Originally baseball players wore no numbers in their jerseys. Around 1890 or so baseball positions were numbered. The pitcher was #1, the catcher #2, and so on. That numbering system is still used today for keeping score. The old 6-4-3 double play is shorthand for the shortstop throwing to the second basemen who then throws to the first basemen. In the early 20s, teams started experimenting with numbers based on a player's position the lineup and this spread around. Babe Ruth and Lou Gehrig wore 3 and 4 respectively because they hit third and fourth in the Yankee lineup. Within a few years this system was ended and players began picking their numbers almost at will and being known by their numbers. That system spread to almost every team sport today, with rugby (where players wear the number of their position) and test cricket (where players don't wear numbers) being the only exceptions that I can think of.
But, what if baseball teams just stuck with numbering based on positions but placed those numbers on uniforms to help fans. If the guy wearing #8 is at-bat, you know that the center-fielder is batting.
While obscure in and of itself, I wonder what effects that might have on players' egos and sports marketing.
Would other sports have adopted position numbering, unnumbered jerseys, or would they have developed their own squad numbering system? Would players like Wayne Gretzky (99), Michael Jordan (23), Jackie Robinson (42), etc. be known as numbers when the number on their back of their shirt was nothing important?
Retired numbers would almost certainly be out of the question, but would selling jerseys be too? Walking around wearing your team's #5 jersey would mean that you care about the current 3rd basemen, the last 3rd basemen, or were just a fan of 3rd basemen.