First of all, get rid of this type of language--deep. It's either a strike or a ball, not deep, wave hand to the side, etc.
I was taught to see every pitcher a 6 ft tall to judge the 12' arc. Remain standing tall until the pitch reaches the top of the arc, then drop to where your eyes are even with the top of the batter's zone. Remember to stay in 'the slot'. It DOES NOT matter where the ball lands; through the strike zone, STRIKE! No--Ball.
I hope this helps-----good luck!