As quid pointed out, it's impossible to accept an answer where none exists. So the issue should be separated into two:
- Percentage of questions that get at least one answer
- Percentage of questions with at least one answer, where an answer gets accepted.
It't not necessary to write queries for this, the site search gives the same information (with the help of search parameters). E.g., one can look at the posts that are 3 months old with created:3m
, or at all posts in 2015 with created:2015
.
I'll take created:3m
so that the very recent posts, many of which are on their way to deletion, do not distort the picture.
So, more than half of questions with an answer have an accepted answer.
For year-to-year comparison, the numbers from 15 months ago:
It's remarkable how similar the numbers are, except for the first one. A major factor here is that abandoned questions (0 score, 0 answers, 0-1 comments, low views) are automatically deleted after a year. Presumably, this is also the fate of many of the 16,233 questions created 3 months ago.
More generally, I don't see a reason to ever worry about acceptance. The question author probably posted the same question on five sites, got an answer on three, of which they read one (not the one on Math.SE), and went on about their life. If other users care about the answer, they'll upvote.
If nobody cares about the answer... you still had fun writing it, haven't you? If it isn't fun any more, stop doing it.