1) The number of attempts from startups to go after a fairly well-defined idea (more specific than general). A high number of attempts indicates a problem is unsolved. A low number indicates unexplored terrain.
Ideally I'd also like to know a bit more, like the most common angles attempted (in general terms, not specific), although I can imagine how this might be disclosing people's ideas. Example: x% of attempts at idea A going after the high end failed, but y% of going after the low end survived and morphed or expanded to something else that has potential.
2) Which areas have the most statistically significant change in number of applications since the previous funding cycle. e.g. Developer Tools vs Developing Countries. Because it could point to upward and downward trends.
Ideally I'd also like to know about ideas in general too.
3) The top 3 questions on the YC application that startups answer most poorly.
4) The top 3 questions startups that are accepted and/or do well answer the best.
5) The biggest mistakes you see in applications and how they can be avoided (if they can.) Or the most common things missing.
6) The most convincing arguments you see in applications, and how they're made (e.g. by providing numbers and percentages, rather than saying "we're growing a lot".) Example: "if X is true, then Y" is more convincing than "I know Y will work", because you show that at least you're aware of X and are digging into it.
7) What most applications think will never work for a fairly well-defined idea, because it's such a good source of new ideas. But only if it's safe to assume the startup that applied won't pursue it, as to not run into confidentiality issues.
This can be information in the aggregate. e.g. show the top 2 things most applications think will never work, which could account for 80% of the applications, but don't show the outlier 20% which may be a good idea. In other words, provide corrective information, but don't provide what might be the answer.
8) If there's a positive or negative correlation between confidence in the idea and being selected or doing well. Ideally, I'd like to know if I'm writing my application in a way that suggests I have no idea what I'm talking about. But only if you believe providing this will help the startups and the application process.
9) Which parts of the application process that founders often think look like negatives turn out to actually be positives. So startups don't get discouraged.
10) To the extent each question on the application is scored and the score can be useful if it's communicated back to the startup, provide the score back to the startup.
Ideally, do this fast enough so the startup can rethink its answers. e.g. in cases where the startup had better info to supply but didn't, or if you believe it would help.