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As a magika NB, where should I put my champion points?
Read the stars' tool tip and if it helps your build then put some points in it.
Read the big starts tool tip too to see if you want that passive.....and if you do then you will figure out how to optimally fill up that constellation to get the big star's passive. If you don't need any big star passive just put points to help your build like:
reducing magica cost of abilities
increasing magica regeneration
increasing spell power
maybe getting the big star that increases your magica crit rate.
put some points in damage reduction stars...
Thaumaturge and Elfborn are your primary stars for boosting damage. Capping Thaumaturge should be your primary goal, but don't neglect the 12% increased spell crit in the Apprentice tree.
Magician and Arcanist are your primary stars for resource management. Generally I take more reduced cost than recovery, but it's a matter of preference in many cases.
Your defensive stars are more flexible, but I would start by putting points into Hardy. It never hurts to have a little Quick Recovery too. I like to also put points into Thick Skinned and at least one point into Elemental Defender, but as I said it's flexible, and you should adjust these according to your playstyle and preferred content.
Blue Tree:
29CP in Elfborn, 1 CP in Spell erosion (Do this first to get the 12% Crit)
Then max out Thaumaturge to 100
Then keep putting them into Elfborn until you hit the cap.
(Optional)I weave inferno staff and Funnel Health, so I put 10 into elemental expert to boost my staff attacks and Ice Comet as well
Green Tree:
I put most into Magician (reduced cost), and then some into recovery and some into reduced dodge roll. Keep Siphoning Attacks up while weaving and you will have very few resource management issues. My high elf NB has 800 recovery and I rarely run into issues. I have Spell power/Spell Crit/Restore Magicka Potions slotted if I dip too low, but this rarely occurs. Can't stress how good siphoning attacks is eneough.
Red Tree:
This one is up to you. I split most between Hardy and Elemental Defender, and put a few in quick recover, thick skinned, and a few in light armor focus.