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That's what I wanted to do all along, I never said I wanted to get rid of the old fighting styles. If you want your character to be broadly proficient with every one-handed melee weapon, you can, but it you want something more specific to a certain type of weapon, you can have that too.

The reason a greatsword deals more damage than a dagger, the reason a longbow can make ranged attacks, the reason a fireball deals fire damage, is because that's how those things would work in our world. DnD could have abstracted away everything and just made every weapon work exactly the same...

Okay, but by far the most common thing that DnD characters use their weapons for is attacking with them, and as far as attacking with the weapons is concerned, there is no differentiation between the longsword and the battleaxe. Yes they're called different things, yes they look different, yes...

The case where a monster has less HP than you can deal in one swing is the only case where my math doesn't work. You won't always roll your average damage, so if a creature has 20 HP and you deal 1d6+7 damage per hit, your odds of killing the monster in 2 hits are higher than they would be if...

With Dueling Style, a thrown Javelin will outdamage a longbow, 1d6+2 averages to 5.5 while 1d8 averages to 4.5 (note that a thrown melee weapon still counts as melee for the purposes of dueling style)

Why?

When we have less attacks per round, the monsters also have less HP, so the static +2 damage means more. For the extreme case, let's look at level 1. Instead of an Ancient Red Dragon, we'll use a Zombie, which has AC 8 and 22 HP. our longsword attack deals 9.5 (1d8+5) damage with Dueling and 7.5...

I guess this is where we have to agree to disagree, because in my opinion, no it's not. The same way that if WOTC came up with a new class that was completely identical to the fighter class in every way, only having a new name, that wouldn't really count as a different class.

I understand that, but what exists in the PHB isn't describing fighter than can excel with a broader range of weapons, it's describing a fighter that can use a bunch of identical weapons equally well. If you're a fighter with dueling Style, then you're using a weapon that deals 1d8+2+your stat...

The point of this math wasn't to calculate specific DPR, it was to calculate the amount your DPR would increase by having or not having the Great Weapon fighting style. Yes the Precision attack will increase your damage, but it will increase your damage by the same amount if you had Great Weapon...

Okay, let's do that then: Shield Master + Dueling: using the shield bash to shove your target prone: Adult Red Dragons have a strength bonus of +8. With Expertise in Athletics (which you can get from 1 level in Rogue) you can get your check up to +18, which means the dragon would have to roll...

But if you have a damaging fighting style, you'll be able to defeat that dragon/wizard in fewer rounds, leaving them fewer opportunities to use their abilities on you. Let's look at the most extreme case, which is archery style in combination with the feat sharpshooter. An Adult Red Dragon has...

Well in that case there's always the magic weapon spell, or the Improved Pact Weapon Invocation.

And if the dragon breathes fire at you, or uses its frightful presence on you, or the enemy wizard casts dominate person on you, then Defense style is saving you nothing, because it doesn't affect saving throws.

There are two reasons I didn't want these to be feats: firstly, it gives a big advantage to fighters as compared to Paladins and Rangers: Fighters already get 7 ASI as compared to the usual 5 and can work with a single stat instead of needing two. Assuming you start with 16 in your relevant...

For fighters, the effectiveness of static damage bonuses scales with the number of extra attacks you get. +2 damage per hit for one hit is a lot less than +2 damage per hit for 4 hits. A 20th level fighter who uses action surge and makes one attack as a bonus action can trigger the damage bonus...

That's true, but the current fighting styles mostly have that problem as well. If you have the dueling style and find a +1 Longbow, or a +1 Maul, you can't use it effectively. The DM still has to tailor the magic items they drop if they don't want to give the PCs something they can't or don't...

Except in the extreme cases where an opponent hits you on less than a 1 or misses on more than a 20 (where +1 AC does nothing), adding +1 to AC always decreases your chance to hit by exactly 5%, since 5% is the odds of your attacker rolling the one dice result that would hit if you didn't have...