Arcane Tradition: Copy Mage
Copy mages have the uncanny ability to observe magic and break it down into its component parts, allowing them to copy spells they have seen. As such, they have an easier time learning new spells than other wizards.
Arcane Mimicry
At 2nd level, you gain the ability to analyze and learn spells when you see someone cast them. As a reaction, when someone you can see within 60 feet of you casts a spell, you can make an Intelligence (Arcana) check against a DC of 15 + the spell's base level. For instance, if you were trying to copy a fireball cast with a 4th level slot, the DC would be 18 because fireball is a 3rd level spell. On a success, add the spell to your list of prepared spells.
To learn a spell this way you must be able to see and hear any somatic or verbal components, the spell must be in the wizard spell list, and it must be at least 1st level and of a level that you can cast. When you finish a long rest, the spell is removed from your list of prepared spells. You may copy the spell into your spellbook by spending time and gold, as if you were copying it from a scroll or another wizard's spellbook. Once you copy a spell this way, you can't use this feature again until you finish a long rest.
Normally at second level, you get a feature related to how you learn spells and a feature that defines the flavor of the archetype. In this case, one feature does both. The idea is that you can watch someone cast a spell you can learn, then you can use it until you either write it down or forget it.
Is this good for a 2nd level feature? It's similar enough to the Arcane Trickster's 17th level feature that I'm worried.
Arcane Awareness
Starting at 6th level, you've spent enough time observing magic to gain supernatural perception of it. You may cast detect magic at will without expending a spell slot.
I figured the best solution for balance was to just copy the Eldritch Sight invocation. If a warlock can take it at 2nd level, it should be balanced for a wizard at 6th.
Alternative option. If you detect the effects of a wizard spell with detect magic or identify, you can attempt to copy it at disadvantage.
Acquired Immunity
At 10th level, you have been hit by enough spells to learn how to take a hit. You have advantage on saving throws against spells you know. Furthermore, you are resistant against the damage of spells you know.
This is the abjuration school's Spell Resistance feature, limited to only spells you know to balance out the fact that you get it earlier. If that's still too strong, I could limit it to spells that you have prepared instead, but that might be too much. I could also swap it to 14th level.
Combat Copy
By 14th level, you have copied so many spells that you can do it by reflex. As a reaction when you take damage from a spell, you can expend a spell slot to reduce the damage you take five times the spell slot's level. If you reduce the damage to 0, you can use your Arcane Mimicry feature to copy the spell as part of the same reaction.
Is this balanced? It's sort of the Bladesinger's 10th level feature limited to only spells, plus the Arcane Trickster's 17th level feature, except it doesn't disable their usage of the spell.
Other Feature Ideas
Copy more spells per rest, swapping out prepared spells. Copy 1 non-wizard spell/long rest, but not record it in spellbook. Absorb spell to restore slot 1x/rest. Add proficiency bonus to counterspell/dispel magic.
Balance notes
Arcane Mimicry DC Balance
| Spell Level | Wizard Level | Proficiency Bonus | Int Modifier | Arcana Modifier | 10 + spell level (necessary roll) | Xanathar's Method | 10 + 2x spell level | DC + spell level |
|---|---|---|---|---|---|---|---|---|
| 1st | 1st | +2 | +3 | +5 | 11 (6) | 16 (11) | 12 (7) | 14 (9) |
| 2nd | 3rd | +2 | +3 | +5 | 12 (7) | 17 (12) | 14 (9) | 15 (10) |
| 3rd | 5th | +3 | +4 | +7 | 13 (6) | 18 (11) | 16 (9) | 18 (12) |
| 4th | 7th | +3 | +4 | +7 | 14 (7) | 19 (12) | 18 (11) | 19 (12) |
| 5th | 9th | +4 | +5 | +9 | 15 (6) | 20 (11) | 20 (11) | 22 (13) |
| 6th | 11th | +4 | +5 | +9 | 16 (7) | 21 (12) | 22 (13) | 23 (14) |
| 7th | 13th | +5 | +5 | +10 | 17 (7) | 22 (12) | 24 (14) | 25 (15) |
| 8th | 15th | +5 | +5 | +10 | 18 (8) | 23 (13) | 26 (16) | 26 (16) |
| 9th | 17th | +6 | +5 | +11 | 19 (8) | 24 (13) | 28 (17) | 28 (17) |
10 + spell level is just sort of a baseline to compare to. Xanathar's Method is 15 + spell level, and comes from the Identifying a Spell section on p85. The other two methods are me trying to create something that actually makes it more difficult to copy spells of your level, rather than scaling with level
Combat Copy Reduction Balance
| Slot Level | Wizard Level | 5x Spell Level | Wizard level + Spell level | Wizard level + Spell level + Int mod | Wizard level + Spell level + 1d10 |
|---|---|---|---|---|---|
| 1st | 1st | 5 | 2-21 | 2-26 | 3-31 |
| 2nd | 3rd | 10 | 5-22 | 5-27 | 6-32 |
| 3rd | 5th | 15 | 8-23 | 8-28 | 9-33 |
| 4th | 7th | 20 | 11-24 | 11-29 | 12-34 |
| 5th | 9th | 25 | 14-25 | 14-30 | 15-35 |
| 6th | 11th | 30 | 17-26 | 17-31 | 18-36 |
| 7th | 13th | 35 | 20-27 | 20-32 | 21-37 |
| 8th | 15th | 40 | 23-28 | 23-33 | 24-38 |
| 9th | 17th | 45 | 26-29 | 26-34 | 27-39 |
Minimums are based on +0 Int, 1 on d10, and lowest level you can possibly have that slot level. Maximums are based on +5 Int, 10 on d10, and 20th level wizard