Closing questions is a pretty important part of site moderation, and one of the aspects that a new site needs to figure out to be successful.
Getting useful statistics about closing is pretty much impossible because closed questions are automatically deleted in many cases. But those statistics could be helpful especially for new sites to spot problematic trends or support meta discussions.
The statistics I'm thinking of are the following:
Percentage of new questions closed. This should be available as a graph over time in the moderator analytics. This probably needs to exclude the newest questions and only start calculating the percentage after the questions had a chance to be closed.
Percentage of new questions closed by moderators alone or average number of close voters per closed question. This would help to see how well the community manages to close, and how much the moderators still have to intervene.
Number of times the custom close reasons are used. This would help to distinguish the useful custom close reasons from the ones that could be removed or replaced by something more useful.
A list of questions, deleted or not, closed with a specific custom close reason. This would be useful to investigate how a specific close reason is used in practice.
The easiest place to put those statistics would be the moderator-only analytics, but they could also be made public.