This was our experience during the YC interview as well. Since we had an end of day slot, most of the partners were yawning as we walked in :/
Agree on Startup School - amazing resource for us that we keep revisiting
https://www.wired.com/2011/04/judges-mental-fatigue/
Does YC has stats about acceptance vs the time of the interview? That would be interesting.
There are tons of great applicants to YC, moroever, as you hint, it's going to be pretty hard to really evaluate these entities on a case by case basis.
Though I've never been on the finance side of days-long pitches, I have however done this for hiring, and I always felt bad in those situations wherein I was very tired and had some smart people in front of me, and I had to make a decision that was barely going to affect my life, but would definitely affect theirs quite dramatically; and one has very little information to go off of.
It's inherently noisy channel.
Just do your thing, and try not to worry about it.
I'll bet that anyone who makes it to any stage of interviewing has pretty good chops on some level.
(Easier said than done of course)
I don't think you can expect to be completely objective/unbiased in this kind of situation...
For an example of why: my startup was initially rejected from Startup School, then accidentally accepted, and then we kicked butt and won the YC Startup School Grant out of 10,000+ startups. Then we got a YC interview and were rejected for what (I think objectively) was a pretty random reason. And I understand that the stated reason isn't necessarily the full reason.
It was still a very enjoyable and super helpful experience overall. The advice, $10k cash, and cloud credits have helped tremendously and it's still helping a lot.
I just wish I could have competed against other startups for acceptance into the core YC program, rather than have a few people attempt to judge how much of an "animal" I am in 10 minutes as they groggily try to wake themselves up with coffee. Not a knock against them at all (still a very long-term PB fan!), just the process.
Because I know I'm much better at competing with hard sustained effort over the long-term than I am at seeming super impressive on first impression.
Anyway, that's my suggestion.
We will hopefully be ramen profitable soon, and may not try for YC again because it is mentally exhausting. But whatever we do, Startup School was a huge boost for us and YC asked nothing in return, so thank you very, very much.