Once again the redneck from NC here (which coincidentally is the home of Jerry Narron). I used to exclusively throw the ball to F1. I've noticed my throwing isn't so hot so now I will hand the ball to F2 if he stays put and toss the ball to F1 if the catcher is gone. Usually F1 has come toward the plate and it's only about a 40 ft throw to him.
We have very few on deck batters that chased passed balls with no one on and foul balls to the screens. Catchers almost exclusively handle this. I actually think it's good for them on a true passed ball, it teaches them to catch the dang ball instead of screwing it up
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Lawrence