Another question asks about opting out of the Hot Network Questions list for a few months to see if that's better or worse for us (or ends up not mattering). See the other (unresolved!) question for details on that.
If we decide to try the experiment, we'll need a basis for evaluating the results that's better than everybody's subjective gut feelings. What factors should we measure? Assume we'd collect before-and-after stats, seasonally adjusted or year-over-year.
The following methods of collecting information are available to us:
Public on-site information: close/reopen stats, advanced search, site anlytics, etc.
Stack Exchange Data Explorer (SEDE): SEDE doesn't have everything, but it has a lot. Think about SQL queries that would be useful.
On-site moderator tools: search of deleted posts, total flags (but no breakdowns), number of deleted comments (but not reasons), maybe other stuff. The flag and comment stats are crude; at any given time we can see totals for the last month, quarter, or year, but we can't get those stats for specific date ranges.
Things that require database access: in the past, CMs have sometimes been willing to query the live database directly for information not exposed through the UI. We might be able to get a breakdown of flag types in a date range, for example.
Some feel that having our questions on the HNQ list is harmful for us. What is "harmful" and how do we measure it? And what is beneficial about being on it and how do we measure that?