As in startup investing generally, the expected value comes mainly from a small chance of a big hit, multiplied by lots of investments. You're hoping that if you invest in 100 startups, one will be a Dropbox or Airbnb.
For this to work, you have to (a) invest in a lot of startups and (b) they have to be drawn from a pool that could include big winners.
The latter could actually be a problem, if you're not founders' first choice. If you lose the big winners, your returns might be orders of magnitude smaller, even if you get everyone else.
Yes, you do have to invest for years before you end up in the black, even if things go well. That's also true for startup investing generally.
When we started YC, the returns seemed completely unpredictable. (They still do actually.) What allowed us to do it was that we didn't care if we made money.