The Sixth Circuit, where I clerked more than a decade ago, has sixteen active judgeships. At present, there are four nominees from President George W. Bush (Sutton, Gibbons, Griffin, Kethledge) and six nominees from President Trump (Thapar, Bush, Larsen, Nalbandian, Readler, Murphy). And there are two nominees from President Clinton (Moore and Clay), one from President Obama (Stranch), and three from President Biden (Davis, Mathis, Bloomekatz).
One might think that an en banc court with ten appointees from Republican Presidents and six appointees from Democratic Presidents would consistently lean to the right. But not so. To command a majority on this even-numbered court, you need nine votes. And in recent years, finding those nine votes has been tougher and tougher. For starters, Chief Judge Sutton has long taken the policy that en banc review should be used sparingly, as the Supreme Court can correct errors. Maybe that policy made some sense a decade ago, but with the Supreme Court taking fewer and fewer cases, and circuit splits festering, the en banc/certiorari calculus should be rejiggered. (Sutton may have departed from that policy, at least in part).
Making the math even tougher is that two of the W. Bush appointees have voted more and more with the Court's liberals: Judge Richard Alan Griffin from Michigan and Judge Julia Smith Gibbons from Tennessee. One such case from 2021 was the OSHA Vaccine mandate case. The en banc court split 8-8, with Judges Griffith and Gibbons declining to join Judge Sutton's dissental. In reality, what looks like a 10-6 court on paper is probably closer to a 9-7 or 8-8 court in practice.