Over simplification I think.
The difference between Alpha and Beta is physical attraction, wealth, intelligence and most importantly confidence. If you have the right amounts of any of those, women will be attracted to you. Women will be attracted to ugly men who are rich and confident because the confidence and the ability to provide makes them alphas. They'll also be attracted to good looking poor guys, because the confidence and raw sexual attraction, overcomes the need for financial security.
Betas can also be good looking, rich and intelligent, but they often lack the confidence to approach women and to attract them.
The bad boy is typically an alpha, the swooning after psycho killers is just women being f**ked up though. Those women are attracted to what they consider the masculinity of the man, his ability to cause harm and behave recklessly, but it's only a handful of damaged women that go to that extreme.