Sorry, Ken, I was not clear about that. HOBS could be used at any range, but at a cost. At longer range (let's say BVR for argument's sake) you gain a lot by doing as much of the mx's work as possible pre-launch.
If the mx has a lot of work to do to achieve a collision with its target, it will lose a lot of kinetic energy by turning, thereby reducing its ability to do manoeuvre to counter target manoeuvre or for end-game navigation. So at longer range, you'd be better off doing as much manoeuvre as possible with the aircraft to achieve the best firing solution so that all the mx has to do it fly where you've pointed it. In very simple terms.
As for LO (radar or IR), the effectiveness decreases exponentially with decreasing range. Up close you can see it with eyeballs, radar and IR. The visual fight environment.
I've been slightly vague there for obvious reasons, but I hope you get my meaning.