# How do flat modifiers (like those from magic weapons) affect DPR comparison in GWF vs TWF?

This question has some answers with fantastic calculations comparing the Great Weapon Master feat to the Dual Wielding feat.
I'm interested in comparing Great Weapon Fighting and Two Weapon Fighting from the Fighting Styles available to the Fighter Class.

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, even if the new roll is a 1 or a 2. The weapon must have the two-handed or versatile property for you to gain this benefit.

Two-Weapon Fighting: When you engage in two-weapon fighting, you can add your ability modifier to the damage of the second attack. - PHB pg.72

My understanding is that, all other things being equal, TWF beats GWF in average DPR until ~level 5 at which point GWF takes over. However, I wonder if adding in extra per-hit modifiers would favour TWF for longer, and if so, how much longer, and how big would the modifier have to be?

Assuming the following base character, but with whichever undefined features best support the fighting style, Which out of TWF and GWF facilitates the highest DPR build, and if it swaps over at a certain level, which level?

• Human Fighter
• STR 18
• No Feats Allowed
• GWF uses a Greataxe(d12) and TWF uses two Shortswords(d6)

Give 3 result sets:

1. All weapons are +1 magical weapons (to hit and damage)
2. All weapons are +2 magical weapons (to hit and damage)
3. All weapons are +3 magical weapons (to hit and damage)
• Jul 26, 2018 at 21:17

# Base Damage (at Level 1):

GWF

• Without GWF, d12 has 1/12 chance of base damage 1 through 12, so each round is 1d12 + Strength Mod or 6.5 + 4 = 10.5 avg DPR.

• With GWF, rollin a 1 or 2 triggers a re-roll, returning on average 6.5. (I was initially confused about how to calculate this, so I had to ask this math.se question) Replacing those results with their average returns gives an average damage roll of 7.33, so:

• GWF, STR 18 (mod 4) yields 7.33 + 4 = 11.33 avg DPR.

• As Spear Carrier pointed out, using a 2d6 weapon synergises better with GWF as there are twice as many chances to get a re-roll. This brings the Greatsword's average damage up to 8.33, which gives 12.33 when STR Mod is added.

TWF

• Without TWF, d6 has 1/6 chance of base damage 1 through 6, so with two attacks, each round is (1d6 * 2) + Strength Mod or (3.5 * 2) + 4 = 11 avg DPR.
• With TWF you get to add the ability modifier twice, so:
• TWF, STR 18 (mod 4) yields (3.5 + 4) * 2 = 15 avg DPR.

Basically TWF lowers your base weapon damage, but gives you 1 extra full attack action for the price of your bonus action. Before 5th level, this makes a considerable difference, especially if you're looking for crits, due to the extra attack roll (though at low levels your build probably isn't optimized that much for crit-fishing).

# Charts to lay out average DPR:

Assuming you're not going to get more damage out of a bonus action (which Eldritch Knight's War Magic (PHB p. 75) might give you, or some of the Battle Master maneuvers (PHB p. 74), for example) it scales like this:

As you can see, even without magic weapons, TWF is easily in the lead before level 5, and then still out-performs the greataxe with anything better than just the STR Mod from a score of 18. But because the only thing TWF gives you that scales is one extra use of your modifier, it's got to be high to offset the extra (greater) weapon damage that great weapons give on each attack once we start stacking more attacks on.

# Getting TWF to beat GWF at Level 20

Once you get 4 attacks per turn at level 20, even without GWF a Greatsword outperforms two Shortswords with TWF until the modifier reaches+10 - that's a +3 magic weapon (DMG p.213) and a Belt of Fire Giant Strength! (DMG p.155) Make it a Belt of Storm Giant Strength and you can beat the Greataxe with GWF due to a combined modifier of +12, but to beat the GWF Greatsword you'd need a whopping +16, and I'm not sure where you'd get that:

Of course, before Level 11 a total modifier of 7 is enough for TWF to stay in front, and even then they tie at 58 Avg DPR with a modifier of 11 - tough, but doable. More than that and TWF pulls ahead again for 19 full levels.

# What about with Flame Tongue?

Spear Carrier's answer referred to Flame Tongue weapons (DMG p.170) as a way of helping TWF's viability, which intrigued me: that doesn't add to your bonus, but rather stacks on extra (fire) damage die. So I decided to check it out and see how far it got you. Assuming a Flame Tongue weapon is available to either party, it doesn't do a lot, though - at level 20 you still need a total modifier of 15, which I'm pretty sure can't be achieved with official material. (Basically it amounts to adding 7 average damage per attack for both builds.)

# Final considerations

The only reason I can imagine going for TWF for a L20 Fighter if optimization is what you're after is if you're going crit fishing, and that one extra attack might land it for you. Even then, though, you're losing that bonus action that a Battle Master or Eldritch Knight could use to add more damage every time, rather than just 3/20 of the time, and GWF only needs 1 magic weapon, leaving an extra attunement slot.

Thanks András and Protonflux for pointing out my calculation errors in an earlier edit!

• 1d12 with GWF has an average of 7.33 (6.5*12+13-3)/12 Feb 25, 2019 at 10:58
• @András where do you get that? Dice gets rolled max 2 times, a second time only if it's on a 1 or 2. This yields 12 potential first rolls, two of which yield another 12. That's 34 possible results. Expanded out, the sum of these possible results is (1+2)*2 + (3+4+5...+11+12)*3 which yields 231. Divide by number of eventualities (34) yields a mean of 6.79411764705882. I'm curious how you arrived at that calculation - could you explain it to me? Feb 25, 2019 at 22:10
• the calculation is simpler, and the result is higher than yours Feb 26, 2019 at 6:25
• it is pretty well explained on my link too, with more than 60 upvotes... Feb 26, 2019 at 9:01
• On your table for lvl 20 TWF starts beating GWF at a StrMod + Wpn Bonus of 10 not 12 as the colour coding appears to indicate. Feb 26, 2019 at 10:47

# GWF is better from level 5

With the right weapon (Greatsword) GWF wins if no magic items are involved. Also, 2 magic weapons are twice as hard to obtain, and might take up 2 from your 3 attunement slots.

## The numbers

Greatswords do the best damage, with GWF it is 8.33 per hit.
Shortswords will be used for comparison, without Dual Wielder 3.5 is the best damage you can do with TWF.

I comared damage output on levels 1, 5, 11 and 20, so 1, 2, 3 or 4 attacks with GWF, one more with TWF. The charts go from +3 damage bonus (everyone should be able to start with 16 in their primary ability), and they end at 13. It is more than the sum of the bonus from 20 Str (+5) plus Flame Tongue (+7).

### Level 1

TWF: 2 * ( 3.5 + 3 ) = 13
GWF: 1 * ( 8.33 + 3 ) = 11.33
TWF wins from the beginning.

### Level 5

TWF: 3 * ( 3.5 + 4 ) = 22.5
GWF: 2 * ( 8.33 + 4 ) = 24.66
GWF wins at the beginning, TWF gets the lead at +7 bonus, but that is already hard to achieve. You need two +2 magic weapons, or need to be raging, or something similar on top of a high Str (or Dex)

### Level 11

TWF: 4 * ( 3.5 + 5 ) = 34
GWF: 3 * ( 8.33 + 5 ) = 40
GWF wins at the beginning, TWF gets the lead at +12 bonus, but that is close to impossible. Two Flame tongues plus 20 Str is enough.

### Level 20

TWF: 5 * ( 3.5 + 5 ) = 42.5
GWF: 4 * ( 8.33 + 5 ) = 53.33
GWF wins at the beginning, TWF gets the lead at +16 bonus. Two Flame tongues plus Belt of Storm Giant Strength is needed, using up all your attunement slots for TWF.