With the Data Explorer you can find the answers you are looking for. The caveat is that it requires some SQL and digging around in the data.
I did something like that and posted about it on my blog. I do think this is a pretty important thing to track for more mature communities. Here’s a query I used to see how many people remained engaged a month after they joined:
select
to_char(date_trunc('month', u.created_at), 'YYYY Mon') "Join Date",
cast(sum(case
when first_post_created_at-u.created_at <= interval '30 days'
then 1.0
else 0.0
end) /count(*) as float) "Contribution Rate"
from users u
join user_stats s
on u.id = s.user_id
where u.created_at > '2004-10-01T00:00:00.000Z'
group by date_trunc('month', u.created_at)
order by date_trunc('month', u.created_at)
This was useful to look at for College Confidential because it has very obvious cyclical patterns: High school seniors start thinking about applications in November, get decisions by March and forget about the application process over the summer. Not every community will have that sort of regularity.
One word of warning: I have found myself wrapped up in the data so much I miss obvious things I could have learned just by looking around the site. Having objective data helps verify or refute subjective observations. It can be dangerous to make decisions from data without context. (Maybe more talking to myself than you!)