FormerlyHemlock
Hero
Sure, but the Bladesinger doesn't have 55-60 HP and the ability to take half damage on 1/3 to 1/2 of the attacks they'll take like the Barbarian. And it's not like the Barbarian's AC has to be so much worse; at level 5 while the Bladsinger can rock a 20 AC for two fights each rest using Mage Armor and throw the odd fireball, the Barb could easily be running a 15-18 AC unarmoured depending on DEX and whether or not they're using a shield. Honestly, Barbarians have superior defense overall, and superior melee capability, even comparing them at level 6 so they both have extra attack. A Bladesinger needs to use spells to match a Barbarian in this capacity, maybe Mirror Image or some such. But that's okay, and I think kind of the point - a Bladesinger is a powerful melee character provided they invest in it. And for every Mirror Image cast, that's one less Scorching Ray, or Shatter, or Detect Thoughts, or Hold Person.
Let's compute some numbers to make this concrete. I don't have any preconceptions here, I have no horse in this race and don't know how the numbers will turn out, but I do like computing numbers and I think it might be useful to talk in specifics instead of generalities here, so let's compute some.
Since you're talking about 55-60 HP, it sounds like we're dealing with a Barbarian of 5th or 6th level. I'll arbitrarily choose 5th level--at that level a Con 16 Barbarian has 55 HP. Let's arbitrarily assume a Str 18 Dex 14 Con 16 GWM + Polearm Master human barbarian (so, stats are on the high side) and a Dex 18 Con 14 Int 19 high elf bladesinger (originally Int 17, also high-ish stats) who spent his ASI on Int +2. Let's run a round from a mob combat against CR 1/2 Orcs, and a round from an elite combat against, say, a CR 8 Githyanki Knight.
Barbarian: AC 17, 55 HP, 2x +7 for d10+6 (+2 for d10+16), can Reckless Attack, resistance to all (I know he doesn't resist the Githyanki's psychic damage but let's pretend he does, for the sake of analysis), gets bonus d4 attack and gets a reaction attack in mob scenario
Bladesinger: AC 21, 32 HP, 2x +7 for d8+4 (or +7 for 2d8+4, 2d8+4 to 2nd creature with Greenflame Blade), can Mirror Image or Blur, can Shield
Barbarian: AC 17, 2x +7 for d10+6 (+2 for d10+16), can Reckless Attack, resistance to all (I know he doesn't resist the Githyanki's psychic damage but let's pretend he does, for the sake of analysis), gets bonus d4 attack and gets a reaction attack in mob scenario
Bladesinger: AC 21, 2x +7 for d8+4 (or +7 for 2d8+4, 2d8+4 to 2nd creature with Greenflame Blade), can Mirror Image or Blur, can Shield
Barbarian vs. AC 13 Orcs (+5 for d12+3), Reckless attack: Barbarian will Recklessly power attack four times (including the haft strike) for 64.10 points of damage. Each surviving orc inflicts 4.15 points of damage in return after resistance. (Loss ratio: 15.44 : 1)
Barbarian without Reckless: 42.45 inflicted for 2.64 per orc received. (Loss ratio: 16.08 : 1, slightly better than Reckless)
Bladesinger vs. AC 13 Orcs (+5 for d12+3), Rapier, Bladesong, no Shield: inflicts 13.20 damage on orcs. Each orc inflicts 3.20 points of damage in return. (Loss ratio: 4.20 : 1)
Greenflame Blade: increases damage dealt to 19.95 (second attack cannot crit). (Loss Ratio: 6.23 : 1)
Shield: decrease damage inflicted by orcs to 0.90. (Loss ratio w/ Greenflame Blade: 22.17 : 1)
Mirror Image: An orc has a 60% chance to hit a mirror image, so each Mirror Image spell will block a total average of five orc attacks, preventing 16 damage total if no shielding is being done.
Blur: Decreases damage inflicted per orc to 0.74. (Loss ratio w/ Greenflame Blade: 26.96 : 1)
Blur + Shield: Decreases damage inflicted per orc to 0.05. (Loss ratio w/ Greenflame Blade: 399 : 1, a clear case of overkill)
Barbarian vs. AC 18 Githyanki Knight (2x +9 for 5d6+6), Reckless attack: Barbarian will Recklessly power attack three times (including the haft strike) for 28.22 points of damage. Gith inflicts 21.89 points of damage in return after resistance. (Loss ratio: 1.29 : 1)
Barbarian without Reckless: Regular attack twice and power attack with the haft to inflict 16.80 damage on the knight. Gith inflicts 15.89 damage in return after resistance. (Loss ratio: 1.06 : 1, significantly worse than Reckless)
Bladesinger vs. AC 18 Githyanki Knight (2x +9 for 5d6+6), Rapier, Bladesong, no Shield: inflicts 8.95 damage on gith. Gith inflicts 22.90 points of damage in return. (Loss ratio: 1 : 2.56)
Greenflame Blade: not applicable/advantageous
Shield: decrease damage inflicted by githyanki to 11.15. (Loss ratio: 1 : 1.24)
Mirror Image: Gith has an 80% chance to hit a mirror image, so each Mirror Image spell will block a total average of 3.75 gith attacks, preventing 85.88 damage total if no shielding is being done or 41.81 Shield is being used. (May also decrease number of Shields expended.)
Blur: Decreases damage inflicted by gith to 9.61. (Loss ratio: 1 : 1.07) Note that the Gith hits hard enough to have an excellent chance of breaking concentration.
Blur + Shield: Decreases damage inflicted by gith to 1.97. (Loss ratio: 4.5 : 1)
TL;DR against orc mobs, a bladesinger with Blur who does not Shield does half as much damage as a barbarian while taking 20% as much damage--but he has only half as many HP. With a healer in the group, the Bladesinger comes out ahead, otherwise they are even unless the Bladesinger expends Shields.
Against Githyanki Knights, a barbarian does three times as much damage as the bladesinger while taking between two and ten times as much damage in return. Mirror Image is better against Githyankis than against orcs but it only buys you two rounds, barely enough to time to scratch the githyanki's warpaint. (It's better for sorcerers who can Quicken it.) The barbarian can grind though the Githyanki solo with luck--the Githyanki will die after just over three rounds, whereas the barb can expect to die after about 2.5, so it's close enough that he could win sometimes. The bladesinger takes about ten rounds to kill the Githyanki, by which time he'll have run out of shields and already long ago died. The barbarian is clearly stronger against the Githyanki unless the bladesinger stops pretending to be a fighter and pulls out some wizard spells like Lightning Bolt or Hold Person.
Additional factors: The barbarian has a better action economy, because he gets to attack (with no bonus haft attack) while the Bladesinger is busy putting up Blur or Mirror Image. The Bladesinger probably should will an Owl familiar who can Help him get advantage on attacks, not factored into the above computations. (Would increase rapier damage vs. Githyanki to 11.29, a 26% boost.) The Bladesinger likely has a more effective ranged attack (elven weapon training, longbow, high Dex) and the ability to kite if desired (Expeditious Retreat). The Bladesinger is a full wizard with all the non-melee options that implies: Hypnotic Pattern, Wall of Force, Animate Dead, etc. The barbarian does not actually have resistance to githyanki psychic attacks, which will increase his damage taken against an actual githyanki knight by about 50%.
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