I have been doing some testing and here's what I've found.
Going head to head with a MiG-29 at same altitude/airspeed (25,000, 500knots) I can get a very good hit percentage from inside 15nm, 10nm is easy money. From behind, flying the same heading, I'm getting hits at 8nm.
That's not great range but it's an improvement over the AIM-7. That turd has an effective range equal to the AIM-9.
Also, the missile is self guiding well beyond these ranges, I've let one go and broke lock immediately and it guided from 25nm. It didn't hit but the point is if you are in range to score a hit you are in pitbull range so fire and forget. For that matter, the AIM-120 is worth it for just this reason alone, fire then move on to another target rather then holding lock to impact.
ETA/ I'm getting a shoot cue at 20nm head on but I haven't scored an actual hit from that range yet. But the shoot cue from a rear aspect is pretty accurate for a good hit percentage.