getting this bad a streak is 3%. Mr Mehta seems to be acting as a frequentist and thus rejecting the null hypothesis that nothing has changed. All sorts of things to be said about frequentists vs bayesians but I don’t think that’s a super incoherent thing to say.

Jonathan Kariv – i don’t understand your interpretation. To reject the null hypothesis would be to say “assuming there was only ‘luck’ at play, the probability is <[5%] that Buffett would underperform as he has". Rejecting the null hypothesis would NOT imply "there is only a 3% (or <[5%]) probability that luck is involved, given that Bufett has underperformed."

I agree you can make the former claim (assuming you have done the analysis to back it up), but this NYTimes writer clearly makest he latter claim.

I’m interpreting it as him doing the hypothesis test calculation mechanically and then either not understanding what the calculation means or messing up the wording of what he wants to say very badly.

which isn’t what came forth in my original comment. sorry about that. just looking for an interpretation which made some sort of sense. this might not have been the way to go

“I’m interpreting it as him doing the hypothesis test calculation mechanically and then either not understanding what the calculation means or messing up the wording of what he wants to say very badly.”

totally agree.

i do think that this is a bit more than just “randomly” messing up in the sense that it is a lot more satisfying to say “there is an X% chance that what just happened was luck” than to say “assuming just luck, there is an X% chance of observing what we have just observed.” Unfortunately the former claim is much much harder to back up. Hence people [e.g. this NYTimes writer] may be drawn toward the former claim, in error.

Yeah it’s a somewhat common problem. 1:20-1:30 of this https://www.youtube.com/watch?v=bVMVGHkt2cg makes me feel slightly better about it.

Finally i quit my day job, now i earn a lot of money

on-line you should try too, just search in google – bluehand roulette system

I see you share interesting stuff here, you can earn some additional cash,

your blog has big potential, for the monetizing

method, just type in google – K2 advices how to

monetize a website