The Position Numbers
Every position has a number, they are not in an obvious order, and every scorebook in the world uses them.
What it actually is. Pitcher is 1, catcher 2, first base 3, second base 4, third base 5, shortstop 6, left field 7, center field 8, right field 9. That is why a ground ball double play from shortstop to second to first is written 6-4-3, and why a fly out to center is F8.
What somebody who knows the game gets out of it. The order looks arbitrary and it is historical: it follows roughly how often each position handled the ball in the 1860s, when the shortstop was a roving fielder rather than a fixed infield spot, which is why third base got 5 and shortstop got 6 rather than the other way round. Learning the numbers is the entry fee for reading a scorebook, and reading a scorebook is still the fastest way to understand what a game actually looked like from a piece of paper.
The numbers worth knowing. Nine numbers, plus 10 for the designated hitter on a lineup card. In a scorebook 4-6-3 is second to short to first and 6-4-3 is short to second to first, which are different plays with different pivots.
What people get wrong about it. The numbers describe positions, not people. If the shortstop is playing in the shift on the right side of second and fields the ball there, it is still 6, because the number belongs to his position rather than to where he was standing.
At Little League and travel ball. This is worth teaching to youth players directly rather than leaving to the scorekeeper, because it is the vocabulary coaches use to describe plays. A 10U player who knows he is the 6 understands a 6-4-3 instruction and a cutoff assignment much faster than one who does not.
Batter's Eye: look up anything in baseball