Good question and a good idea. Thanks for posting.
It would be interesting to see how often Circuits are affirmed or reversed by large majorities of the Supreme Court. That analysis gets a little complicated because even in cases where there is, say, a 7-2 vote, the seven Justices in the majority may concur only in a result but write separate opinions explaining how they got there, leaving the rest of us to wonder which of several rationales will really represent the view of the Court when the next case comes around. Furman v. Georgia, which overturned capital punishment in this country before Gregg v. Georgia outlined how it could be restored three years later, resulted in numerous opinions that makes, to this day, Eighth Amendment analysis enormously complex.
Another factor that makes vote counting analyses difficult is that the role of the Supreme Court is to set precedent and not to correct error. I think the consensus view is that if all a litigant has to hang his hat on in is that a great injustice was done, the Supreme Court will almost certainly not take the case. The Supreme Court's Rules specifically prescribe that petitions for appeal are granted based primarily on how important a precedent will be set by the case. The Court looks most often to conflicts between and among the federal Courts of Appeals and the highest courts of the states and to whether an important federal question has been raised that needs addressing by the Supreme Court. All of which is to say that looking at the rate of Supreme Court reversal isn't a very good gauge of lower courts' error rates since the Supreme Court is not set up, in that Court's view, to simply correct errors - it is set up to set precedent and make law.
Thanks again for posting!
Cullen