After gathering some data on the upgrading rates and characteristics of skills I came up with these formulas and understandings of what each skill means and does exactly:

Resonance is very straightforward. It increases your damage. This means that at the endurance monster hp cap you hit the breaking point for necessary damage at a lower gem grade(slightly) and that you require less mana worth of gems on the way up to that point to defeat a given wave. It also means you can handle angering larger numbers of creeps to build mana.

1/((x)**(137/91+22**x/91)) = percent gain per skill point cost for increasing a Resonance level where x is your current Resonance level.

Replenish is a bit more complicated. The mana gain from monster kills is increased. This is useful in the very initial game when you are setting up your mana farm but are still relying on killing monsters to give you the necessary mana. The usefulness of it after you’ve established a good mana farm drops off significantly though. The mana replenish over time effect is negligible at all times but the absolute start.

(23/(87+23*y))/(3/2 + y/14) = percent gain per skill point cost for increasing a Replenish level where y is your current Replenish level.

Focus is the most controversial one of all. Initially all it means is you have a higher starting mana amount(and pool max), which is useful but typically is nowhere near as important (until very high wizard level) as your wild gem. It has been proven elsewhere that once your mana pool has hit the point that it requires a 95% pool cost to extend the pool, all pool sizes have the same requirement in effective mana gain (Mana before mana pool collection multiplier) to extend any given amount. Basically it means that having a high Focus level just means your don’t hit the 95% pool cost point until later, but that your multiplier increases are more expensive until you do. This is a negative side, but you also have a higher max mana to work with once you have reached that point without having to upgrade nearly as massively. At this point any bonus this skill has provided in the early and mid game turns to zero.

Your mana pool is a lot bigger when you reach the 95% cap, but your multiplier is lower and equivalent upgrades go just as quickly as if you had level 0.

(144/(169+144*z))/((28 + 3*z)/19) = percent gain per skill point cost for increasing a Focus level where z is your current Focus level. This does not take into account the Battle Amulets base mana nor the wild gem.

I typically like to keep all three of these at the point where their marginal increase per level is equal. This both eases my OCD and eases the beginning and middle game

To beat an endurance map I usually find the first point on the map at which all paths converge and I can build a 6x amped trap. I create a 2O/1L/1B gem and keep the trap gem 2 grades higher than the amp gems. I typically am able to defeat waves, increase my multiplier, and upgrade my gems to the breaking point where my mana farm gains damage faster than the monsters gain health (Around a G8 core) before they even pass the farm. (The shadow is nothing a G9 Yellow gem bomb can’t handle)

The formulas simplified at higher levels have approximately the following ratios:

1:1.82:1.23 = Resonance:Replenish:Focus