This is another "new skill mod" I made, along with Unarmored. I have made the skill exactly comparable in advancement to One-Handed.
SKSE Required - http://skse.silverlock.org/
If you are familiar with my mod Unhindered, this works somewhat similarly to the compatibility version. Merely by hitting people while Unarmed, you will gain experience towards the next rank equal to what it would be in One-Handed. The formula for how much experience is required per level is also the same as One-Handed.
The formula for unarmed damage is .4 * Skill rank + racial natural unarmed damage. Khajiit no longer have their 'Claws' spell, which made them extremely overpowered at early levels.
(As in, I made it through Bleak Falls Barrow on Master difficulty without taking damage at level 1).
Khajiit do however begin with a rank of 25 in Unarmed, while argonians have only 15. The other 'warrior' races (Redguard, Orc, Imperial, Nord) have a starting rank of 20. All other races begin at 15.
By using a 0 mana spell you will start the game with called Check Unarmed Stats, you can do just that and it will tell you your current rank and how far you are towards your next rank.
There is also a spell that summons a big ball of light that if talked to will grant you perks (should you have perk points to spend, otherwise the spell does nothing) according to the following tree:
Pugilist: 5 ranks, each granting a 20% bonus to unarmed damage leads to the following two perks
(Skill rank 15, 20, 40, 60, 80 required)
Brawler - Unarmed power attacks deal 25% more damage per rank (2 ranks) (Skill Rank 30, 50 required)
Pressure Points - Unarmed attacks ignore 20% of armor per rank (2 ranks) (Skill Rank 30, 50 required)
Brawler leads to Float Like A Butterfly - 3 ranks of 20% reduction in Unarmed power attack stamina cost (Skill Rank 45, 65, 75 required)
Butterfly leads to:
Paralyzing Palm: Unarmed Power attacks have a 10% chance of paralyzing the target for 5 seconds (Skill Rank 80 required)
Immobilize - Unarmed Power attacks have a 30% chance of slowing targets down by 35% for 5 seconds (Skill Rank 80 required)
Internal Wounds: Unarmed Power attacks cause 3 damage/sec for 6 seconds (Skill Rank 80 required)
Pressure Points lead to:
Sting Like a Bee - Unarmed strikes have a 1% chance to kill per rank a target under 50% health (3 ranks) Skill Rank 45, 65, 75 required
which leads to:
Take the Wind: Unarmed strikes deal 20 stamina damage
Concuss: Unarmed strikes deal 20 magicka damage at skill rank 80
Disarming Strike: Unarmed strikes have a 5% chance of disarming the target at rank 80
Oh yeah, and your gauntlets armor rating is automatically added onto your unarmed damage. It is the base value and does not include your armor skill bonus or smithing bonuses. (That is possible, but would be extremely unbalanced.)
I recommend the version without Claws if you play Khajiit, as Claws upsets the delicate numerical balancing act I've done with this mod. However, it is possible that it would be incompatible with another mod (although EXTREMELY unlikely, as Claws is a rarely edited thing) so I've made the other version available. Also for people who like easy gameplay, or are using mods that make the game significantly harder to the point of requiring a bit more oomph behind their punches.