That's the argument from A Random Walk for index funds: even if such skills exist, they're indistinguishable from luck, therefore one can't make an informed choice of active fund.

It's impossible to perfectly distinguish them. Anyone that seemed to be skillful could just be incredibly lucky.

But you can get determine a likelihood that they are lucky by monitoring their performance over a long time / lot of games. It's just that if you are evaluating a whole lot of people looking for a rare skillful person, you need a whole lot more time/games to be sure they aren't lucky than if you just had one person to evaluate.

You cut that sentence short...

"How do you distinguish between pure luck, actual skills, and illegal manipulation?"

I believe his point is that you can't, because "actual skills" need not exist. It might ALL be luck, and outliers will exist. And, their existence doesn't prove anything about luck or the lack of it.

Conversely, if the difference between luck and skill is unknowable, everyone who wins might be skillful. As you said, the existence of winners is not revelatory about the existence of skill.

Related: one can be highly skilled and still lose to someone who is highly lucky.

You should see that your candidates will falter as time passes.

Suppose there are 10 funds with the track record of RenTech. In 10 years, you wouldn't expect them all to be as stellar.

You do more MATHS :D

There are models to model the risks and the potential outcomes.