"Pay up" is right, as you no doubt know you're up against the well-heeled sports crossover collectors. By far the most common baseball player you'll find on a box is Al Simmons, a brand that was made in Milwaukee for some forty years or so. Joe Tinker is probably the second most encountered box, but is by no means common. There is a Wagner and a Cap Anson, along with a few other examples that I saw in Barry Halper's collection, but they're very tough to track down.
Generic Victorian scenes of baseball, like the box pictured below, are numerous but scarce and highly collectible.
Cigar boxes differ from comics in that many boxes are either unique or maybe have at best two or three surviving examples. Action 1 and Detective 27 would be considered "plentiful" if they were cigar boxes!