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Fixing the Eldritch Knight with War Caster

There is a lot of discussion that Eldritch Knight in 5e is suboptimal when compared to battlemaster fighter / wizard multiclass builds.  There is also discussion that war caster is a feat tax since divine casters can use their shield as a holy symbol for casting.

I think the simplest fix is to interpret war caster with a special case for touch spells.  When casting a touch spell with a weapon in a hand using war caster, the caster can make their melee spell attack using their weapon attack and add weapon damage to the spell effect.  So for example, shocking grasp would grant a single weapon attack with a bonus 1d8 lightning damage.

Is this overpowered?  I don't think so.  The feat comes at level 4 or later.  The attack only gains a significant bonus if the weapon is magic.  Compare this to the rogue's sneak attack at a bonus of 1d6 for no feat cost at level 1.

The following spells could work with this combo (touch spell, no material component, offensive, grants a melee spell attack):  shocking grasp (cantrip) @ 1d8, Inflict wounds @ 3d10(1st level), contagion that inflicts a disease (5th level), vampiric touch @ 3d6 (3rd level)

These again don't seem overpowered considering the spell casting and feat requirements for spell
level.

For an eldritch knight, the feat comes at 4th level, which could be used in combination with shocking grasp.  Not a considerable boost since casters can do this damage at first level, but enough to make eldritch knight more comparable to the multiclass. At 8th I could add vampiric touch.

At higher levels, the trade off becomes spell vs multiple attacks, and so balance is also maintained.

I already talked with my DM about the touch spell with war caster, and he is on board, so hopefully I can prove the balance in game.  Certainly it closely resembles the pathfinder magus which is both fun and balanced.

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