I just think he spends too much time rhetorically splitting hairs. . . . "Most child prodigies are highly successful—but most highly successful people weren't child prodigies."
This is absolutely not splitting hairs. This is an important point about statistics that people generally have poor intuitions about. Put very generally, the probability of A given B can be very different from the probability of B given A, yet people treat them as equivalent.
Here is a cartoon that may help. In the cartoon the "frequentist statistician" is calculating the probability that the machine says the sun exploded (A), if in fact the sun didn't (B); but he is
using this as a proxy for the probability that the sun didn't explode (B) if the machine says it did (A). Which does not follow at all, leading the Bayesian statistician to bet money that the sun hasn't exploded.
Returning to the case in the article: What are the chances that a child prodigy (B) will go on to do great things (A)? Pretty high. What are the chances that the next Great Thing Doer (A) was a child prodigy (B)? Not the same thing.
Let's run some numbers. Just for the sake of argument, let's say a child prodigy who goes into the field of physics has a 1 in 100 chance of winning a Nobel prize (we'll use that as our stand-in for greatness). And let's say that the chances for a non-prodigy physicist are a paltry 1 in 10,000.* Now, when this year's Nobel prize for physics is announced, will you bet on that person having been a child prodigy, or not having been a child prodigy? If you choose "prodigy,"
you are going to be wrong 99% of the time. This type of error is called "ignoring base rates."
*These numbers are completely made up for the sake of argument. The point is about the intuitions that follow from them.
