In the spirit of the thing and to provide some evidence around Ben Lee's answer I'm answering my own question - maybe get a badge :-).
Looking at the number of self-answered, unclosed, questions over time it actually seems quite high; very roughly around 10% of the total:
Year Quarter Questions Self-answers Q positive A positive
---- ------- --------- ------------ ---------- ----------
2008 3 18110 3743 3332 2264
2008 4 39802 6125 5063 3489
2009 1 54446 6556 5001 3741
2009 2 76326 7864 5460 4366
2009 3 99633 10329 6757 5414
2009 4 114279 11806 7014 5540
2010 1 144109 15151 9907 6944
2010 2 160336 17184 10380 7619
2010 3 188286 19679 11383 8418
2010 4 206172 20742 11607 8820
2011 1 268050 25260 13796 10694
2011 2 298260 24505 13736 10063
2011 3 312311 26820 14294 10421
2011 4 316651 27854 14287 10546
2012 1 405211 33204 15742 11475
2012 2 431504 37818 16350 12100
2012 3 452622 43812 16901 11678
2012 4 461240 43526 16874 9145
2013 1 23733 1564 545 290
However, the number of self-answered questions with a positive question/answer score is significantly lower, which would seem to indicate that Ben's answer is correct. A large proportion of self-answers could be lost to badge chasing.
As 2012 is the most recent complete year, and therefore the most representitive of the future I'm going to concentrate on that. There are 158,360 self-answered, unclosed, questions in that year. This number will be slightly skewed because some will be closed in the future but I'm going to ignore that for the time being.
Taking into account the rules around automatically deleted questions 12,037 of these self-answers are actively preventing a question from being deleted, not necessarily a bad thing. However, if we change the rules slightly to something that makes slightly more sense in this context and ignoring the comment restriction:
If the question is more than 30 days old, and ...
- has −1 or lower score
- has no positively scored answer
If the question is more than 365 days old, and ...
- has a score of 0
- has no positively scored answer.
- has a viewcount <= the age of the question in days times 1.5
This number rises to 62,810. That's 50 thousand questions that people have prevented from deletion by self-answering and where their answer hasn't managed to garner a single up-vote.
I'm going to discount these questions from further analysis as I don't see a reason to keep them around. This leaves 95,550 questions that this feature-request may adversely affect.
There's another group we can remove, those questions self-answered over 24 hours after they were asked. These would not be affected by the suggestion of the badge as the OP. In total these number 64,599.
This means we're now looking at:
- questions with a score of 0 or more, those people who according to Ben might avoid self-answering to wait for the question-upvote.
- self-answers with a score or more than 0 because there all these people have done is avoid their question being deleted
- self-answers less than 24 hours after the question was asked, those people who might wait around for the upvote.
This number is 54,396. Restricting once again to answers that managed to gain a score of 1 or more; those that are, in all likelihood, have an answer that's worth saving this number falls to 18,584.
Then, removing those questions that were answered with a positive score by someone else prior to the OP answering, a situation where the OP knows they would not be able to get a badge, this number falls to 14,794.
There's something else that should be considered; is the answer likely to be helpful to future visitors. A positive score is not the sole measurement of this, we can look at the length of the answer body to come up with some sort of measurement, it's 777 characters. I know there's some extremely long self-answers out there, one of them is mine! If we take a rather arbitrary 200 characters as the minimum needed to provide a semi-decent answer but to correct any mistakes include those answers with a body length less than this but 2 or more upvotes the number reduces to 13,604.
Lastly, here is that number broken down by users and reputation:
Questions Users Reputation "level"
--------- ----- ------------------
38 36 1 - 11
3536 3410 11 - 200
4284 3634 200 - 1k
2781 2042 1k - 3k
900 554 3k - 5k
752 473 5k - 10k
389 256 10k - 20k
384 222 20k +
As you can see the number of users affected is less, 10,627. Of these, 1,505 have more than 3k reputation and could be classified as experienced.
In actuality there are only 4,344 questions and 3,984 users where the question score is 0 and it was self-answered within 24 hours.
tl;dr
In effect this might negatively impact the site in the cases of 10,627 users. 15% of whom could reasonably be expected to rise above it. There are only 4,344 questions where the OP might definitively not self-answer as the question score is 0. Compare these numbers to:
- the 370,551 questions posted in 2012 with a score of 1 or more and without an answer with a score of 2 or more
- the 137,382 questions posted in 2012 with a score of 1 or more and without a postively scored or accepted answer.
- or, the 62,619 questions posted in 2012 with a score of 1 or more and without a single answer
If it doesn't work then it doesn't work and the experiment can be stopped but it's worth making an attempt.