Frank Cross reports some preliminary results on his empirical study of Chief Justices on case results:
I have completed a preliminary analysis of the 2004 term. There appears to be some result from Rehnquist's absence on outcomes. For example, in the cases over which Rehnquist presided, he had a 10% dissent rate. In the cases over which Stevens presided, Rehnquist had a 30% dissent rate. While this is a fairly small sample, and the changed probability of a Stevens dissent is much less, this is suggestive that Rehnquist's absence may have had an effect.
I went by their appearance at oral argument with help from some of your readers and found 40 cases for Stevens and 30 for Rehnquist, just using cases with full argument and full opinion.
He also adds a caveat (and invitation):
Posting it would be great, though please caveat that it's preliminary. It's only going to be a small part of the article, but getting this out there for discussion might uncover any mistakes I made. We'll be using a broader database to test the past effect of the Chief, i.e., what happened when Rehnquist was elevated? Did it affect his votes or the votes of others?
Sounds like a great research project.