As the posts in this thread suggest, Chief Justice Roberts' analogy between judges and umpires has many antecedents. Lawprof Eric Muller takes the prize for finding the earliest judge-umpire analogy so far, a 1912 district court decision.

Many people criticize the umpire-judge analogy because the rules of baseball are much clearer than those of constitutional law and give umpires less discretion than judges have. This criticism is, I think, overstated. Umpires exercise a great deal of discretion over the size of the strike zone, when to throw players and managers out of the game, and other important issues. As in legal theory, there are even broad philosophical disagreements as to the best method of umpiring. For example, some believe that the umpires should strictly enforce the rules as written (a position roughly analogous to textualism in legal interpretation). Others adhere to longstanding traditions that in some cases diverge from the letter of the rules (e.g. - the rule against catchers blocking the plate is often left unenforced); this is similar to precedent-based reasoning in law. There are also some umpire practices that seem analogous to "purpose-based" legal interpretation.

Where the judge-umpire analogy really breaks down is not in the realm of interpretative theory but in that of incentives. Unlike federal judges, baseball umpires don't have life tenure. Major League Baseball can fire them or discipline them if it determines they aren't doing a good job. MLB also has a lot of discretion in deciding which umpires will call which games (e.g. - picking only the best umpires to do the World Series). On the other hand, federal judges are extremely difficult to remove, and the political branches of government don't have much control over which judges will hear which cases - especially at the Supreme Court. Thus, unlike with umpires, it's much more important to pick the right people for the job from the start. If you pick the wrong ones, they're likely to plague you for decades to come.