If you switched projects four times, I can only assume that the last company, the one that YC accepted, has the most potential... otherwise, you would have continued working on the other projects.
I think it's way more than serendipity. I think the YC staff is extremely good at identifying where good teams and good products meet.
This was over a series of years. There are lots of reasons why we stopped working on the different projects, but I'm not sure I believe there was any less potential in them - especially Prospector.
While I agree that they've gotten very good at identifying potential good team/product pairings, that just means they have relatively few false positives. It makes no claim to how many people they pass over who may in fact have an amazing team and product. As the noise in the process increases, you're bound to end up with more and more people who for completely random reasons didn't end up being what they wanted that day. This isn't a purely objective process (thank goodness).
All other things being equal, anything that relies on the judgement of a few people has an element of serendipity to it.
I think Prospector sounds very interesting, even only from a three word description. I know three friends running startups in the healthcare market and it's a tough one (with a lot of entrenched interests).
"All other things being equal, anything that relies on the judgement of a few people has an element of serendipity to it."
Also recall that the judgement is made on the basis of a 10minute interview. Ask any of these startups if they'd ever hire a group of strangers into their company based on a 10 minute interview. (I'm aware that's not really a fair comparison, but it should still make people think).
"When we realized that multiple YC partners had already independently contributed to the Kickstarter project because they wanted to use Light Table themselves, it was not a hard decision." --thread: http://news.ycombinator.com/item?id=3992343