This didn't get any input before, but I have some of my own.
My playtesting of the archetype went about as expected:
1. The archetype is ridiculously powerful if the Cavalier is mounted, and attacking a challenged foe (see below).
2. The archetype is on a par with the other PHB Fighter archetypes if on foot and fighting a challenged foe.
3. In virtually every other circumstances, the Cavalier is a "meh" fighter, not quite on a par with the Champion.
My observations on balance are as follows:
The archetype produces a very, very specialized character, one which is very, very good at a narrow task list. While the powers appear at face value to be remarkably powerful, they are only applicable in a narrow set of circumstances. The behavioral strictures (taken almost wholly from the 1e Cavalier class found in the Unearthed Arcana sourcebook) also produce balance in their rigidity, and the almost foolhardy requirements of engagement. The amount of times the Cavalier will find herself in a position to be exercise her specialized skills are few, and otherwise she's a set of background resources who can't (won't) tank mobs.
Anyway, here's the text, followed by a link to a pretty Homebrewery PDF version. Tell me what you think, and let's discuss it!
The Cavalier
The quintessential knight in shining armor, the Cavalier focuses on being a hero worthy of a minstrel’s song. They are knights-errant, proving their mettle against powerful foes in single combat, as well as practicing the courtly arts. Usually (but not always) born of noble stock, they are as adept at navigating high society as they are dealing blows with the lance. In combat, the Cavalier will seek powerful, intelligent foes, for such foes can see her heraldry, know she is defeating them, and add to her renown. She will attack without regard for whether or not the engagement is wisdom or folly. She will ignore the horde of orcs to get at the orc king and engage him in single combat.
The cavalier will never use missile weapons, as such things are the province of poor infantry and incapable of granting renown. Likewise, they will never wear non-metallic armor; they will go without armor before wearing anything other than at least chain mail. The Cavalier will never use a mount other than a standard, non-magical warhorse. Lesser steeds are beneath the dignity of a Cavalier, and magical or monstrous steeds are eschewed by Cavaliers as they bestow an unfair advantage. She will have either the Knight or Noble background. The Cavalier will be – or once have been – a member of a knightly order.
A Cavalier may never have another character class, nor may she take the Mounted Combatant feat.
Knightly Challenge
Your purpose is to cover yourself in glory by conquering powerful foes in single combat. When you choose this archetype at 3rd level, during combat when you are not incapacitated and don’t already have a foe designated, you can issue a challenge against an enemy you can see. The enemy must be able to understand you.
Once you issue a challenge, you cannot designate a different enemy as your challenged foe until either you or your challenged foe is defeated or you end a round without attacking your challenged foe.
While challenging a foe, attacks made by you or your foe against targets other than each other are made with disadvantage.
Valorous Strike
When you choose this archetype at 3rd level, you gain a number of extra damage dice you can deal against your challenged foe.
These dice consist of 1d8 for every three Cavalier levels, e.g., a 9th level Cavalier can deal an extra 3d8 damage to a challenged foe. These dice may be used one at a time or all at once, at your option. Once used, you cannot use these dice again until you have finished a short or long rest.
Jouster
Starting at 3rd level, your training allows you to make a special attack while mounted. As an action when mounted, you can have your mount move up to its base speed, but at least 20 feet, and then you can make a single attack with a lance. On a hit, you deal extra damage equal to three times your proficiency bonus.
When fighting your challenged foe, if he is also mounted you gain advantage on contests to dismount him or being dismounted by him. Should you lose the contest and are unhorsed, you land on your feet, not prone.
Cavalry
Starting at 3rd level, your warhorse can use its attack abilities as a bonus action on your mounted attack.
Improved Mount
You have learned to discern the best mount to use, and any mount used by you is brought to the peak of its performance. Starting at 3rd level, your mount has its maximum possible hit points.
Master of the Joust
Starting at 7th level, when you use your Jouster ability, your attacks score a critical hit on a roll of 19–20. You do not provoke opportunity attacks when using your Jouster ability.
Improved Cavalry
Starting at 10th level, while mounted you combine your warhorse’s hit point total with yours. All damage directed at either of you may be divided between you and your mount however you specify. In addition, when spending hit dice during a short rest, you may spend your mount's hit dice to heal your mount.
Ride Down
Your mount now charges through enemies. Starting at 15th level, when you use your Jouster ability, all enemies on foot between you and your target must make a Strength saving throw or fall prone. Enemies with more than two feet on the ground have advantage on this saving throw.
Mounted Agility
You and your mount are as one. At 18th level, whenever you are mounted and are subjected to an effect which allows a save for half damage, you and your mount take no damage on a successful save. On a failed save, you and your mount take half damage.
Last Stand
Your determination to defeat your challenged foe knows no bounds. At 20th level, you do not fall unconscious from dropping to zero hit points while your challenged foe remains undefeated. This includes dying from taking massive damage, but not effects that kill without dealing damage, such as the Power Word: Kill spell. If your challenged foe dies or falls unconscious, or you end a round without having attacked your challenged foe, this effect ends and you begin to die as normal.
View attachment Cavalier.pdf