Fighter Barbarian Primal Path Homebrew

[BRKNdevil]

K, So with the input of a few people i decided on this following setup

Fighter Barbarian
You are a trained madman who keeps focus and remembers his training in the red haze of RAGE.

Fighting Style
At 3nd level, you adopt a style of fighting as your specialty. Choose one of the following options. You can’t take a Fighting Style option more than once, even if you later get to choose again.

Dueling: When you are wielding a melee weapon in one hand and no other weapons, you gain a +2 bonus to damage rolls with that weapon.
Great Weapon Fighting: When you roll a 1 or 2 on a damage die for an attack you make with a melee weapon that you are wielding with two hands, you can reroll the die and must use the new roll. The weapon must have the two-handed or versatile property for you to gain this benefit.
Protection: When a creature you can see attacks a target other than you that is within 5 feet of you, you can use you reaction to impose disadvantage on the attack roll. You must be wielding a shield.
Maybe Two Weapon Fighting as well?

Improved Critical
At 6th level, your weapon attacks score a critical on a 19 or 20

Ability Score Improvement
At 10th Level...
Ability Score Improvement or Feat
With the extra training you put yourself through you train your body or learn more tricks than the average barbarian.

Extra Attack
Beginning at 14th level, you can attack 3 times when you make an attack action

Reason for this setup is to show a barbarian that went through professional training and study like a fighter would normally endure. So then it leverages the higher crit range and his reckless attacks to trigger the additional weapon dice from the barbarian class features to add to the critical hits. With the extra attack gained at the end i think its like a 50% chance to get a crit once a round. But for some reason I can do force moment balance equations but statistics i screw up on so if someone else can do the math that would be lovely.