I know this isn't an answer but it's far too long for a comment. There's a problem with your SQL, caused by the LEFT OUTER JOIN; you're counting questions multiple times so the problem is both slightly better and slightly worse than what you think.
I also disagree with your definition of a "good" answer. By definition an accepted answer is "good" as it has helped the OP (unless of course they've been pushed into accepting it by loads of comments but that's another matter). I've excluded Community owned questions and answers as I don't really think they are relevant (and it helps the query to work!).
Your first set of results on the number of open questions by quarter now returns the following:
Year Quarter Questions Answered GoodAnswer ---- ------- --------- -------- ---------- 2008 3 18142 99.98% 99.78% 2008 4 39557 99.85% 97.89% 2009 1 54286 99.71% 95.96% 2009 2 76133 99.51% 93.85% 2009 3 99291 99.18% 91.91% 2009 4 114135 98.97% 91.02% 2010 1 144028 98.56% 89.97% 2010 2 160493 97.91% 87.36% 2010 3 188612 97.41% 86.03% 2010 4 207395 97.23% 85.47% 2011 1 269672 96.71% 84.21% 2011 2 301200 95.34% 82.10% 2011 3 335106 88.66% 75.21% 2011 4 339592 87.62% 73.92% 2012 1 409490 85.61% 70.71% 2012 2 419391 81.33% 64.74%
As you can see the percentage of answered questions is a little worse than you thought, but the percentage of questions with a "good" answer is a little better. Personally I think the telling point here is not necessarily the number of questions but where the differences lie between my results and your own. For Q4 2008 you have 122,616 and I've got 39,557 questions, which implies that every question received over 3 answers. For Q2 2012 the difference is minimal, on average questions receiving about 1.2 answers.
I've also run this for questions with a score >= 0:
Year Quarter Questions Answered GoodAnswer ---- ------- --------- -------- ---------- 2008 3 18084 99.98% 99.78% 2008 4 39374 99.85% 97.91% 2009 1 53930 99.71% 95.98% 2009 2 75565 99.51% 93.86% 2009 3 98411 99.18% 91.94% 2009 4 112677 98.96% 91.06% 2010 1 142475 98.54% 90.03% 2010 2 158929 97.90% 87.39% 2010 3 186719 97.38% 86.04% 2010 4 205092 97.20% 85.52% 2011 1 266760 96.68% 84.26% 2011 2 296514 95.27% 82.13% 2011 3 327715 88.40% 75.11% 2011 4 330472 87.28% 73.74% 2012 1 395629 85.10% 70.48% 2012 2 402573 81.11% 64.78%
I think the surprise here is how little difference it makes. It reflects well on Stack Overflow that no matter if the question is not as good as it could be you are just as likely to get a "good" answer. Obviously, closed questions would skew this massively and as a number of "poor" questions get closed not too much can be read into this.
Lastly, here the same query is for questions with a score >= 1:
Year Quarter Questions Answered GoodAnswer ---- ------- --------- -------- ---------- 2008 3 16312 99.98% 99.83% 2008 4 33304 99.88% 98.81% 2009 1 41506 99.76% 98.12% 2009 2 53316 99.70% 97.33% 2009 3 64491 99.53% 96.49% 2009 4 67875 99.30% 95.56% 2010 1 97743 98.97% 94.19% 2010 2 101814 98.41% 92.33% 2010 3 113190 97.94% 91.29% 2010 4 118231 97.81% 90.87% 2011 1 146083 97.48% 90.11% 2011 2 161480 96.51% 88.55% 2011 3 158318 95.30% 86.54% 2011 4 154275 94.38% 85.07% 2012 1 166750 93.16% 83.35% 2012 2 150147 91.25% 80.49%
As you can see the number of answered questions and the number of questions answered "well" significantly improves though the same drop-off is observable.
My own conclusion from these statistics is that a finesse to the system to remove unanswered questions, or whatever it might be, is not what is required. The number of answered "good" questions at over 91% is, in my opinion, a pretty high number.
What seems to be needed is an increase in the number of people who answer questions. Whilst Stack Overflow has had an ever increasing number of people asking questions there hasn't been a commensurate increase in the number of people answering them.
I ran a little query to test this hypothesis:
Year Quarter Questioning Answering ---- ------- ----------- --------- 2008 3 6451 9091 2008 4 10755 13366 2009 1 13739 16085 2009 2 18966 21351 2009 3 24511 25774 2009 4 37479 36660 2010 1 47564 42199 2010 2 57072 47838 2010 3 66546 53524 2010 4 73404 61090 2011 1 95670 76315 2011 2 109801 79702 2011 3 127506 86461 2011 4 125765 90960 2012 1 152582 109684 2012 2 164801 114608
As you can see in the "early" days the number of users answering questions was more than the number of people asking them. This has now been completely reversed and the questioners are in the ascendant.
What the solution is, I'm not entirely sure. What seems certain though is that Stack Overflow needs to find a way of converting question askers into question answerers. Without flooding the place with crap answers.
