I should have noticed this before. But it turns out that Fifth Circuit Judge Jerry E. Smith (the judge co-conspirator Todd Zywicki and I clerked for) analogized judging to baseball umpiring some two years before Chief Justice John Roberts famously used the same metaphor in his confirmation hearing for the Supreme Court. In a February 2003 interview with Howard Bashman of How Appealing, Judge Smith said that "A judge should not consider his or her personal preference as to outcome, any more than an umpire should call balls and strikes based on which team is his or her favorite." I don't claim that the Chief Justice got the idea from Judge Smith. I don't even know if Judge Smith's use of the analogy was the first one. However, it does seem to be the case that Judge Smith used it before Roberts. Since Judge Smith is a big baseball fan, it's not surprising that he would use an analogy from that sport.
Like most metaphors, the judge-umpire analogy is an oversimplification of reality. For example, there is much more disagreement over judicial philosophy than over umpiring philosophy. On the other hand, umpiring is more complex than some detractors of the metaphor realize. Just as judges differ in interpretive philosophy, umpires differ in their definition of the strike zone, the amount of offense they are willing to tolerate from players and managers before kicking them out of the game, and so on. Limited as it necessarily is, the judge-as-umpire metaphor is a good shorthand way of emphasizing the judge's duty to set aside his policy preferences and be impartial between litigants.