hate cut off point

What is the point at which a player will no longer attract violence from mobs?

As I understand it, the desire of a mob to attack a player is based on the quantity of hate that the mob has for that player, so I am assuming that the reason for certain mobs attacking a player is based on this thing called hate.

I am trying to understand, what it is that determines whether a mob will attack a player or not when running around in the open.

In my experience I have noticed that when I first started playing certain mobs would attack me immediately. But after some time has now passed and my character has various abilities and powerful items, those same mobs ignore my character when it passes by them. Also, certain mobs that previously attacked very soon, only attack if my character goes very close to them. What controls this? Is it hate, or is it something else? Please explain how this works.