In the sidebar of SU there are various stats on the different pages about Questions - questions without answers, count of questions.
According to this the time to answer a question monthly average is around a day.
If I am a new user, coming to SU and haven't found an answer to my question, I have to make a decision about whether I should go to the trouble of creating an account and asking a question, or I should keep searching and perhaps ask elsewhere.
So putting the average time to answer as a statistic in the sidebar might help a new visitor make the decision to stick around. In chat, the main objection raised was that this might set an expectation for a quick answer to a low quality question.
This could be mitigated by having a text link that directs people the "how to ask a good question" section of help. "What kinds of questions get answered quickly?" for example.
Let Me Paint You a Picture
The Unknown User arrives at SU. They have the best question in the world. They have the type of question that once answered will help people for generations. It is the type of question that will get Ramhound salivating at the opus he might write in response. But we don't know what the question is, because they haven't asked it yet.
"Is this for me?" they think, as they look at the home page. "Wow, 300,000 questions asked, lots happens here". So they proceed to click around.
"Oh look, unanswered questions. Hmm, nearly 100,000 unanswered questions. So one in three questions does not get answered. Perhaps the site is in decay. Perhaps they can only answer questions about topics other than my question. Perhaps I will look for an alternative resource that focuses on my specific topic."
And the Unknown User departs, and takes with them the best question ever to be asked.
My first thought when considering this is, perhaps an indication of activity would be better than an indication of inactivity. So perhaps an average time to an answer might tell the Unknown User to not go elsewhere, that here is the place for their extraordinary question.
It doesn't have to be average time to answer. Or median or mode. It could be anything. Numbers can tell a story very quickly, which is why the site is peppered with them.
So let me rephrase this question - what kind of statistic do you think would be the most compelling for the Unknown User to invest their time in asking their incredible question at SU rather than elsewhere?
Here I am trying to shift the consideration away from those users that will ask crappy questions and demand fast answers. We will deal with those like we always do. They will come no matter what.
I am trying to fix your attention on those that have the brilliant questions, and I am asking if a question count and an unanswered question count are the ideal metrics to show these amazing question holders to send the message that this is the best place for their question.