So banerett already improves second wind. Making that even bigger is what I usually do.
I heavily redid the Banneret. I can post it if people want, but it is quite a bit different in my home-brew than it currently stands
Samurai's advantage is strong. Stronger than champion crit range when active (at cost); advantage gives as much of a crit boost, and an accuracy boost. In games with easy advantage, it is weaker. In games with more fights/day it is weaker. It doesn't match BM even in good situations at 3.
Existence of non damage meanuevers only makes BM stronger, not weaker. Subclasses with mainly only damage shouldn't fall behind damage from subclass with choice of damage or alternatives.
For cavalier, I would compare baselien BM to a Cav that gets its bonus attack every round.
BM 4 16 str 1d10 polearm gwf with pam+gwf on a 15 ac foe. Uses precision and -5/+10.
Over 3 rounds, 1 reaction, 3 bonus, 3 regular, for 4d10(22)+3d4(7.5)+91=120.5. Hits on 14 (35%), crits on a 20(5%).
Before meanuver dice, 43.7 damage.
If use die for missed by 1 to 6, that happens .3 per attack (2.1 total) for 68% of a hit each. Average hit is 17, 11.5 ish per die, for 24 damage.
0.35 crits at 9 damage per crit, for 3 ish damage.
No ripsote. So total of 70ish damage for 2 and a half dice burnt. (out of 4, short rest refresh)
Same cavalier, but gs, 18 str, gwm, and -5/+10 with advantage bonus attack.
6 taps. 8+ on normal for 11 (70% hit), 13+ on bonus for 23 (64% hit). 0.45 crits for +7 each. about 70 damage.
Uses 3/4 daily punishment uses used. Same damage.
Cavalier also imposed disadvantage on the attacks that ignored them.
In ideal circumstances, Cav just bearely matches simple BM.
I mean, a sentinal Cav that was ignored might exceed BM damage?
I'm going to admit man, you are throwing a lot of stream of consciousness snippets at me, and I'm having a hard time parsing them into full ideas and arguments.
The idea that the Champion at level 3 should match the Battlemaster using all damage abilities at level 3 is a bit problematic for me, because like I said, the Battlemaster might not have all damage maneuvers. This is important, because if the Champion matches the Battlemaster who is going all out damage, then they are more powerful than most other Battlemasters. Now, I get the argument that the Battlemaster has choices and that makes them more powerful, but the point of the Battlemaster is to have choices, and the point of choices is to choose your power level.
If the Battlemaster is the most powerful subclass at all levels, then we need to buff the other fighters perhaps, but we need to do it equally. And if right now the Battlemaster is the most powerful subclass, but the other subclasses are just about equal, then I'm fairly okay with that. But, you keep comparing everyone to the Battlemaster, and I was talking more about whether or not they are all balanced among themselves.
Also, you compared a Variant Human level 4 Battlemaster fighter with Polearm Mastery and Great Weapon Master with a Cavalier with 18 str, a Greatsword and Great Weapon Master. There is already a disconnect here by showing a fighter with a native 3 attacks (allowing for a +39 damage) compared to one with two native attacks (for +28). The Cavalier does match with their mark ability, but that shows a fairly solid balance. When I would be balancing a subclass for the fighter, unless otherwise inappropriate (Arcane Archer) I try and focus on using a Longsword and Shield, no feats. This is because balance between them shouldn't rely on also answering the question "Is Polearm Master Balanced against getting a +2 strength". You have to compare comparable builds, with as few feats and such as possible, then look into if any feats should be considered.
As most subclasses fall behind BM, and I like BM, I like adding second wind riders to every other subclass. And maybe a lesser one for BM, like "if you have 0 dice left, you get one back" at, mid high levels.
I can understand that sentiment, I'm just not sure how much I agree.