Our system has been working pretty well for us since we started teaching it last year. When a ball is in the air in the infield, there are some simple rules we follow:
1. Every infielder has precedence over the pitcher.
2. Generally, the deeper the infielder plays, the more we want them to call off the other players. So, 3b and 1b have precedence over the catcher. SS and second have precedence over 3b and 1b.
3. SS has precedence over all infielders.
4. Outfielders coming in have precedence over all infielders.
5. CF has precedence over all fielders: infielders and outfielders.
So, if we were to rank the fielders in order of precedence, they would be"
1. Center field
2. Left field or right field (depends on whose side the ball is hit to)
3. Shortstop
4. Second base
5. Third or first base (depends on whose side the ball is hit to)
6. Catcher
7. Pitcher
Lastly, players need to communicate. There is no worse feeling than thinking that someone else is going to run into you when a fly ball is hit. The player who has the ball in his sights and has the precedence calls out "get out, get out" and the players who defer to him call back "you, you, you" to let him know they are not coming to get the ball.