This is the priority rule for fly balls. If the infield flyball is toward the third base line, then the third basemen has priority. Around homeplate the catcher has priority and first base line the first baseman has priority. We (pitchers) were always taught to point straight up if it was around home plate, thus the catcher immediately knows. Anyone can go after a fly ball in these situations but whomever has the best chance has to call someone off. That's usually whomever thinks they have the best chance yelling out "I got it" three times loudly and the other fielder saying "Take it". We practiced this in college all of the time. Fly ball priority goes through all of the positions.
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