I think you and a few other people in this post have a misunderstanding on how air to air missiles work, the motor only burns for a few seconds accelerating the missile to mach 4 after that the missile is coasting to the target like an arrow constantly losing speed to airdrag.
If you fire it from up high in an arc there is very little air resistance and you can get the claimed max ranges, if the missile have to go through dense air or the target cranks forcing the missile to turn the range reduces drastically. A 150 km range missile when fired from down low against another low defending target is more like 30-40km effective range and even less if the target turns cold.
Here is a clip from a simulator of how a 1vs1 bvr fight might look like and shows how close you have to get when both are down low.
Now this is a simulator but it is considered the most accurate public one out there and does model airdrag etc and while exact performance numbers are not available the missiles still follow the laws of physics and ball park estimates can be made.