What kind of background would be best for a Supreme Court Justice?

Does the background of a Supreme Court justice influence the way she decides a case?  Linda Greenhouse's column today in the New York Times details Chief Justice Roberts ruminating on the current situation in which after Alito took O'Connor's place on the Court, there was a period of only former Courts of Appeals Judges on the Supreme Court.  That changed when Elena Kagan arrived.  Kagan, a former Harvard Law School Dean and Solicitor General, had never served on the federal bench before.   Greenhouse was at an event with the Chief Justice in which he was asked what difference, if any, the background of a justice made  on the Supreme Court.  The Chief Justice responded as follows:

“If you view it more in terms of playing a political role – not in a partisan politics sense, but as part of the political process, maybe the way a constitutional court in the European countries does – well, then maybe it makes sense to have people who’ve been active in the political realms, either in the executive branch or in the legislative branch. It has to be saying something about the role of the court in terms of what the makeup is.

...

“If you’ve been a president, if you’ve been a governor, if you’ve been a senator, you have a particular way of looking at issues and matters of public policy. If you’ve been a judge on a court of appeals, it seems to me you have a very different way of looking at it.

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“So you have to decide what types of questions you think the court should be deciding, and if they call for people who have one way of looking at public policy as opposed to people – you said ‘technocrats,’ not the right word – a more focused way of drilling in on the law. And maybe you think there’s a mismatch between the kind of question the court’s being asked to decide and the type of personnel that have to decide it.

“And you can obviously resolve that tension one way or another. But I do think it’s not simply a coincidence or a happenstance that you have a court that looks so different than what it looked like in the past.”

Ms. Greenhouse spends the rest of her column assessing Roberts' comments and whether the meant that there is a mismatch between what the people want the Supreme Court to do (provide profound answers to complex questions of the day) versus what they are equipped to do with their Courts of Appeals background (provide small bore answers rather than broad explications and visions of public policy).

The idea that one's background (in this instance, one's career) but including one's racial, ethnic, religious, sexual background influences in profound ways one's worldview is nothing new to social scientists.  It is gratifying to know that the Chief Justice is aware of this, even as many of his colleagues on the federal bench will insist, at least publicly, that they "just apply the law". 

These recent comments are a bit of a revelation from John Roberts who in his confirmation hearings used the age old analogy that he saw his job as like an umpire, just calling balls and strikes and not swinging case outcomes one way or another.  Roberts is explicitly saying here that the way you do your job as umpire is influenced by what job you used to do before.  So it's not just as simply as calling balls and strikes?