Why is two-weapon fighting considered subpar for fighters?

I know this has been discussed before, but I've yet to find a mathematically sound explanation of why two-weapon is vastly inferior to two-handed. I could understand if there are ultimately negligible differences between them, but from what I've read round the vast interweb, TWF is significantly worse than other options the fighter has.

Assuming we roll a 20 STR character, after lvl. 5 raw damage output would look something like this:

TWF (Attack x2 + Bonus + Dual Wield): 1d8x3+15= 39 max

GWF (Attack x2): 1d12x2 = 24+10= 34 max

Dueling (Attack x2): 1d8x2+10+4= 30 max

Now I'm aware GWF allows the reroll of a 1 or 2 in damage, probably bringing its average DPR up higher.

Bonus action-wise, I don't really know of many useful things that you could do/cast without a few multiclass levels, so I don't see a problem with using that bonus every turn to get another hit in, especially for playing a pure Fighter. Sword n' Board does get the useful Shove action with Shield Master, but I can't think of much else.

TWF does require the extra Dual Wielder feat to be useful, but +1 AC is pretty good. (I combo'd with the UA Blade Mastery feat for extra +1 to Hit, and a useful reaction)

As a half-orc Fighter with Champion archetype, 1 extra swing x turn is an amazing chance to keep those crits coming. Same with Battle Master, just an extra attack to get a manuever in. Let alone if you multiclass into Barbarian and use Reckless attacks to essentially roll 6 times for a crit. Heck, an extra hit is an extra Smite for a Paladin.

Even weapon-wise, TWF is an added advantage, letting you use a different damage type, or stacking two magic weapons over one (assuming you find them). So instead of 1 Magic Sword, you'd have maybe a Damage/Element weapon in one hand and an affliction one! Very dependent on your game/DM however.

Why is two-weapon fighting considered subpar for fighters?

• When questioning claims you’ve seen, it helps massively to link to those claims. It will make the question much easier to answer, getting you an answer more quickly, and much more likely to be answered well, covering the specific claims you’re looking at. – KRyan Aug 21 '18 at 15:43
• – NautArch Aug 21 '18 at 15:51
• – NautArch Aug 21 '18 at 15:58
• I am curious: if we look at levels 1-20, is this question actually "Is Two Weapon Fighting a trap option for Fighters?" Or is that question too narrow? – KorvinStarmast Aug 21 '18 at 21:58
• I'm curious why you are comparing TWF with a Feat that benefits it to the other styles without their useful Feats. Wouldn't it be more accurate to compare the TWF style using only light weapons (1d6) to the other two styles you've written out here (which would bring the TWF max damage to 33)? Either that, or mention the Great Weapon Master or Polearm Master feats (which can help out GWF and/or Dueling)? – Gandalfmeansme Aug 22 '18 at 0:03

Okay, so, let's start from your wrong premises

Max Damage does not matter - average does

And you are using the wrong weapon for GWF based on that - Greatsword is better than Greataxe. Greatsword is already superior to Greataxe, but it becomes even better with GWF, when the probability of rolling 1s and 2s is higher.

For reference, the average damage from 2d6 with GWF is $\approx 8.33$ (you reroll 1s and 2s). The average damage of 1d8 is $= 4.5$.

So, for TWF, you deal damage equal1 to $$d_T = (a + 1) \cdot (4.5 + \textrm{Str})$$ where $a$ is the number of attacks you have and $\textrm{Str}$ is the STR Modifier. For GWF, you deal $$d_G = a \cdot (8.33 + \textrm{Str})$$

We can check when things start going badly for TWF, e.g., for a +5 STR modifier (which, by the way, is not exactly a common roll for a 5th level character, but let's bear with your premise)

$$13.33a > 9.5a + 9.5$$ $$3.83a > 9.5$$ $$a > 2.48$$

So, at 5th level ($a = 2$), you are still doing more damage with TWF than GWF. After 11th level, with one more attack, that's no longer true. It gets worse and worse.

Action-Economy

Another thing is: for that extra attack you are using your bonus action. Also note that features like Action Surge will benefit GWF more, since it essentially means $\tilde{a} = 2a$, not allowing you to get an extra bonus action. So, for example, in your Barbarian Multiclass, you would be unable to Rage and make the extra attack in the same turn. As the levels go by, you also get more and more uses for your Bonus Action that will not be used because you are using it for an extra attack.

Opportunity Attack

If you are able to make an OA, GWF is superior again, since it's equivalent to increasing your $a$ by 1. There isn't much to say here other than that.

Better damage dealing feats

Great Weapon Master exists. And it is insanely good. And I'm not even talking about the extra attack you get on critical or killing hits, I'm talking about the second bullet.

Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack's damage.

This increases your DPR considerably. On the other hand, TWFs have... Dual Wielder.. which is not as amazing2, sorry.

Stacking magic weapons

I'm not sure what you meant by Stacking magic weapons, but if you have two +3 weapons, they don't give you a +6 bonus.

You have a bonus to attack and damage rolls made with this magic weapon. The bonus is determined by the weapon's rarity.

This means it's actually harder to get magic items as a TWF, because if you want to apply the +3 in every attack, you need TWO +3 magic weapons, while GWF only needs one.

1 Note: the actual damage would be $p \cdot d_T$ and $p \cdot d_G$, where $p$ is the probability of actually hitting. I'm assuming both have the same attack hit modifier (i.e., +5), so they have the same probability of hitting, thus the probability is irrelevant here3. It changes considerably the comparison of DW vs GWM though, thus the math is left aside for that one. If you want the math, I suggest asking a new question about it.

2 Okay, I got a little confused here - I went by OP's words on this one, but then I double checked and Dual Wielder does not give you a reaction or +1 hit/+1 damage. Either way, GWM is usually better than a +2 ASI, which would give you exactly the +1 hit/+1 damage.

After the edit, OP mentions Blade Mastery, but that can also be used with Greatsword, so all it does is increasing $p$ for both the styles (see below). As V2Blast mentioned in a comment, Blade Mastery doesn't give you +1 damage either, but let that aside.

3 As noted by nitsua the cool sheep, it's not completely irrelevant because critical hits exist. I'll make the actual math here and let the body as it is. Let $p$ be the probability of a normal hit, given by $$p = (21 - \textrm{AC} + B) \cdot 0.05$$

where AC is the AC and $B$ is the modifier to hit, and $p$ is capped at 0 and 0.95 (i.e. you always miss rolling 1 and the probability can't be lower than 0). Let $d_{Ta}$ be the average damage per attack that hit for TWF, $d_{Tc}$ be the average damage per critical hit for TWF, $d_{Ga}$ be the average damage per attack that hit for GWF and $d_{Gc}$ the average damage per critical hit for GWF. The exact average damage of TWF is given by $$d_T = (a + 1) \cdot (p \cdot d_{Ta} + 0.05 d_{Tc})$$

and the average damage of GWF is given by

$$d_G = a \cdot (p \cdot d_{Ga} + 0.05 d_{Gc})$$

Choosing your values of STR modifier, we have $d_{Ta} = 9.5$, $d{Tc} = 13$, $d_{Ga} = 13.33$, $d_{Gc} = 21.66$. Assuming 14 AC (quite usual), we have $p = 0.6$, giving us

$$d_T = (a + 1) \cdot 6.35$$

and

$$d_G = a \cdot 9.081$$

Finding $a$ again, we have $$9.081a > 6.35a + 6.35$$ $$2.731a > 6.35$$ $$a > 2.325$$

So, taking into account critical hits actually makes GWF become even better - because the damage on the dice rolls is larger for GWF.

• It might be helpful to clarify why Dual Wielding (I think you mean Dual Wielder) "is not as amazing, sorry." It's not at all obvious without an explanation, and it seems kind of fundamental to explain it when you go to lengths to explain the alternative (GWM). I might also suggest a friendlier introductory tone to the question: it starts rather abruptly with references to the OP's wrongness, which may be factual, but... honey and vinegar. – Bloodcinder Aug 21 '18 at 17:29
• @Bloodcinder I didn't go to lengths to explain GWM, I was just clarifying which part of it is better and linked the answer explaining. As I added now in the footnote, GWM x DW would be an entire new question - I can make a Q&A if you want, but detailing it here would take time. But the TL;DR is: +1 to hit and +1 to damage don't increase your DPR as much as GWM does against regular enemies (i.e. not a guy with 20+ AC) - or, in other words, GWM is better than +2 ASI, which is exactly what Dual Wielding is giving you. – HellSaint Aug 21 '18 at 17:34
• @Bloodcinder Actually, OP got me confused. I was comparing GWM to +1 hit/+1 damage, but that isn't even what Dual Wielder does... It's actually even weaker than that. – HellSaint Aug 21 '18 at 17:39
• Thanks HellSaint! This definitely clarified the maths. Definitely seems like TWF does pretty well until lvl.11, when it's outclassed by GWF. Also I must have been confused on the feat, not sure where I got those numbers either (gets confusing sometimes). Thanks for the thorough answer! – Rickz Aug 21 '18 at 18:24
• @Rickz Yeap, but it being good at 5th level is true because you rolled insanely high on Str. The usual 16 STR, giving a +3 modifier, would make TWF become worse at level 5 already. – HellSaint Aug 21 '18 at 18:50

Investment and scaling is the concern

• TWF: Two Weapon Fighting
• THF: Two Handed Fighting
• AS: Action Surge

TL;DR The Two Weapon Fighter does well, if you have a feat and a style and a bonus action every single turn. The Two Handed Fighter does almost just as well without needing any of those things, and is straight up better at high levels.

In your example, you are describing TWF in the best case scenario, using the relevant fighting style and a relevant feat. The other examples you have listed only mention a relevant fighting style to their calculations. Great Weapon Master comes to mind.

Unfortunately, I don't have the resources to calculate that myself, but we could reasonably assume that the feat for TWF is relatively similar in power to the feat for THF, and similar logic for the fighting styles.

Even under the assumption that you have all of the relevant investments for TWF, it doesn't scale well. In the end, TWF gives you a single extra attack. Because it requires a bonus action, we can assume it's going to be used by a class that has almost no use for a bonus action. Fighters are the best example of this.

Assuming we have a TWF fighter with the necessary feat and style and a THF fighter with no feat or style, we could compare how they stack up in terms of levels:

Level 2 (Impossible to have 20 STR and a feat, highest possible is 18)

• TWF: (1d8 [4.5 avg] + 4) x 2 = 17 (AS: 25.5)
• THF: (2d6 [7.0 avg] + 4) x 1 = 11 (AS: 22)
• Difference: +6 (AS: +3.5)

Level 5

• TWF: (1d8 [4.5 avg] + 5) x 3 = 28.5 (AS: 47.5)
• THF: (2d6 [7.0 avg] + 5) x 2 = 24 (AS: 48)
• Difference: +4.5 (AS: -0.5)

Level 11

• TWF: (1d8 [4.5 avg] + 5) x 4 = 38 (AS: 66.5)
• THF: (2d6 [7.0 avg] + 5) x 3 = 36 (AS: 72)
• Difference: +2 (AS: -5.5)

Level 20

• TWF: (1d8 [4.5 avg] + 5) x 5 = 47.5 (AS: 85.5)
• THF: (2d6 [7.0 avg] + 5) x 4 = 48 (AS: 96)
• Difference: -.5 (AS: -10.5)

The concern here is that, while pre-level 5 grants you a whopping +6 damage for a bonus action, it falls flat as soon as you get your extra attack (+4.5 damage for a bonus action at that level is pretty average).

Another concern is the fact that a higher ability score works in favor of the TWF. A more average score of +3 would mean the TWF would have a -2 to all of the differences listed above.

As you level up, you are going to have more access to options that utilize your bonus action, either through multiclassing, your subclass, or by magical items. The TWF version also requires a feat and a fighting style to keep up, and will definitely fall short without those investments.

Abilities like Hunter's Mark (Ranger) and Hex (Warlock) can be beneficial to improve the damage of TWF, but so can the bonus action availability of the War Cleric feature for THF. Where Hunter's Mark might grant an extra 3.5 damage per attack, the War Cleric could add 12 damage per turn (for up to 5 turns a day).

• "we could reasonably assume that the feat for TWF is relatively similar in power to the feat for THF" - nope, that assumption would be mostly wrong :P If you are focusing on DPR, GWM is vastly superior to DW. – HellSaint Aug 21 '18 at 17:25
• @HellSaint I was saying that in favor of OP's question. I don't have the means of proving that one is better via calculations, but saying they're equal (and thus one is not better than the other), it gives enough reason to exclude either of them for the sake of an accurate number. Without feats, THF is better hands down. With only TWF having feats, TWF is only slightly better. That was the point I was trying to make. Saying Great Weapon Master was simply better would have only been an assumption if I couldn't back it up. – Daniel Zastoupil Aug 21 '18 at 17:28
• 20 strength at level 1 seems less than likely; doubly so when you also have a feat boosting it. – Yakk Aug 21 '18 at 19:00
• @Yakk That is a great point. At level 1, he'd either be a variant human (to start with DW feat) and rolled a natural 18 (+4 mod) or he'd be a different race with a +2 to strength (to be at 20 strength and +5 mod) and no feat. It is impossible for him to be level 1 with 20 strength and a feat. – Daniel Zastoupil Aug 21 '18 at 23:12

TWF is subpar for everyone except for Rogues

Without a feat

Drawing a weapon is an object interaction, drawing two will use up your action.
The fight has just started, and the figher with the two weapons is already behind. You could walk around with one weapon drawn, but most civilized places dislike it.

Everyone can cast spells while holding a two-handed weapon in one hand, but you need Warcaster to be able to cast while you have both hands full.
Paladins and Clerics can even cast with a weapon and a shield.

With a feat

You compare a fighting style + a feat (TWF+DW) to other fighting styles. It is only fair to add a feat there too.

I will not repeat the calculations of other answers, but from level 51 (Dueling or GWF) + ASI is better for your DPR against most ACs, not to mention GWM or Shield Master.
Actually, even TWF + ASI is usually better than TWF + DW.

Bottom line

You can spend a feat to bring TWF to mediocre levels, a bit ahead of GWF or Dueling. However, if you spend a feat on those two, you can achieve real greatness.

Classes

I already mentioned Clerics and Paladins who are hurt more than avarage by TWF, but it is generally bad for casters, like Eldritch Knights.

Rogues

If a Rogue misses with an attack, a lot more damage is lost than just 1d6+Dex. So for them, a second chance to deliver Sneak Attack outweighs the usual hindrances of TWF, unless they can cast Booming Blade or Green-Flame Blade.

1) 6 for Valor Bards etc, whenever Extra Attack comes.

There are a lot of extremely potent bonus actions you can take with core class features, so keeping that bonus action that two weapon fighting removes hurts it.

Others have noted the mechanics and maths, so I'm going to comment more on the bonus action power.

Courtesy of Abdiel, a list of bonus actions.

Barbarian

Enter or end Rage - Barbarian level 1 Rage feature.

Make a melee weapon attack while raging - Barbarian/Path of the Berserker level 3 Frenzy feature.

Dash - Barbarian/Path of the Totem Warrior level 3 Eagle Totem Spirit feature.

Knock a Large or smaller creature prone when you hit it in melee - Barbarian/Path of the Totem Warrior level 14 Wolf Totemic Attunement feature.

Fighter

Second Wind - regain 1d10+CL HP - Fighter level 1 feature.

Commander’s Strike - give a friend a free attack as a reaction - Fighter/Battle Master maneuver.

Feinting Attack - get advantage on the next attack roll - Fighter/Battle Master maneuver.

Rally - add temporary HP to a friend - Fighter/Battle Master maneuver.

Summon a bonded weapon - Fighter/Eldritch Knight level 3 Weapon Bond feature.

Weapon attack when you cast a cantrip as your action - Fighter/Eldritch Knight level 7 War Magic feature

Weapon attack when you cast a spell as your action - Fighter/Eldritch Knight level 18 Improved War Magic feature

Cast a Paladin spell with a casting time of 1 action - Paladin/Oath of the Ancients level 20 Elder Champion feature.

Vow of Enmity - advantage on attack rolls against one creature - Paladin/Oath of Vengeance level 3 Channel Divinity feature.

Feats

Make a weapon attack or shove a creature when you use the Dash action - Charger feat.

Attack with a hand crossbow when you attack with a one-handed weapon - Crossbow Master feat.

Make a melee weapon attack when you crit or reduce a creature to 0 - Great Weapon Master feat.

Melee weapon attack with the opposite end of a weapon - Polearm Master feat.

Attempt a grapple when you hit with unarmed strike or improvised weapon - Tavern Brawler feat.

If used well, I agree, two weapon fighting can be quite potent, but the loss of a bonus action is costly, as you could be healing, or entering a rage, or getting advantage on attacking an enemy.

Second wind, for example, could be the difference between falling unconscious and doing no damage, and staying conscious. You can do this when you attack someone with a great sword with no loss of a bonus action. If you rage, you will be halving your damage against some sources and doing extra damage. That could be much more potent than extra damage, which won't always be accessible as others have noted.

If you're in a situation where you can reliably make an extra attack, with great weapons master and easy to kill enemies, then a two handed 2d6+strength extra damage a round is far going to swamp out any damage from a light weapon.

• How are you comparing damage dealt by the TWF bonus actions against those other bonus actions? Or are you saying that all of them are all better? – NautArch Aug 21 '18 at 16:43
• This seems like an interesting list of bonus actions, but without any analysis it does not answer this question at all. Also, note that it seems the question is focusing on fighters specifically. – Rubiksmoose Aug 21 '18 at 17:00
• Two weapon fighting removes your bonus action, and OP noted that this loss was unimportant because bonus action didn't matter. I'm noting why bonus actions make two weapon fighting less useful. – Nepene Nep Aug 21 '18 at 17:17
• Please see my first comment - using any one of those listed bonus actions also removes your bonus action. Can you show why/when/how those are inherently better than TWF? – NautArch Aug 21 '18 at 17:19
• But not doing damage isn't necessarily a bad thing. Knocking an enemy prone for your allies can be a big deal in and of itself. I think you could vastly improve this answer by assessing and comparing TWF vs the other relevant Bonus Actions for a Fighter rather than just a list. – NautArch Aug 21 '18 at 17:48

At high level, you gain magical items.

There are several very useful magical items that require you to spend your bonus action:

• Bag of Tricks
• Boots of Speed
• Dancing Sword
• Quaal's Feather Token (whip, 1 use)
• Scimitar of Speed

So all other things being equal, the TWF guy won't be able to benefit as much from those.

Let's compare PCs modes of 2 fighters using the best "average damage" weapon possible. Also, let's not mix it with armor / more AC too much. Just TWF vs GWF. (Note: the letter $$\S\$$ below represents the "attacking stat bonus")

Level 3 comparison:

I'll use Level 3, because the "RAW" rules seem to imply that leveling up through levels 1 and 2 has to be "fast". So level 3 is probably the first level where the character finally has his subclass and will be played for a more respectable number of games.

Given the normal array (15, 14, 13, 12, 10, 8) it is quite normal to start with a main attack stat of 16 or 17. So I'll assume $$\S\$$ = 3.

TWF Guy (No feat, with 2 light weapons, Fighting Style = TWF):

$$\text{Damage} = (1d6+S) + (1d6+S) = (2S) + 7 = 13$$

vs

GWF Guy (No feat, with greatsword, Fighting Style = GWF): $$\text{Damage} = 2d6 \text{ (rerolling each 1 or 2 once)} +S = S+ 8.3333 \text{ (see note below)} = 11.3333$$

Note: Avg dg of 1d6 is 3.5. Avg dg of 1d6 with "reroll 1 or 2" is thus basically when you roll 1 or 2, it is as if you roll 3.5 because the avg of the reroll is a normal 1d6 thus an avg dg of 3.5. So, listing all 6 results, summing them, and averaging: $$\frac{3.5 + 3.5 + 3 + 4 + 5 + 6}{6} = \frac{25}{6} = 4.166666$$

As for critting: TWF: 2 chances of critting, but you crit for +1d6 dg. GWF: 1 chance of critting, but you crit for +2d6 dg. So, even if you are a Fighter Champion, those seem about the same.

TWF seems to have the advantage here, right? After all he deals 2.6666 more damage!

If you add in a power that relies on being usable per each attack, like a Paladin's Divine Smithe, or a Fighter Battle Master's Manoeuvers, then TWF allows you to go through your Spell Slots or Superiority Dice quicker. You become able to "nuke" more, which may win some fights, especially the type of deadly fights where you need to down some enemy ASAP because it can deal a lot of damage back so the quicker you kill it the better it is.

If you add is a power that is more likely to trigger when you have multiple attacks, like a Rogue's Sneak Attack, then TWF seems even nicer because it greatly increases your odds of getting that nice Sneak Attack damage in.

But wait. For Fighters, we forgot Action Surge. This basically adds 1 attack.

$$\text{TWF Guy Damage} = [ 2 \times (1d6+S) ] + (1d6+S) = (3S) + 10.5 = 19.5$$

vs

$$\text{GWF Guy Damage} = [ 2 \times 2d6 \text{ (rerolling each 1 or 2 once)} + S ] = 2S + 16.6666 = 22.6666$$

Ouch. Now GWF clearly beats TWF, and we're only in the very low levels yet! However, Action surge is only once per Short Rest, so... not a big deal. Fights are usually quite short (let's say 3 rounds), and it is approx 2 fights per short rest (usually), so it's like adding 3.16666 divided by 6, or only 0.5 damage. Not enough to "catch up" to the 2.6666 damage advantage of TWF.

But when you level up, it only gets worse and worse. Basically, the more attacks are gained (mainly through Extra Attack but Haste can often be a staple effect for this too), the more your TWF guy will become lagging behind.

Sure, he's got a 2.666 dg advantage initially, but only at low levels! At level 5, even without Haste he's already lagging by 3.16666 damage. At level 11 it's even worse etc. And if Haste is cast, it gives more "bang for the buck" for the spellcaster to cast it on the GWF guy than on the TWF, for the same reason: the spell adds 1 attack and with each 1 extra attack mister GWF will definitely deal more damage than mister TWF. So it sucks because the wizard never casts Haste on you, it always goes to the barbarian or something.

All the while you don't have your bonus action. In some campaigns, that can be crippling.

And then, magical items. At first, everybody in the party will get one. It would be unfair for your TWF guy to get his second magical weapon when someone else doesn't even have one. So you can't have as much damage or even bonus to hit because you have only 1 magical weapon. Or you have 2, but yours are both +1 while the only +2 weapon in the party goes to somebody else. Because it wouldn't be fair for you to have not only the best magical weapon, but also more magical weapons than the others, right?

And worst of all, even if you are in a campaign where you can "buy" your magical items, it will always cost you twice as much as everybody else! After all, you need 2 weapons, while they need only 1!

So you're condemned to suck. The higher level the campaign is, and the more magic is accessible and abundant, then the worst it becomes.

And that is why it is considered a subpar choice.

• Wow superb edit by Someone_Evil. I'm sorry if this comment shouldn't be here, but I'm new here and despite searching I have not found out how to: a) Send a message directly to someone (private message) without making it into a comment. b) How to do those nice bullet points. c) How to make math formulas look so nice. Thanks! – Pat Sep 6 '19 at 9:39

Let us consider the most extreme example of a level 20 champion fighter, one with two-weapon fighting (dual rapiers) and the other two-handed fighting (great axe).

Two-Weapon Fighting:

1. Adds ability modifier to offhand damage (Two-Weapon Fighting Style)
2. Uses a D8 weapon from the feat (Dual Wielder)
3. Gains +1 AC from the feat (Dual Wielder) - not relevant to these calculations
4. Can make one extra attack as a bonus action (Two-Weapon Fighting)
5. Has a +5 modifier to hit/dam (20 in primary stat)

Two-Handed Fighting:

1. Rerolls 1's and 2's (Great Weapon Fighting) will be ignored in these calculations
2. Can optionally take a -5 hit/ +10 damage to attacks (Great Weapon Master)
3. Can make one extra attack as a bonus action on a crit/kill (Great Weapon Master)
4. Can use a 2d6 or 1d12 weapon
5. Has a +5 modifier to hit/dam (20 in primary stat)

A level 20 fighter can make 4 attacks a round as a standard action, and 1 additional attack a round as a bonus action (Two-Weapon Fighting / Great Weapon Master) - giving each fighting style potentially 5 attacks.

Two-Weapon Fighting

• Standard: 4x(1d8+5)
• Bonus: 1d8+5
• Total: 5d8+25
• Damage(Min/Avg/Max): 30/47.5/65

Two-Handed Fighting

• Standard: 4x(1d12+5)
• Bonus: 1d12+5
• Total: 5d12+25
• Damage(Min/Avg/Max): 30/57.5/85

Two-Handed Fighting taking -5 hit/+10 dam

• Standard: 4x(1d12+5+10)
• Bonus: 1d12+5+10
• Total: 5d12+75
• Damage(Min/Avg/Max): 80/107.5/135

Now the calculations above are "potential" damage output. The bonus action for the two-handed fighter is conditional on crit/kill within the round. The -5 hit/+10 dam attacks have a lower chance to hit. The problem with this scenario is that two-weapon fighting has no option to try to increase damage. The penalty to hit can easily be offset by advantage, bless, additional +hit modifiers (higher strength etc.). The two-weapon fighting style allows 1 additional attack a round, but the great weapon master feat can allow for that as well, making the two-weapon fighting style seem less unique. For further insult, let us calculate the "dueling" fighting style (+2 damage) and see how well a duelist with a shield does for damage (gaining an extra attack as a bonus action through great weapon master)

Duelist with GWM to gain +1 attack as a bonus action

• Standard: 4x(1d8+7)
• Bonus: 1d8+7
• Total: 5d8+35
• Damage(Min/Avg/Max): 40/57.5/75

As we can see here, even a "sword and board" warrior has the potential to out-damage the two-weapon fighter (albeit conditionally, with a crit/kill in the round).

Summary:

Two-weapon fighting, even with the dual wielding feat is less powerful than a sword and board fighter with great weapon master, and pales in comparison to a two-handed fighter with great weapon master as its total damage potential is less than half that of a great weapon fighter with great weapon master.

This is compounded further by the fact that a two-handed weapon is better with: haste, opportunity attacks, high damage thresholds for concentration checks, criticals, scaling better with +hit bonuses like bless, cutting through flat damage reduction (such as the feat heavy armor master granting -3 damage), Only needing to find one magical weapon, casting spells (free action to take one hand off the greatsword and hold it to cast a spell, where two-weapon fighter must sheath/re-draw or drop/pickup), easier for two-handed to grapple (can't fight with weapon, but does not need to drop/sheath in a pinch), and does not suffer from "underkill" (not dealing enough damage in 1 blow to kill a creature, so a second attack must be performed - while there is the potential for overkill on a great weapon attack, the attack isn't wasted and ensuring something dies is usually a prudent action in combat).

There are probably more examples, but all of these paint a pretty poor picture for two-weapon fighters.