Eldritch Battery and Discipline math question

If I have Eldritch Battery (EB) and I add the Discipline aura, I know that it will raise my maximum mana and as a result it will also raise my mana regeneration rate too. Whenever I have used EB + Discipline I have never had an increase in usable mana, that has always gone down.

Is it possible to use Discipline with EB and end up with a net positive gain in usable mana?

There is a lot of stuff that can affect your numbers:
Aura Effect passive nodes
Buff effect passive nodes
% max mana nodes
% max energy shield nodes
Level of your Discipline aura skill gem
Reduced mana reservation nodes
Reduced Mana support gem

If you account for various changes to all of those stats (and any others I may be missing), is there some sort of break-even point where you might start gaining extra usable mana with Discipline aura active?

I assume that since the aura has a percentage-based mana reservation along with a flat amount of energy shield gained (mana in this case), that the mana reservation would always win because it is a percentage and would be hard if not impossible to overcome.

You're going to be using the 60%*(modifiers) of the new mana total, so in theory yes you could get a net mana gain, but in practice probably not, especially if you're using other % auras. But for the sake of argument let's roll through some math

You're running EB so lets through out that you have around 2000 base mana (remember that a higher base will actually make what you're trying to do harder.)

and the only % aura you're running is disc, and you're a boss so you have a level 21 in an alphas, and which gives you 366 es and between es/mana/aura/buff aura/buff gets you 96% bringing you to around 700 es then lets say you get enough mana es nodes to get up to 200, and every reduced reserved passive(except for the one behind blood magic) gets you down to 25% for discipline.

This brings us from 2000 to 4000-1000=3000 mana so yea you probably can do it, but you need to devote your entire tree to mana/es/buff/aura nodes to do it, so it's probably not worth.

In fact, the % reserved will be the same one, but when you take EB, and increase your mana pool with discipline, your max mana goes way up and you reserved mana too (because the % reserved refers now to a greater number). But you will have more mana anyway, specially if one of those auras is Clarity, which reserves a fixed amount, not a %. So, if you have 60% mana reserved and, lets say, 400 mana for clarity and originally has 2000 mana, it means you have 1600 mana reserved and 400 usable mana. If your max mana goes up to 3000 with Discipline, the 60% reserved now takes 1800 mana points, but clarity still takes 400 and your usable mana would be 800, a great usable mana increase (plus the mana regen). But they are going to nerf EB anyway, so it won't matter until we get the "final" version of whats to come.