If this is the case something has already gone terribly wrong and any situation where you can what if it all day is hard to explain how to beat it.
So you have a Spit 9(type fighter) 1K behind your K4....you have E and they manuever ed to get there on your 6 (this is the situation I'm reading from your posts)...
If they maneuvered to get there and have less E then you...a zoom climb to get above your opponent is easy. You base your pitch not off a standard say like 45 degrees but off what your opponent decides to do with his pitch. If they match your pitch, make yours steeper, if they shallow out to keep energy you can shallows yours....I would also suggest adding a spiral into it to force them to lose that energy to follow you...in a spiral climb your objective is to create an angle where they flip their plane over to follow your spiral....this is where they burn the most energy because gravity and lift are both pointed toward the earth.
If the plane is closing on you....going vertical is the best way to close the energy gap between you and your opponent. A lot of people preach the split s but you are just giving up the fight over and over...yea it's safe but it's going to end poorly.
You use a vertical manuever to force an overshoot. Going vertical in a reverse is risky but if done correctly leads to better position to force a rolling scissors or vertical scissor or even to gain a shot opportunity as the enemy flys by. You do this by starting a turn creating an obtuse angle between their nose and your wingtip. As they get closer you tigthen that turn to create a 90 degree angle from your fuselage and their nose...at this point just before they have guns you go vertical into a barrel roll as the over shoot you try to keep your roll behind their 3 9 line (their wings) kinda like you would in a turn fight...
These are hard to type about, I do feel like the community deserves a good video explanation because a lot of players struggle against this.
So essentially, it is an understanding of turn circles and pursuit curves.
When I break I'm trying to create angles on the bandit (Aspect angle and Angle off) and increase closure on the bandit to make him solve the problem of how to get back on my 6. The issue is the bandit may just pull lead for a gunshot and there is no problem left to solve if you don't recognize this.
So a bandit can't use turning ability of his aircraft to solve for Aspect or Angle off until he gets to your turn circle. The distance he is outside of your turn is "free angles"...I think everyone knows if you turn early enough, you will meet the guy nose to nose (180 aspect)...most don't do this (for whatever reason).
So since most guys pull lead for a shot against a turning bandit here is what is happening. When you pull lead against a bandit in a break, you are increasing aspect angle, increasing angle off, and increasing closure (all things that I said you want to do TO the bandit when you are defensive correct? So this is actually helping me when I'm defensive!!). But you (as the attacker) are doing it for a reason...a gunshot attempt.
So as the defender, you do your turn, you see the bandit, you roll to put him on a wingtip and then pull up to avoid the gun attempt (remember he needs 3 things for an effective gun shot--he has to be IN RANGE, IN LEAD, and IN PLANE OF MOTION). This gets you out of the PLANE OF MOTION, and is the start to the barrel roll that Junky talked about. The key here is to assess line of sight (LOS) of the bandit across the tail, if it is low, barrel roll may not work. If it is high, it will work).
Here is the video Junky asked for....it is a P-51 coming in with E on me, when I'm on the deck. As junky said...it is easier to watch then try to explain:)