Allow me to insert another question on this topic.
When I see a batter take 3-0 and go to 3-1, the odds would say that a struggling pithcer would throw the next pitch for a ball. I think this is especially true if he thought the batter was not swinging at the 3-0 and is likely swinging at the 3-1. The "careful " pitcher , scared of the bat, usually throws ball 4.
Do you take twice with the 7-8-9 hole batter. I see many times where I wished we had when we swing at ball 4 .