Best Weapons

[Hytheter]

What are the best weapons to use in this edition?

From a quick glance, it seems to me that the Greatsword and Maul are way more powerful than anything else if you have Great Weapon Fighting, with a minimum damage of 6 before modifiers and an average of 9.
At the very least, the Greataxe is seemingly totally obseleted by them. Is there ever a reason to use a greataxe?

[SaintRidley]

It really depends on what you're doing as far as fighting style.

[Oscredwin]

At the very least, the Greataxe is seemingly totally obseleted by them. Is there ever a reason to use a greataxe?

Barbarian and Half-Orc features as well as the Savage Fighting feat all favor the d12 weapons over the 2d6 weapons.

[Sidmen]

Well, firstly. The Minimum damage is still 2 - you get to reroll 1's and 2's on the dice, but only once (if the second roll is a 1 you must keep it).

So while, yes, the lower damage levels will skew higher for the Greatsword and Maul - it isn't as extreme as it first appears. In general, though - the greataxe is going to be an inferior choice by pure numbers.

[Logosloki]

Trident and Net is still a big favourite of mine.

[Hytheter]

Barbarian and Half-Orc features as well as the Savage Fighting feat all favor the d12 weapons over the 2d6 weapons.

The Barbarian and Half-Orc ability only applies on a critical hit, which means you'll do 3 extra damage, once every 20 hits, or 5% of the time. That doesn't seem worth it when the sword and maul do 0.5 more damage 95% of the time, meaning that those 19/20 add up to be way more than the occasional critical.

Savage Attacker works equally well with either weapon since you don't have to roll only one dice.


Well, firstly. The Minimum damage is still 2 - you get to reroll 1's and 2's on the dice, but only once (if the second roll is a 1 you must keep it).

So while, yes, the lower damage levels will skew higher for the Greatsword and Maul - it isn't as extreme as it first appears. In general, though - the greataxe is going to be an inferior choice by pure numbers.

Oh yeah, good point.

[Giant2005]

Lances are obviously awesome if you are mounted, being the most powerful single-handed weapons.
Glaves and Halberds are also top tier due to the awesomeness of Polearm Master and Sentinel (Technically Quarterstaves are just as good regarding Polearm Master but without the reach, Sentinel becomes less useful).

[Giant2005]

The Barbarian and Half-Orc ability only applies on a critical hit, which means you'll do 3 extra damage, once every 20 hits, or 5% of the time. That doesn't seem worth it when the sword and maul do 0.5 more damage 95% of the time, meaning that those 19/20 add up to be way more than the occasional critical.

Savage Attacker works equally well with either weapon since you don't have to roll only one dice.
Mathematically with the Orc bonus, both weapons average the same damage on a crit anyway, so you are better off taking the Greatsword or the Maul for the higher non-crit damage. Although that balance would change with Barbarian levels.

[OldTrees1]

Whip(reach) + Shield(AC)
Not high damage dealing but it does have perks.

[Yorrin]

You can reduce the simple melee weapon list to:
Spear- best overall stats for a simple weapon
Dagger- only simple finesse weapon
Javelins- dirt cheap throwing weapons
Quarterstaff/Club- shillelagh

For martial melee weapons, there are also a handful of useful choices:
Rapier- best finesse weapon
Shortsword- best light finesse weapon
Maul- Best 2h as such
Battleaxe- best non-finesse 1h weapon
Pike- best reach weapon
Lance- for all your horseback needs

Everything else is either less good in some way to these weapons, or equal but more expensive.

Ranged weapons aren't as numerous, and so don't collapse as far.
Simple:
Light Crossbow- best simple ranged dmg
Shortbow- for iteratives on ranged
Sling- 1h and cheap as dirt

Martial:
Heavy Crossbow: great damage output
Hand Crossbow: your 1h option (see also the Crossbow Master debate)
Longbow: for iteratives on ranged

[Naanomi]

Everything else is either less good in some way to these weapons, or equal but more expensive
This ignores damage type, but overall is a good list. I'd add:

whip, the one handed reach weapon;
net: does something no other weapon does;
Scimitar; for the finesse druid?

[Yorrin]

This ignores damage type, but overall is a good list. I'd add:

whip, the one handed reach weapon;
net: does something no other weapon does;
Scimitar; for the finesse druid?

Fair points. Damage type was indeed ignored because I have yet to see a situation in which it matters in 5e. Whip and Net are fine additions, and I did forget the niche of finesse druids, though in many cases Shillelagh will still end up being a better choice.

[Giant2005]

Fair points. Damage type was indeed ignored because I have yet to see a situation in which it matters in 5e. Whip and Net are fine additions, and I did forget the niche of finesse druids, though in many cases Shillelagh will still end up being a better choice.

You also forgot Glaves and Halberds which are requirements for the powerful Polearm Master/Sentinal combo.

[DrLemniscate]

The 2d6 weapons become a lot better when you introduce GWF.

The average damage of a 1d12 is 6.5, which becomes 7.333 (repeating of course) with GWF. An increase of 0.833

The average damage of a 2d6 is 7, which becomes 8.333 with GWF. An increase of 1.333.

One benefit the 1d12's have is other abilities or feats that involve rolling or rerolling weapon die, such as Half-Orc or Savage Attacker feat.

[Yorrin]

You also forgot Glaves and Halberds which are requirements for the powerful Polearm Master/Sentinal combo.

...wow. For some reason I thought Pikes qualified for that. Turns out they DO qualify for the AO, but not for the bonus action attack, which seems like an odd design choice.

[DrLemniscate]

...wow. For some reason I thought Pikes qualified for that. Turns out they DO qualify for the AO, but not for the bonus action attack, which seems like an odd design choice.

Pikes are more stabby stabby. Glaives and Halberds have more of that swing that prompts a follow through.

That extra swing from Polearm Master ends up doing a lot.

You can add your Strength modifier to it.
You can add other modifiers to it, such as your magic weapon (it's the same weapon, just the butt of it).
It's still 2-handed, so GWF applies. This bumps the average damage of just the 1d4 from 2.5 to 3.
GWM also applies, so you can take a -5 to hit for a +10 to damage (which is recommended, unless they have a high AC).
Combined with GWM, you can go through all your extra swings hoping for a crit to proc GWM, but if not you can then take your Polearm Master extra swing. This is because you are limited to 1 bonus action.


edit: for Great Weapon Fighting overall, using a 1d10 with Polearm Master and Great Weapon Master is better than a 2d6 with Great Weapon Master. Not just for damage, but also utility with those extra AoO and possible use with Sentinel.

[Yorrin]

Pikes are more stabby stabby. Glaives and Halberds have more of that swing that prompts a follow through.

That extra swing from Polearm Master ends up doing a lot.

You can add your Strength modifier to it.
You can add other modifiers to it, such as your magic weapon (it's the same weapon, just the butt of it).
It's still 2-handed, so GWF applies. This bumps the average damage of just the 1d4 from 2.5 to 3.
GWM also applies, so you can take a -5 to hit for a +10 to damage (which is recommended, unless they have a high AC).
Combined with GWM, you can go through all your extra swings hoping for a crit to proc GWM, but if not you can then take your Polearm Master extra swing. This is because you are limited to 1 bonus action.


Oh absolutely. I am in no way saying the feat is bad or the extra swing is not worth it. I'm just surprised that they're including Pikes on one part of the feat but not the other. I understand it from a simulationist perspective, but it seems like it goes against the general design principles of 5e's simplicity.

[DrLemniscate]

Oh absolutely. I am in no way saying the feat is bad or the extra swing is not worth it. I'm just surprised that they're including Pikes on one part of the feat but not the other. I understand it from a simulationist perspective, but it seems like it goes against the general design principles of 5e's simplicity.

I think 5e is going not only for simplicity, but flavor and customization. Just from classes, there is an insane amount of customization compared to other editions. Feats just add another way to sculpt your character.

This feat represents trying to make some of these things make sense, maybe to improve the Theater of the Mind. There are a few other odd restrictions out there, such as Druids will refuse to wear metal.

[Person_Man]

The 2d6 weapons become a lot better when you introduce GWF.

The average damage of a 1d12 is 6.5, which becomes 7.333 (repeating of course) with GWF. An increase of 0.833

The average damage of a 2d6 is 7, which becomes 8.333 with GWF. An increase of 1.333.

One benefit the 1d12's have is other abilities or feats that involve rolling or rerolling weapon die, such as Half-Orc or Savage Attacker feat.

It's easy to calculate the benefit of a Critical Hit. You just multiply the probability of the critical hit (.05) times the extra damage gained from the critical hit (double all damage dice, add one additional die if you're a Half Orc and thus have Savage Attacker).


Base damage, assuming 20 Str:

Maul: 2d6 + 5 = 12 average damage
Greataxe: 1d12 + 5 = 11.5 average damage


With Critical Hit Calculation

Maul: 2d6 + 5 + (.05 * 7) = 12.35 average damage
Greataxe: 1d12 + 5 + (.05 * 6.5) = 11.825 average damage

With Critical Hit Calculation and Half Orc Savage Attacker

Maul: 2d6 + 5 + (.05 * 10.5) = 12.525 average damage
Greataxe: 1d12 + 5 + (.05 * 13) = 12.15 average damage
With Critical Hit Calculation and Half Orc Savage Attacker AND Great Weapon Fighting style

Maul: 2d6 (reroll 1s and 2s once) + 5 + (.05 * 13.5) = 14.008 average damage
Greataxe: 1d12 (reroll 1s and 2s once) + 5 + (.05 * 14.66) = 13.66 average damage.


So in every case, the Maul produces better average damage then the Greataxe, though not by much. (Also, this demonstrates why bonuses to critical hits are very marginal benefits - they just don't occur very often).

The exception to this rule is when you KNOW that you are going to roll a critical crit. As far as I know, the only auto-crit ability in the game comes from the Assassin Rogue 3 subclass ability, and only for the first round attacking an enemy who has not yet taken their Action. For that specific build, if you happen to be a Strength based Half-Orc Fighter or Barbarian 2/Rogue 3 using a Greataxe would be a good idea. But only on the first round of combat. (And you'd want to pick up the Extra Attack class feature from somewhere, followed by a reliable way to make an attack with your Reaction).

Also, I'd like to say that I hate all these fiddly simulationist differentiations. Just have all Simple weapons be Light Finesse Thrown weapons that deal 1d6 damage, and have all Martial weapons be Two Handed Weapons that deal 2d6 damage (with the option of being Ranged, which gives you 300 ft range, but Disadvantage on adjacent). Rewrite the Half Orc or other crit abilities as needed to make them more or less useful as you see fit. Then allow optional rules in the DMG for all the fiddly differences if that's what floats your boat. The end. I do not need or want charts full of garbage trap options.

[Vowtz]

he exception to this rule is when you KNOW that you are going to roll a critical crit. As far as I know, the only auto-crit ability in the game comes from the Assassin Rogue 3 subclass ability, and only for the first round attacking an enemy who has not yet taken their Action. For that specific build, if you happen to be a Strength based Half-Orc Fighter or Barbarian 2/Rogue 3 using a Greataxe would be a good idea. But only on the first round of combat. (And you'd want to pick up the Extra Attack class feature from somewhere, followed by a reliable way to make an attack with your Reaction).

It's critical on a surprised foe, without surprise and before a creature acts it's only advantage.

[DrLemniscate]

Also, I'd like to say that I hate all these fiddly simulationist differentiations.

Sorry. I'm a Statistician, so whenever I see multiple options, I'm already calculating minute differences.

And everything does need to be taken with a grain of salt.

Some people may prefer the 1d12, simply because they like rolling big numbers. The 1d12 is 3 times more likely to hit roll a 12 than 2d6.

Others might still prefer the 2d6 even if for some reason the 1d12 pulled ahead by a little bit. Even if it didn't have a higher expected value, it gives you more consistent results and less subject to randomness. The 1d12 has an equal chance of rolling a 1 as it does a 12, while the minimum that a 2d6 can roll is 2.

edit: A few other exceptions can arise when you factor in hit chance, or are facing something with a very high AC. Consider the scenario where only a 19 or 20 results in a hit. You still are only rolling a crit 5% of the time; but when you do hit, 50% of them are crits. This probably won't come up very often, but it's just another way to think of crits. Factoring in hit chance makes it more difficult to treat crits as a multiplier; the multiplier would need to become ( 1 + crit chance / hit chance ).

[Person_Man]

@DrLemniscate

I get that there are permutations, and that there are small benefits to using X weapon over Y weapon in Z circumstance. I just think its terrible game design.

Lots of other players are not statisticians, and they're going to make less optimal choices based on other considerations. (In pretty much every gaming group I've ever played in, there is at least one guy who has some kind of emotional attachment to using a certain weapon or unarmed strike, regardless of their class). I don't think games should have trap options. Each of the options should be good at the thing they're designed to do, this difference should be meaningful/significant (and not a +1ish bonus to damage), and this difference should be crystal clear to anyone who read the rules (and not require calculations and/or rules mastery).

[Shining Wrath]

And the differences in general seem to be small enough that you could choose the great axe over the maul, or the longsword over the battleaxe, just because it suited your image of the character (e.g., noble background = longsword). The big step is simple to martial; if you have the proficiency, you should use the martial weapons.

[Simian]

Sorry. I'm a Statistician, so whenever I see multiple options, I'm already calculating minute differences.

And everything does need to be taken with a grain of salt.

Some people may prefer the 1d12, simply because they like rolling big numbers. The 1d12 is 3 times more likely to hit roll a 12 than 2d6.

Others might still prefer the 2d6 even if for some reason the 1d12 pulled ahead by a little bit. Even if it didn't have a higher expected value, it gives you more consistent results and less subject to randomness. The 1d12 has an equal chance of rolling a 1 as it does a 12, while the minimum that a 2d6 can roll is 2.

edit: A few other exceptions can arise when you factor in hit chance, or are facing something with a very high AC. Consider the scenario where only a 19 or 20 results in a hit. You still are only rolling a crit 5% of the time; but when you do hit, 50% of them are crits. This probably won't come up very often, but it's just another way to think of crits. Factoring in hit chance makes it more difficult to treat crits as a multiplier; the multiplier would need to become ( 1 + crit chance / hit chance ).

Also, Champion Fighters improved criticals would mean that you could have 100% of your hits as crits or 50% but for a range of 15-20 instead of 19-20 for example.

Just out of curiosity for the math wizards. What % of hits as crits would it take to make an orc champion fighters damage average higher with a great axe?

[BW022]

Completely depends on your build and preferences.

Using a glaive, halberd, or pike gives you reach and therefore the ability to move-attack-move without drawing attacks on yourself, to gain more attacks as people leave your (larger) reach, and to be able to reach more folks when your current opponent drops -- without utilizing more movement. You can effectively block a larger area, attack people higher up, etc.

That said, just carry a halberd and a maul.

[Shadow]

...wow. For some reason I thought Pikes qualified for that. Turns out they DO qualify for the AO, but not for the bonus action attack, which seems like an odd design choice.Oh absolutely. I am in no way saying the feat is bad or the extra swing is not worth it. I'm just surprised that they're including Pikes on one part of the feat but not the other. I understand it from a simulationist perspective, but it seems like it goes against the general design principles of 5e's simplicity.

I think it makes perfect sense.
The pike weighs eighteen pounds. It's not exactly an easy to maneuver weapon. It's big, long, and heavy. It weighs almost twice as much as a greatclub or a maul.
Whipping the other end around to quickly strike with the haft is not a reasonable expectation.
With the glaive and halberd weighing six pounds each (quite literally one third of the weight of the pike) it becomes a much more fluid and controlled motion.

[Rummy]

But did pikes really weigh 18 lbs? That seems high to me.

[EvilAnagram]

But did pikes really weigh 18 lbs? That seems high to me.

13lbs was towards the heavy end. Alexander the Great armed his phalanxes with what were essentially 20-ft. pikes that weighed 14.5 pounds according to wikipedia. So, yeah, a bit heavy, but not terrily

[Totema]

Lances are obviously awesome if you are mounted, being the most powerful single-handed weapons.
Glaves and Halberds are also top tier due to the awesomeness of Polearm Master and Sentinel (Technically Quarterstaves are just as good regarding Polearm Master but without the reach, Sentinel becomes less useful).

And if you pick up Dual Wielder, you can wield two lances at once. Awesome and effective!

[Yorrin]

I think it makes perfect sense.
The pike weighs eighteen pounds. It's not exactly an easy to maneuver weapon. It's big, long, and heavy. It weighs almost twice as much as a greatclub or a maul.
Whipping the other end around to quickly strike with the haft is not a reasonable expectation.
With the glaive and halberd weighing six pounds each (quite literally one third of the weight of the pike) it becomes a much more fluid and controlled motion.

Like I said, from a simulationist perspective I get it. I'm just confused from a game design perspective. Not that it's going to affect me much- I don't like reach weapon builds in general.

[odigity]

That extra swing from Polearm Master ends up doing a lot.

Combined with GWM, you can go through all your extra swings hoping for a crit to proc GWM, but if not you can then take your Polearm Master extra swing. This is because you are limited to 1 bonus action.



I don't get this. If you always have the option of using the Polearm Master-granted bonus action attack, doesn't that make the "cleave" feature of Great Weapon Faster completely redundant? I intend to get PM, and therefore so little benefit to GWF. (Not that big a fun of trading to-hit for damage, and static bonuses don't multiply, and if I'm not a Fighter I'm never going to get 3-4 attacks as part of a single action, so...)

[MaxWilson]

Trident and Net is still a big favourite of mine.

Unfortunately Net has some mechanical problems: it always attacks with disadvantage (ranged weapon at 5' = disadvantage, and anything beyond 5' is long range so = disadvantage) and it eats up all your attacks for that round.

[Easy_Lee]

@DrLemniscate

I get that there are permutations, and that there are small benefits to using X weapon over Y weapon in Z circumstance. I just think its terrible game design.

Lots of other players are not statisticians, and they're going to make less optimal choices based on other considerations. (In pretty much every gaming group I've ever played in, there is at least one guy who has some kind of emotional attachment to using a certain weapon or unarmed strike, regardless of their class). I don't think games should have trap options. Each of the options should be good at the thing they're designed to do, this difference should be meaningful/significant (and not a +1ish bonus to damage), and this difference should be crystal clear to anyone who read the rules (and not require calculations and/or rules mastery).

From my reading of the weapons table, the choices are actually quite meaningful.

In previous editions, slashing was the most reliable damage type, so I can understand paying more for it.
Halflings and gnomes can't use heavy weapons, meaning the distinction between heavy crossbows and longbows vs crossbows and shortbows is actually significant for a halfling (as significant as 1 damage, anyway).
It's appropriate that the weapons which allow the most potentially broken tactics, such as crossbow expert with hand crossbows, are most expensive. Hand crossbows are actually the most expensive weapon on the list by 25 gold, 50% more expensive than a greatsword.
When funding an army, having cheap options like pikes is very useful.

I like the weapons table because there are no obvious "best" options like there were in 3.5, where certain exotic weapons were just plain superior to everything else (halfling skiprock for master throwers, for example). That said, there are a few things I don't like about the table:

Why are tridents more expensive, heavier, martial-only versions of the spear with no benefits?
Why would anyone use a greatclub when a quarterstaff is cheaper, lighter, does the same damage with versatile, counts as a polearm, and can be used one-handed?
Why does the sickle exist with no special properties when the handaxe is better in every way (besides minor cost)?

Overall, I think the table's fine.

[MaxWilson]

Sickle exists because farmers use it. (That may explain the lower cost as well.) Try reaping grain with a handaxe some time.

[Easy_Lee]

Sickle exists because farmers use it. (That may explain the lower cost as well.) Try reaping grain with a handaxe some time.

IRL I get that, I'm just not sure why it wasn't differentiated somehow to make it a viable choice.

[Shadow]

IRL I get that, I'm just not sure why it wasn't differentiated somehow to make it a viable choice.

Two reasons.
1: commoner weapons
2: druid weapons

The sickle wasn't designed to be a "viable" weapon choice. It was included as a low cost option that a farmer might have. It is a thematic weapon for a druid. It is a thematic weapon for a monk (in the sense that a kama is really just an altered sickle).
It was not included and intended to be a quality choice for most PCs, but rather only for certain niche PCs for flavor, or for commoner weapons.

[Rummy]

I love that crossbows get love in 5e. Light crossbow is the weapon of choice for s halfling rogue.

[emeraldstreak]

But did pikes really weigh 18 lbs? That seems high to me.

it's high-ish but possible for Swiss ash pikes that were 20-25 ft long


on another note, lances are the highest dmg one-handed weapons, although that's not as important in 5e as TWF is just another way to bonus action attack.

[Hytheter]

it's high-ish but possible for Swiss ash pikes that were 20-25 ft long

Somehow though I don't think DnD pikes are that long, or they'd be able to reach at least 5-10' further.

[Easy_Lee]

Somehow though I don't think DnD pikes are that long, or they'd be able to reach at least 5-10' further.

They'd also be pretty worthless for single combat. Pikes are useful when there's a line of them, but not so much for just dealing with one person.

[Sartharina]

Half-orc Champions might get more mileage out of a d12 weapon than a 2d6 weapon thanks to the augmented crit range. And, critting more matters more against harder-to-hit foes.

[Easy_Lee]

Half-orc Champions might get more mileage out of a d12 weapon than a 2d6 weapon thanks to the augmented crit range. And, critting more matters more against harder-to-hit foes.

There's some discussion about that in other threads. Basically, a greatsword deals the same or better damage than a greataxe half orc or not. Really hard to hit targets, where you basically only hit on a crit, could skew that. But for most targets, who you'll hit on a ten or better, greatswords and mauls are better for everyone.

I'm hoping they release some feats or archetypes that change that. Having a barbarian who could roll guaranteed crits X times per short/long rest would be awesome, and could skew it back in favor of greataxes for that archetype.

[OldTrees1]

Half-orc Champions might get more mileage out of a d12 weapon than a 2d6 weapon thanks to the augmented crit range. And, critting more matters more against harder-to-hit foes.


There's some discussion about that in other threads. Basically, a greatsword deals the same or better damage than a greataxe half orc or not. Really hard to hit targets, where you basically only hit on a crit, could skew that. But for most targets, who you'll hit on a ten or better, greatswords and mauls are better for everyone.

I'm hoping they release some feats or archetypes that change that. Having a barbarian who could roll guaranteed crits X times per short/long rest would be awesome, and could skew it back in favor of greataxes for that archetype.

A Half Orc Champion 18(for 18-20 crits) with 20 Str*, the Great Weapon Fighting Style and nothing else will always** deal more damage with a Greataxe than with a Greatsword.

*The bonus to damage from Strength was accounted for but does not make a difference since it is the same for both weapons and the same for all hits.
**Disadvantage was not taken into account but for normal attacks Greataxe >= Greatsword even when hitting on a 2. (Advantage would obviously favor Greataxes)

To Hit Average AC = X where 1<X<18

<miss>((X-1)/20)0
+<hit>((20-X-2)/20)1d12+5[reroll 1s and 2s once] = 6.5+10/12[rerolling]+5 = 12.33
+<crit>(3/20)3d12+5[reroll 1s and 2s once] = 3*(6.5+10/12[rerolling])+5 = 27
Expected result: (3*27 + 18*12.33 - X*12.33)/20 = 15.1500 - 0.6167X.

<miss>((X-1)/20)0
+<hit>((20-X-2)/20)2d6+5[reroll 1s and 2s once] = 2*(3.5+4/6[rerolling])+5 = 13.33
+<crit>(3/20)4d6+5[reroll 1s and 2s once] = 4*(3.5+4/6[rerolling])+5 = 21.67
Expected result: (3*21.67 + 18*13.33 - X*13.33)/20 = 15.2500 - 0.6667X.

15.1500 - 0.6167X =15.2500 - 0.6667X
0.05X = 0.1
X = 2

When X = 2,
15.1500 - 0.6167X = 13.9167
15.2500 - 0.6667X = 13.9167

When X = 18
15.1500 - 0.6167X = 4.0494
15.2500 - 0.6667X = 3.2512

Edit: Disadvantage math
Half Orc Champions prefer a Greatsword over a Greataxe when suffering disadvantage.

To Hit Average AC = X where 1<X<18
While Disadvantaged:
To crit you must roll 18+ on both dice. 3/20*3/20=9/400
To miss you must roll under X on one or both dice. 2*(X-1)/20*20/20 - (X-1)/20 *(X-1)/20
(1/400) * (40X-40 -(X^2-2X+1))
=(1/400) * (-X^2 + 42X - 41)
To hit but not crit you must not crit or miss
(1/400) * (400 - 9 +X^2 -42X +41)
= (1/400) * (X^2 -42X +432)

<miss>((-X^2 + 42X - 41)/400)0
+<hit>((X^2 -42X +432)/400)1d12+5[reroll 1s and 2s once] = 12+1/3
+<crit>(9/400)3d12+5[reroll 1s and 2s once] = 27
(1/400)( (X^2 -42X +432)*(12+1/3) + 9 * 27 )
=(1/400)( (12+1/3)X^2 - 518X + 5328 + 243 )
=(1/400)( (12+1/3)X^2 - 518X + 5571 )

<miss>((-X^2 + 42X - 41)/400)0
+<hit>((X^2 -42X +432)/400)2d6+5[reroll 1s and 2s once] = 13+1/3
+<crit>(9/400)4d6+5[reroll 1s and 2s once] = 21+2/3
(1/400)( (X^2 -42X +432)*(13+1/3) + 9 * (21+2/3) )
=(1/400)( (13+1/3)X^2 - 560X + 5760 + 192 )
=(1/400)( (13+1/3)X^2 - 560X + 5952)

(12+1/3)X^2 - 518X + 5571 = (13+1/3)X^2 - 560X + 5952
0 = X^2 -42X + 381
0 = X^2 -21X -21X +441 - 441 + 381
60 = (X-21)^2
7 < X-21 < 8
28 < X < 29
Since the weapons are only are only equal when X is greater than 28 and X was limited as 1<X<18, Half Orc Champions prefer a Greatsword over a Greataxe when suffering disadvantage.

Note: I am still not including the Great Weapon Master feat in either of these. The -5 attack would favor the Greatsword over the Greataxe. The question is how much in the case of HalfOrc Champion18 with Advantage and HalfOrc Champion18 with neither Advantage nor Disadvantage.
Edit:
Actually Great Weapon Master gives a flat damage boost and changes X such that X2=X1+5. So Great Weapon Master would have no affect on weapon choice for a Half Orc Champion 18

Edit: I messed up some of the math, so I will correct it in another post.

[BW022]

What are the best weapons to use in this edition? ...

First, all weapons have advantages and disadvantages. There is no best weapon. As in reality... it is mainly the person using the weapon which determines its usefulness and which weapon is best depends almost exclusively on the character using it and the situation.

A rogue obviously wants to use finesse weapons. A monk, monk weapons. Since they gets special advantages to it. A druid might want to use a club (since they use shillelagh) while a wizard might want to use a staff (since it is their arcane focus). A big fighter may still want to carry a bow... simply because they end up fighting goblins in trees. Someone may want a dagger because it is more easily hidden, can be used in two-weapon fighting, and thrown. A mounted character might wish to use a lance -- because it has both reach and allows the use of a shield. A glaive might be more useful than a greatsword, because it has reach and allows moving, attack, move combinations without drawing opportunity attacks. For some characters, you may have to consider dexterity vs. strength, weight, proficiencies, etc.

Second, there are many in-game reasons why you want to wield or carry certain weapons. Damage types is common, as is finding certain weapons (say silver or magical), fighting in certain locations, concealing weapons, finding certain weapons, money, etc. If a rust monster destroys your greatsword... by all means a spear may now be your best weapon. A +1 longsword is likely still better than a normal greatsword. Certain weapons are also more useful as tools -- a dagger can skin an animal, a glaive can set off traps 10' away, a bow is useful for hunting, and a whip is useful for driving horses.

Third, there are roleplaying reasons why someone might wish to carry certain weapons. You could be from a certain country which specializes in certain weapons. You might just want to look bad-ass. You might not want to look threatening. You might wish to confuse potential foes. A weapon might be given to you by a family member. Your god might have a favorite weapon. You might find a weapon with a crest of your homeland on it. I routinely have my wizard carrying a two-handed weapon. He never uses it... but it often means he isn't targeted, silenced, etc. on the first few rounds of combat.

Forth, yes... there are cases when a greataxe is better than a greatsword. It is slightly less expensive, it is more useful against a heat metal spell, it is easier to repair the haft if broken, it can chop trees down, etc. ... and if you are attacking someone with 15hp remaining who is about to finish the ritual to summon Orcus... (assuming a 16 strength), you have a 1 in 12 chance of stopping him with a greataxe hit vs. a 1 in 36 chance with a greatsword hit. Even with the ability to reroll 1 and 2s, getting a 12 isn't that good with 2d6.

IMO, worrying about insanely small potential damage differences is silly. Any smart player can maximize advantages of their weapons -- or maximum the disadvantages of their opponents weapons. A greatsword is a good weapon... given all the right circumstances. However, if a rogue sees a fighter with a greatsword, he could easily run away and keep tossing darts at him. A warlock could easily cast fly and attack the fighter using a halberd from 15' overhead. A ranger could climb a cliff and rain arrows down on the fighter. A smart monk, could conceal a dagger in his towel at the bath house and attack the fighter who doesn't have his greatsword with him in the tub.

[rlc]

>be large
>use large weapons
>get 2d12 damage
youjelly.jpg

[broodax]

It's easy to calculate the benefit of a Critical Hit. You just multiply the probability of the critical hit (.05) times the extra damage gained from the critical hit (double all damage dice, add one additional die if you're a Half Orc and thus have Savage Attacker).


Base damage, assuming 20 Str:

Maul: 2d6 + 5 = 12 average damage
Greataxe: 1d12 + 5 = 11.5 average damage


With Critical Hit Calculation

Maul: 2d6 + 5 + (.05 * 7) = 12.35 average damage
Greataxe: 1d12 + 5 + (.05 * 6.5) = 11.825 average damage

With Critical Hit Calculation and Half Orc Savage Attacker

Maul: 2d6 + 5 + (.05 * 10.5) = 12.525 average damage
Greataxe: 1d12 + 5 + (.05 * 13) = 12.15 average damage
With Critical Hit Calculation and Half Orc Savage Attacker AND Great Weapon Fighting style

Maul: 2d6 (reroll 1s and 2s once) + 5 + (.05 * 13.5) = 14.008 average damage
Greataxe: 1d12 (reroll 1s and 2s once) + 5 + (.05 * 14.66) = 13.66 average


These calculations are incorrect. Your damage only matters if you hit. Since you never hit with a 1, your multiplier for the crit damage should be at least 1/19. In almost all cases it will be higher than that as well, for instance 1/10 if you need to roll an 11 to hit. This makes the difference even smaller, if it doesn't actually change which is optimal.

[OldTrees1]

Two Handed Weapon Damage:

I will be looking at a 2d6 weapon and a 1d12 weapon both with the Great Weapon Fighting Style.
I will be looking at Crit ranges from 20 to 18-20. The range will be symbolized by the variable C (1<=C<=3).
I will be looking at Half Orc and not Half Orc
I will be looking at using the Great Weapon Master feat and not using the Great Weapon Master feat.
During all of this I will be using the variable X as the minimum roll needed for a hit. I will limit X such that 1<X<21-C except when comparing the Great Weapon Master feat.

Conclusion 1:
Static bonuses are the same on normal hits and on critical hits. Thus they do not impact the choice of weapons unless the static damage bonus comes with an attack penalty. In those cases it is the attack penalty that matters and not the static damage bonus.

Conclusion 2:
Great Weapon Fighting Style increases the damage per die by (2 x Average - 1 - 2)/(Size of Die)=(Size of Die - 2) / (Size of Die)
2d6[Reroll 1s and 2s once] =average> 2(3.5 + 4/6) = 2(3.5+2/3)
2d6 crit =4d6[Reroll 1s and 2s once] = 4(3.5+2/3)
2d6 Half Orc crit =5d6[Reroll 1s and 2s once] = 5(3.5+2/3)
1d12[Reroll 1s and 2s once] =average> (6.5 + 10/12) = 6.5+5/6
1d12 crit = 2d12[Reroll 1s and 2s once] =average> (6.5 + 10/12) = 2(6.5+5/6)
1d12 Half Orc crit = 3d12[Reroll 1s and 2s once] =average> (6.5 + 10/12) = 3(6.5+5/6)


These calculations are only of the damage from the weapon. Strength and GWM damage will be included in the "To GWM or not" calculations later. This is merely to find the weapon choice tipping point (value of X such that 2d6 = 1d12).

Non-Great Weapon Master
<miss>(X-1)/20
<hit>(21-X-C)/20
<crit>(C)/20

2d6: (1/20)(21-X-C)(2)(3.5+2/3) + (1/20)(C)(4)(3.5+2/3)
=(1/20)(3.5 + 2/3)(42-2X+2C)
1d12: (1/20)(21-X-C)(1)(6.5+5/6) + (1/20)(C)(2)(6.5+5/6)
=(1/20)(6.5 + 5/6)(21-X+C)
If C = 1, these are equal when X is greater than our accepted range for X(X<20).
If C = 2, these are equal when X is greater than our accepted range for X(X<19).
If C = 3, these are equal when X is greater than our accepted range for X(X<18).
In other words, 2d6 does more damage.

2d6 Half Orc: (1/20)(21-X-C)(2)(3.5+2/3) + (1/20)(C)(5)(3.5+2/3)
=(1/20)(3.5 + 2/3)(42-2X+3C)
1d12 Half Orc: (1/20)(21-X-C)(1)(6.5+5/6) + (1/20)(C)(3)(6.5+5/6)
=(1/20)(6.5 + 5/6)(21-X+2C)
If C = 1, these are equal when 18<X<19.
If C = 2, these are equal when 16<X<17.
If C = 3, these are equal when 14<X<15.
In other words, Half Orcs do more damage with 2d6 X < 21-2C but do more damage with 1d12 when 21-2C <= X.


Now to include the static bonuses. Using GWM effectively increases X by 5 so it can change the preferred base weapon. I will only be considering the cases where it does change the preferred weapon.

K=static bonuses other than GWM(Str for example).

First the trivial case:
2d6 GWM(X=20) vs 1d12 GWM(X=20)
Both get +10 damage 5% of the time over the 2d6 vs 1d12 comparison in the previous spoiler. Equal increases do not change the preference.

Second trivial case
2d6(15<=X<20) vs GWM 1d12(X=20)
(1/20)(3.5 + 2/3)(42-2X+2C) + (1/20)(21-X)K vs (1/20)(6.5 + 5/6)+ (1/20)(K+10)
(1/20)(3.5 + 2/3)(42-2X+2C) + (1/20)(21-X)K vs (1/20)(16.5 + 5/6 + K)
For X=19, C=1(worst case for 2d6):
(1/20)(3.5 + 2/3)(6) + (1/20)K vs (1/20)(16.5 + 5/6 + K)
(1/20)(25 + K) vs (1/20)(16.5 + 5/6 + K)
So 2d6(15<X<20) deals more damage than GWM 1d12(X=20)

In conclusions: non Half Orcs prefer 2d6 over 1d12 when looking at average damage on normal attacks.

First non trivial cases: Half Orcs with C=1
2d6(X=14) vs GWM 1d12(19=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(17)+(1/20)(7)(K) vs (1/20)(6.5 + 5/6)(4)+(1/20)(2)(10+K)
(1/20)(70.5 + 1/3 + 7K) vs (1/20)(49 + 1/3 + 2K)
2d6(X=15) vs GWM 1d12(20=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(15)+(1/20)(6)(K) vs (1/20)(6.5 + 5/6)(3)+(1/20)(1)(10+K)
(1/20)(62.5 + 6K) vs (1/20)(32 + K)
For Half Orcs with C=1, 2d6 > GWM 1d12 for the key range

Trivial case:
Half Orc with C=2 and X=15
2d6(C=2,X=15) > 2d6(C=1,X=15) > 1d12GWM(C=1,X=20) = 1d12GWM(C=2,X=20)
2d6(C=2,X=15) > 1d12GWM(C=2,X=20)

Second non trivial cases: Half Orcs with C=2
2d6(X=12) vs GWM 1d12(17=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(24)+(1/20)(9)(K) vs (1/20)(6.5 + 5/6)(8)+(1/20)(4)(10+K)
(1/20)(100 + 9K) vs (1/20)(98 + 2/3 + 4K)
2d6(X=13) vs GWM 1d12(18=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(22)+(1/20)(8)(K) vs (1/20)(6.5 + 5/6)(7)+(1/20)(3)(10+K)
(1/20)(91 + 2/3 + 8K) vs (1/20)(80.5 + 5/6 + 3K)
2d6(X=14) vs GWM 1d12(19=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(20)+(1/20)(7)(K) vs (1/20)(6.5 + 5/6)(6)+(1/20)(2)(10+K)
(1/20)(83 + 1/3 + 7K) vs (1/20)(64 + 2K)
For Half Orcs with C=2, 2d6 > GWM 1d12 for the key range

Trivial cases:
Half Orc with C=3 and 14<=X<=15
2d6(C=3,14<=X<=15) > 2d6(C=2,14<=X<=15) > 1d12GWM(C=2,14<=X<=15) = 1d12GWM(C=3,14<=X<=15)
2d6(C=3,14<=X<=15) > 1d12GWM(C=3,14<=X<=15)

Third non trivial cases Half Orcs with C=3
2d6(X=10) vs GWM 1d12(15=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(31)+(1/20)(11)(K) vs (1/20)(6.5 + 5/6)(12)+(1/20)(6)(10+K)
(1/20)(128.5 + 2/3 + 11K) vs (1/20)(148 + 6K)
128.5 + 2/3 + 11K = 148 + 6K
5K = 18.5 + 1/3
K = 3.766...
2d6(X=11) vs GWM 1d12(16=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(29)+(1/20)(10)(K) vs (1/20)(6.5 + 5/6)(11)+(1/20)(5)(10+K)
(1/20)(120.5 + 1/3 + 10K) vs (1/20)(130.5 + 1/6 + 5K)
120.5 + 1/3 +10K = 130.5 +1/6 + 5K
5K = 9 +5/6
K = 1.966...
2d6(X=12) vs GWM 1d12(17=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(27)+(1/20)(9)(K) vs (1/20)(6.5 + 5/6)(10)+(1/20)(4)(10+K)
(1/20)(112.5 + 9K) vs (1/20)(113 + 1/3 + 4K)
112.5 + 9K = 113 + 1/3 + 4K
5K = 0.5 + 1/3
K = 0.166...
2d6(X=13) vs GWM 1d12(18=X)
(1/20)(3.5 + 2/3)(42-2X+3C)+(1/20)(21-X)(K) vs (1/20)(6.5 + 5/6)(21-X+2C)+(1/20)(21-X)(10+K)
(1/20)(3.5 + 2/3)(25)+(1/20)(8)(K) vs (1/20)(6.5 + 5/6)(9)+(1/20)(3)(10+K)
(1/20)(103.5 + 2/3 + 8K) vs (1/20)(96 + 3K)
For X=10, 2d6 < GWM 1d12 for (3.766... <= K) and 2d6 > GWM 1d12 for (K <= 3.766...)
For X=11, 2d6 < GWM 1d12 for (1.966... <= K) and 2d6 > GWM 1d12 for (K <= 1.966...)
For X=12, 2d6 < GWM 1d12 for (0.166... <= K) and 2d6 > GWM 1d12 for (K <= 0.166...)
For X=13, 2d6 > GWM 1d12

Conclusions:
Non Half Orcs prefer 2d6 over 1d12.
Half Orcs with at least a +4 bonus to damage(not including GWM) will only prefer 1d12 if 21-2C <= X.

So a Half Orc Champion 18 with Str 20 will prefer a greataxe over a greatsword if and only if they need a 15 or better to hit their target.