NHFS rule 5.1. 4 . . . After a dead ball, the ball becomes live when it is held by the pitcher in a legal pitching position, provided the pitcher has engaged the pitcher’s plate, the batter and the catcher are in their respective boxes, and the umpire calls “Play” and gives the appropriate signal.
This is one of those rules that most coaches/players and many umpires are simply unaware of. A ball goes foul, the coach tosses it back to the pitcher, and the game goes on. But what happens if the runner takes off when the pitcher is walking back to the mound with the new ball? Or while he is standing on the back of the mound rubbing up the ball? How does your partner know when the ball is live?
I suggest you get in the habit of putting the ball in play after every dead ball, especially when there are runners on base, following the rule cited above. You may have to train the pitchers. Often they will get the ball and get right to straddling the rubber while looking over at 1st base. Get their attention BEFORE they throw to 1st, so you don’t have to take away the pick off or the ball thrown into DBT award.