Why do we do that?

[Rich]

If you don't care about scoring, look below the parentheses.

(When I score games, a fair fly ball gets no designation -- a fly ball to center is simply scored: 8

A foul fly ball, I put an F in front of it. So a foul pop to the first baseman gets an F3, a fair pop to the first baseman is simply scored: 3 (whereas an unassisted putout by F3 is scored 3U).

I've scored many games at the college and high school levels, and this has always worked for me. YMMV. Everyone scores differently :-) )

Now, we don't do any special signaling for scorekeepers. The fair or foul call comes before the "out" or "no catch" call (if the ball isn't routine -- if it is a routine catch, I'll signal only foul or fair with no out signal) because of the reason Bob Jenkins gave. It would look really bad if the ball hit off the glove and was 10 feel foul before the umpire signaled. We simply call it in the order it happens. It is foul or fair before it is caught or not caught).

Rich