Ball ammunition versus various hollow points for self defense with a pistol
I recently read the 6th Edition (IIRC) of "Combat Handgunnery" by Massad Ayoob.
He makes it sound as if hollow points are the only way to go to self defense, and as if ball ammo is not even worth taking seriously if there's a chance that you might have to shoot in a self defense scenario, because he barely even mentions it in his chapter, except to say in a historical sidenote that that 9mm parabellum ball ammo performs very poorly for stopping someone. At other points in the book Ayoob refers to "training ammo" and I think what he means is FMJs, which suggets he thinks FMJs should only be used for training.
On the other hand, I've also been told by a firearms instructor that hollow points are "overrated".
When you read historical analyses and statistics regarding "handgun stopping power", the overwhelming impression I get is of variability. Sometimes a person is shot once and drops, and sometimes a person is shot multiple times and is not. I'd always had the impression, from historical research, that shooting someone with a handgun was a bit of a crap shoot in terms of whether or not the person would go down, which is why people train in failure drills. This is in contrast to the impression Ayoob gives me in his book about certain specific hollow point cartridges which are supposedly very likely to produce a "one shot stop".
Help me sort this out. How important is the use of hollow points, versus the use of ball ammo, in a self defense handgun shooting scenario? Is ball ammo greatly deficient in relation to hollow points?