As far as I'm aware, the majority of US midwives (or CPM's) are not hospital nurse midwives. They do not go off-the-clock, though they sometimes have multiple patients due at the same time so you might still find a backup midwife is covering for your primary care provider.
I'm sure it varies from birth center to birth center - one would have the midwife scramble at any hour of the day or night to get into the room, the other we used had the ball.
I can see the advantages to the ball but the first was overall better I feel (but there are so many variables it's hard to really tell). We've technically never had the doctor/midwife "assigned" on-hand during the actual delivery for various reasons.
