Warriors have an additional attribute: Valor. They gain Valor when they defeat a worthy foe (or cause them to admit defeat, or submit). You lose Valor when you are forced to stand down, admit defeat, or retreat.
A being is considered a worthy foe when they have at least as much valor as you (or, if they are a monster, if they have an equal or higher Rank than your Renown.)
When you’re in combat, you gain the twice the difference between your Valor and your enemy’s as a bonus to your attack and damage rolls.
If you have 3 Valor and your enemy has 1, you get a +2 bonus to attack and damage.
If you have 3 Valor and you are fighting a mixed group of enemy warriors (two at 1 Valor, and one at 4 Valor) you get a +4 bonus against the 1 Valor enemies and no bonus against the 4 Valor enemy (who will themselves get a +2 bonus against you).
As you can see, the only way forwards for a Warrior is to find victory, to never back down, and to continue to challenge themselves in battle.
Note: This can lead to fun scenarios where player characters pick on an old man only for the warrior in the group to realize that this seemingly frail old man is actually a retired weapon master, and also for the warrior to recognize that the big blustering barbarian is actually a big wimp and will fold after a little pushing. It also encourages Warriors to realize that some fights are just not worth their time, which is fun in a very particular way to me.
Note 2: This is intended to work alongside the Dungeon Core rules I was writing, where Warriors inherently get a larger damage die than other classes, better hit points, and an additional ‘feat’ that makes them a little different. DC also doesn’t use attributes, so a Warrior in this scheme has hit points, gear, a Valor score, and some skills.