- 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.
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, d12 has 2/12 chance of re-rolling, so 34 possible results. 1 and 2 are 2/34 each, every other number is 3/34 yeilding a mean of just over 6.79, so:
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 6.79 + 4 = 10.79 avg DPR.
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.
Basically TWF lowers your available weapon dice type (compared to the Greataxe), but gives you 2 full attack actions for the price of your bonus action. Compared to the Greatsword (at Level 1), you roll the same number of dice, but GWF lets you re-roll versus TWF letting you add your bonus an extra time. 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 (it does seem unlikely thatwhich EK's War Magic might give you could, regardlessor some of your buildthe Battle Master maneuvers, for example) it scales like this:
As you can see, even without magic weapons, GWF doesn't getTWF is easily in the upper hand until Level 11lead before level 5, when you getand then still out-performs the extra attack feature forgreataxe with anything better than just the second timeSTR Mod from a score of 18. AndBecause the only thing TWF gives you need a flat +3that scales is one extra use of your modifier, it's got to damagebe high to keep TWF inoffset the leadextra (greater) weapon damage that great weapons give on each attack. At
#Getting TWF to beat GWF at Level 20
Once you get 4 attacks per turn at level 20, I dideven without GWF a Greatsword outperforms two Shortswords with TWF until the mathmodifier reaches+10 - that's a +3 magic weapon and a Belt of Fire Giant Strength! 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:
You'd needOf course, before Level 11 a +3 weapon and other flat modifiers that total 9 to stay ahead with TWF. If the only modifier you can use for itof 7 is STRenough for TWF to stay in front, and once you hit that would mean you'd needthey tie at 58 Avg DPR with a STR scoremodifier of 28 minimum. You're going to need some serious homebrew to manage11 - tough, but doable more than that! and TWF pulls ahead again for 19 full levels.
Of course#What about with Flame Tongue?
Spear Carrier's answer referred to Flame Tongue Daggers as a way of helping TWF's viability, upwhich intrigued me: that doesn't add to Level 19your bonus, you'dbut 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 doing betterachieved with any Strength Modifier + Weapon Bonus combo that totals 7, soofficial material.
#Final considerations
The only reason I can imagine going for TWF for a STR 20L20 Fighter if optimization is what you're after is if you're going crit fishing, and +2 weapon would dothat one extra attack might land it for you. And that's 19 full levelsEven 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.
Thanks András and Protonflux for pointing out my calculation errors in an earlier edit!