They could do things other money managers couldn't - short stocks (i.e. hedging against a fall, hence their names), better analysts, investments in more diversified instruments, early HFT.
They would often take a fee of two and twenty - that is to say 2% of the money you lent them (every year), plus 20% of the profit they made from that money.
If you gave them $10 million, they'd take $200k as a fee every year, then 20% of the profit they made. So let's say they made you $1 mill a year, they'd be paid in the first year $200k fees and $200k performance fees.
However nowadays there's millions of them, and almost all of them lose money as there weren't that many profitable niches to begin with, and a lot of them were lucky anyway (survivorship bias).
Of course any reported results on hedge fund returns are kinda funky for the reason of bias that you mention.
Survivorship bias is huge in this industry. There have been plenty of funds with awesome runs, but few have lasted 20+ years.
PS: The financial industry also loves to point at old funds as being above average while quietly killing off lot's of tiny funds and growing others over time. IMO, this goes past survivorship bias and into the old con where you mail 1024 people the results of a game, then 512 people you got right, then 256... Until you have great history with your last sucker.
There are hundreds of strategies in hedgefunds from HFT to Macro to volatility trading to commercial ground rents to God Knows What™ - so I'd really like to see what was being done for this kind of analysis (and who by and what data they had access to).
Past performance is a lot like the false positive problem in medical testing. A 99% correct test on a condition affecting 1% of the population is not useful. Similarly looking at past performance for a hedge fund is a poor way of identifying those with "alpha" (if you believe true alpha exists at all, which is entirely dependent on your point of view).
Take Mr Buffet as a spurious example. If he leaves the fund, it won't affect past performance for some time. So do you want to buy into B-H without him - just because it used to make money? Or would you go into his new fund because you think he has a process that works.
I watched a documentary recently that suggested that they gain % for every X period they add value (over risk-free rate?), but don't pay back any % for losses they make? This the situation?