That's appreciated. So where I am is it looks to me like most arcane traditions aren't better at wizardry than BS. Maybe Divination is. Maybe Evoker is. Any others?
And then I'm struggling with this Champion thing. He seems to die twice as often as BS! Putting that together with the above.... ?
They are all better at wizarding, because none of them require mage armor as a default cast and reserving slots for shield just to be in melee.
And, if you account for crits properly, the champion does as well as the bladesinger while tanking -- they both die in the first 5 round fight. If you use either of my scenarios -- the 2 round party tanking (which is far more accurate than 5 rounds) or the solo encounter, the champion fares better because of the 1-shot nature of crits against the bladesinger.
i'm a bit frustrated that you haven't addressed the crit issue with your analysis at all and yet still insist on referring to it as if no serious challenge to it has been made made and everyone agrees with it.
Here it is again:
Level 4 bladesinger: INT 20, DEX 18, 14 CON
AC: 17 (mage armor, dex), 22 when bladesinging
HP: 21, effective 36 with 1 use of shield (i find this to be the most efficient way to model shield - just add the damage from one attack to hp)
Attack routine: 1 GFB w/ rapier at +6 to hit, 1d8+4 damage to single target.
Level 4 Champion: STR 20, CON 18, DEX 14
AC: 18 (platemail)
HP: 44, 53 with second wind
Attack routine: 1 greatsword w/ GWM and GW fighting style (assumed to add 1.33 to DPR): +2 to hit, 2d6+16.33 damage to single target, second attack on crit, crit chance 10%
CR 4 melee monster: +3 in controlling stat, +2 proficiency
AC: 13
HP: 125
Attack routine: multiattack 2, +5 to hit, 15 damage each hit, crit damage 26
Combat -- 5 rounds in melee.
CR4 vs Bladesinger:
CR4 hits bladesinger on an 18 or better, so 15% of the time, inflicts 15 damage per attack, attacks twice per round. Ignoring criticals, this is 10% chance of 15 damage twice per round or 3 damage per round. Bladesinger can survive 7 rounds without shield use or 12 rounds with shield. Can survive 2 fights without crits.
Now add in crits: 10% chance of crit per round, damage drops bladesinger. Cannot be added fractionally, as damage does not accumulate. So, after first round, chance of crit ending the fight is the chance of no crit in each preceeding round x 10%.
1 round: 10% chance of fight ending.
2 rounds: 19% chance of fight ending.
3 rounds: 28.1% chance of fight ending.
4 rounds: 37.2% chance of fight ending.
5 rounds: 46.3% chance of fight ending.
The critical chance controls here, so at anything more than 5 rounds, even with shield usage, the bladesinger drops to statistical analysis. And, at 5 rounds, she hasa 46% chance of dropping outright. If you do 2 of these fights, regardless of anything else, the % chance of the bladesinger dropping is 92%.
Now, let's add up the damage output of the bladesinger's contribution to dropping the CR4:
Bladesinger hits on a 7+, or 70% of the time. They deal 8.5 damage on a hit, or 6 damage per round. At the end of 5 rounds, the bladesinger has contributed 30 damage, meaning her party has contributed 95 damage over 5 rounds, or 19 DPR per round. The combined group does 25 damage per round.
CR4 vs Champion
CR4 hits the Champion on a 13+, or 40% of the time, two attacks at 15 damage each. Crits 5% of the time, but crit damage isn't enough to one shot, so we'll add it in fractionally. 35% chance of normal hit plus 5% chance of crit at 26 damage twice per round is 6.55. Champion can last 8 rounds with second wind, 6.7 without, so survives the first fight. Without healing, will not survive the second.
Now, let's look at the damage outlay of the Champion. Using the power attack function of GWM, the champion hits on a 11+ (50%) and crits 10% of the time. So, 40% at 23.33 damage and 10% at 30.33 damage plus an extra attack for a total of 30.33 + another 40% of 23.33. That's 13.3 DPR.
Assuming the same party as the bladesinger's, the damage outlay of the group jumps from 25 damage per round to 32.3 damage per round. Instead of 5 rounds to kill the CR4, the Champion's party takes just 4 rounds. This means the Champion really only takes 28 damage, which is about half of his with second wind total of 53. He'll need a cure spell or potion between fights, but he'll make it.
This analysis gets even better for the Champion at level 5.
Conclusion
So, the bladesinger in melee effectively loses 3 first level slots to do be a melee tank. That's a huge outlay of resources in Tier 1 (and II, honestly), to ape being a fighter. But even with that expenditure, the bladesinger is at serious risk in melee to crits, which she cannot mitigate, because crits can empty her shallow hp pool very quickly. In a pinch, the bladesinger can be a tank, but it's a high risk, high resource cost choice, which seems okay to me and not overpowered. The Champion isn't making that cost choice to tank, and, looking at the damage outlay, the Champion stays clearly ahead and ends fights more quickly, thus reducing his exposure.
And, really, that's the bottom line: the bladesinger can expend a lot of resources to approximate the survival rate of a Champion in the melee tank role. They lose out to EKs and BMs, though, as their abilities significantly improve their tanking. And that's why it's fine -- the bladesinger can do it, but has to pay a lot for the ability, and it's still not better than what the fighter does even with very high stats.
