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In an answer to a related question, linksassin suggests an untested variant rule to apply some wizard flavor to the sorcerer class. I've attempted to formalize this approach and want to verify that I haven't missed any glaring balance issues before playtesting. Have I? You can read the variant rule below:

Variant: Learned Sorcery

Sometimes a sorcerer chooses to study their inborn magic, much like a wizard, and concentrate on a specific type of magic that they can wield. If this is the type of sorcerer you want to create, your Game Master might allow this variant feature at 3rd level, which replaces the Metamagic feature.

Sorcerous Study

At 3rd level, you choose an Arcane Tradition from the wizard class. This becomes the focus of your study. You immediately gain the 2nd-level features from your chosen Arcane Tradition.

At level 10 you gain the 6th-level feature of your chosen Arcane Tradition, and at level 17 you gain the 10th-level feature.

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    \$\begingroup\$ How do you spend your sorcery points? Just to regain spells? \$\endgroup\$ – András Nov 5 '18 at 20:15
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    \$\begingroup\$ @András that's what you'd be limited too, yes. Kind of makes it comparable to Arcane Recovery (since you have wizard features anyway) \$\endgroup\$ – David Coffron Nov 5 '18 at 20:16
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As a Single-classed Sorcerer, this is probably fine

I'd err on the side of feeling this is maybe a bit underpowered (even for Sorcerers), if only because Metamagics are pretty important to Sorcerers. Having the ability to force Disadvantage on a critical spell's saving throw, or being able to cast a spell without doing something to give away its source can have pretty significant ramifications on how an encounter plays out, and taking those features away needs to come with significant benefits. But because many of those benefits still depend on your Intelligence Modifier, there's going to be an upper limit on how powerful those benefits can be, at least unless the Sorcerer permits themselves to put points into INT.

Watch out for Multiclassed Sorcerer/Paladin builds

It is very difficult for a Paladin to gain Wizard levels. They have to maintain decent stats on their Strength, Charisma, and Intelligence scores, meaning other important stats (like, for example, Constitution) are going to suffer. So any Paladin that wants to include some Wizard features in their arsenal has to contend with those limits.

With this variant, one major hurdle has been lifted, and a Paladin would be able to gain access to, say, the War Mage's "Arcane Deflection feature" by only taking 3 Sorcerer levels, and not having to make (significant) sacrifices to their ability scores.

A Multiclassed Wizard/Sorcerer could gain access to two different Arcane Traditions

A Wizard2/Sorcerer3 (or Wizard6/Sorcerer10) will have the ability to pull from the feature set of two different Arcane Traditions, an ability not normally available in the game*, and potentially exploitable in its own right. A Bladesinging Wizard with a 3 level dip in Sorcerer to pick up the War Mage features would have a much higher AC than either of their respective Archetypes were balanced around.

One thing you'll need to evaluate if you permit this variant is what kinds of combos now exist from combining the features of two different Arcane Traditions, and whether you want to permit such a multiclassed character to exist.

Whatever you permit, the INT modifier will limit the power of this variant

So long as the features of these Arcane Traditions still depend on your INT modifier (which for many of them is the case) there will still be some degree of Multiple-Ability-Dependency for any Sorcerer that takes this option, and since INT is generally not that useful otherwise, this will mean that the character will need to devote more points away from stats like Dexterity or Constitution, which are often desirable for spellcasters to boost AC/HP/Concentration checks.

* (except to Theurgy Wizards/Clerics, which generally aren't regarded as being balanced for their own reasons)

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    \$\begingroup\$ The main reason for Paladins to multiclass to Sorcerer is Quicken Spell. Without that, they are better off with Warlock. \$\endgroup\$ – András Nov 6 '18 at 10:10
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It is fine, a bit on the weak side

You are trading something very powerful for the watered-down version of something much weaker.

Metamagic is the most powerful feature of Sorcerers

  • Empowered Spell can save botched roll (I did roll 14 with a Fireball once)
  • Heightened Spell can greatly reduce the risk of wasting a spell slot and your only action
  • Quicken Spell can greatly increase your damage output with the right cantrips
  • Twin Spell lets you target more enemies, again greatly reducing the risk of wasting a spell slot and your only action

Wizards mostly rely on their spells

Arcane Ward is nice, and Portent is great, but ultimately what makes a Wizard is access to more and better spells than anyone else.
Beside Fire Storm I can't think of any spell that a Wizard would want but can't have while Sorceres have it.

Multiclassing

Everyone I have ever seen multiclassing into Sorcerer for optimization did so because of Quicken Spell or some other metamagic. That is what the Paladin/Sorcerer guide raves about, and if you can't have that than Warlocks give better cantrips and features, and Bards a wider selection of spells and better features if you are shopping for a Cha-based full caster.

Yes, Durable Magic with +2 to AC and saves would be awesome for a Paladin, but it comes only on level 17, by that time you could do better with a singel-class Paladin.

Sorcerer/Wizards are so far behind the curve anyway because of MADness that I would not worry about them.
Bladesinger/War mages will have great AC, but not much else, and could only cast cantrips after the turns with that great AC.

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