Is Greatsword superior to Greataxe?

Greataxe
6.5 (1d12) slashing Heavy, Two-Handed

Greatsword
7 (2d6) slashing Heavy, Two-Handed

This is why I think Greatsword is superior to Greataxe:

Since feats for different categories of weapons are not officially published yet (only in Unearthed Arcana), I don't see why people are choosing Greataxe over Greatsword, except for flavor or availability (found enchanted Greataxe).

• All answers in comments have been deleted. – mxyzplk says reinstate Monica Apr 17 '18 at 1:49
• You forgot to mention one important thing. A greatsword is a 'sheated' weapon as oposed to a greataxe that must be strapped to the back. AS part of the free object interaction rule (RAW) greataxe takes 1 action to put or take from your back as opposed to the greatsword which takes a free object interaction to wield or stow away. not a big plus but could be meaningfull in some situations. – KilrathiSly Nov 19 at 17:29

While Netzach makes a very good point, I'd like to add in the die dynamics.

Although the average is very similar the two situations behave very differently.

2d6

Rolling 2 dice creates a bell curve distribution of the possible values. In this case the average (7) has a chance of 1 in 6, while the max has a chance of 1 in 36. Half of your rolls will be 6,7, or 8. With the addition of more dice this curve gets steeper. 4d6 would have an average about 14 (1 in 36) and a max of 24 (1 in 648)

1d12

All numbers have an equal chance of occurring (a uniform distribution), thus your chance of a 12 is 1 in 12. Only one quarter of your rolls will be a 6,7, or 8. And on a crit, 24 is 1 in 144. You have a better chance of rolling higher than average, but also a higher chance of rolling lower than average. Many would argue that this balances out. But when you are in a battle and need a 12, your chances are better with the axe.

In summary

Some prefer the Greatsword because the high chance of average damage is "slow but steady".

Others accept the risk of a low roll with the Great Axe in order to have a better chance at high damage.

• Comments are not for extended discussion; this conversation has been moved to chat. – mxyzplk says reinstate Monica Apr 17 '18 at 22:05
• Those who argue it balance out don't know math. – András Jul 5 at 19:08
• The Greatsword "slow but steady" comment isn't painting a correct picture. 2d6 has a more dependable damage output. In statistics you will look for the expected values: which is the range of values wherein 75% of the result will fall. For 2d6 this is from 4-5 to 9-10. 5-9 has 2/3rds while 4-10 has 83,33% (5/6th) of the results. – El_Jairo Jul 18 at 8:21
• EDIT: I wasn't able to add on. 1d12 Has a uniform distribution, so here it has less meaning. Yet if you would assume that 7-8 is de median value, the expected range would be: 3-10 for 2/3rds and if you want to expand you need to go to 2-11 range. Which means, that it's not dependable, you have more chance for higher damage but as much more chance to do lower damage. – El_Jairo Jul 18 at 8:27

The Greatsword is a better weapon than the Greataxe unless you are playing a Barbarian.

The Greatsword has two big benefits: (1) it has a higher average, and (2) it has a tighter and less random distribution. For classes that can take Great Weapon Fighting, it has an additional edge in the dice re-roll mechanics since each die can be re-rolled on a 1 or a 2.

The second of these points is often misunderstood. It is common for people to wrongly believe that the randomness "balances out" so that it's simply a matter of taste whether you prefer. This is wrong. Randomness counts against the player in the long run and, unlike monsters who appear, die and are never seen again, players are around long enough for the long run to count. The reason for this is simple: low rolls count against you more than high rolls count for you. HPs done in damage over a monsters' hitpoint total are wasted while a blow that fails to fall a monster means they stand for another hit, maybe round.

Consider this graph, showing the distribution of frequencies of number of hits required to kill a 20hp monster with a greataxe or greatsword:

The greataxe has a slightly increased chance to kill in 2 hits, but a much reduced chance to kill in 3 hits and a longer tail of 5 or more hits. That increased chance of requiring many more hits hurts you much more than the increased chance of killing in 2. And, lest you think this is restricted to this one example, consider this graph of mean hits to kill across a range of hitpoint totals (shown with +3 to damage but the effect is similar at all adds) and notice that the Greataxe lags at every hitpoint total shown:

So, in summary, the Greatsword is simply a better weapon. There is no reasonable trade off to be have with high risk, high reward. The Greataxe is just worse. It is only if you have Barbarian-style abilities that boost the Greataxe more than the Sword that it is a better choice.

Other than the high risk/high reward nature of the Greataxe, explained in ravery's answer, the Greatsword is usually the better option.

Mechanically, there are some ways to take advantage of the inherently higher damage die of the Greataxe though.

1. A Barbarian's 9th level ability, Brutal Critical lets him roll one additional weapon damage die, on top of the normal extra dice gained from a critical hit. At higher levels this bonus increases to two and eventually three extra dice.
2. The Half-Orc race has the Savage Attacks trait that gives a similar effect in allowing you to roll one your weapon's damage die one additional time when getting a critical hit with a melee weapon.

To make an example of how this would actually play out, I'll use the Barbarian's ability.

Example:

• Level 9 Barbarian

Greatsword: 2d6 + 2d6 (crit) + 1d6 (extra weapon damage die) = 17.5 + relevant ability modifier
Greataxe: 1d12 + 1d12 (crit) + 1d12 (extra weapon damage die) = 19.5 + relevant ability modifier

• Level 13 Barbarian

Greatsword: 2d6 + 2d6 (crit) + 2d6 (extra weapon damage dice) = 21 + relevant ability modifier
Greataxe: 1d12 + 1d12 (crit) + 2d12 (extra weapon damage die) = 26 + relevant ability modifier

• Level 17 Barbarian

Greatsword: 2d6 + 2d6 (crit) + 3d6 (extra weapon damage die) = 24.5 + relevant ability modifier
Greataxe: 1d12 + 1d12 (crit) + 3d12 (extra weapon damage die) = 32.5 + relevant ability modifier

As you can see, the average damage of the Greataxe exceeds that of the Greatsword and at higher levels the difference is significant.

Now, a Half-Orc Barbarian that can consistently score critical hits would be a thing to see.

The problem is that this advantage that the Greataxe has over the Greatsword, only comes into play when a Barbarian and/or Half-Orc rolls a critical hit. A critical hit is rare on its own and for the Greataxe to outperform the Greatsword, you need a specific class/race.

On the other hand, as you mention, the Greatsword has a higher minimum damage, slightly higher and thus more reliable average damage and benefits more from Great Weapon Fighting, making it more preferable under most circumstances.

As mentioned in Netzach's answer, a barbarian's brutal critical is better when used with a 1d12 weapon instead of a 2d6 weapon. However, he doesn't account for the probability of a critical hit. Therefore, I wanted to provide a calculation whether a barbarian actually has a higher average damage when using a 1d12 weapon, compared to a 2d6 weapon, and if so, at which barbarian level.

I will be assuming that rolls of 8 and lower (leaving 12 other possible results) don't hit at all.

Instead of the in-post calculation, I switched to using Libre Office Calc. See the results below, now in the form of a graph:

The calculations with Reckless Attack were done using probabilities taken from this website, using the "Dice Roll String" 2d12D1+8.

Note that the Superior Critical and Reckless Superior Critical bars are the same values for 1, 2, 3 or 4 extra damage dice, since Superior Critical cannot be combined with Brutal Critical due to the character cap at level 20. One extra damage dice is, however, possible by choosing the Half-Orc race.

• I wouldn't use the 2d12D1+8 calculation for Advantage on the attack. I made a spreadsheet calculation with different results for different to hit chances. I can share the results if you want. You ether need +2 Critical Dice or +1 with Superior Critical to start having an advantage on the lower to hit chances (-50%). Which is logical since the chance to critically hit is relatively higher. Same goes for GWM feature, when you trade off hitting less with dealing more damage. – El_Jairo Jul 18 at 8:52
• Why show Superior Critical (which is only available to a Champion level 15) with 2-4 extra critical dice if they are impossible in DnD? Sure, you have now simply copied the values from the +1 critical hit die but it is confusing. – El_Jairo Jul 18 at 9:25

TLDR: Yes the Great Sword is superior to the Great Axe because it has more dependable damage output. So you will kill enemies with fewer hits. Even when you boost the average damage from the great axe beyond the great sword, this is done by having a higher chance to critically hit and deal more damage on average by a critical hit. Yet was this extra damage from a critical hit actually needed to kill the enemy? Or are you using the same number or even more attacks to fish for that critical hit, if normal hits would have killed the enemy in fewer tries. Especially as a Barbarian, Reckless Attacks does expend a resource: your health, because you will be that much easier to hit and damage. If that is your plan for being the tank, more power to you.

Introduction

In my current DnD 5e campaign I play a half-orc barbarian and I wanted him to be wielding the most iconic weapon: the great axe.

The problem explained in other responses here, quickly became apparent to me: there is no statistical advantage to wield a great axe over a great sword. In former editions the Great Axe had some appeal by having a x3 critical hit multiplier instead of the regular x2.

So I went on looking in the current rules to find some features to make 1d12 a good choice.

A principle I use to determine the probability value of a weapon is the expected range, which is the range of results where 75% of the rolls end up in. I'll come back to this when I have a graph to make this more clear. Yet for 2d6 this is meaningful, as it has a clear median (7, which is the result most rolled 1/6 times). For a 1d12 roll this is useless as all results have the same probability.

Looking at some options to mitigate the problems of 1d12 weapon

The first place I went looking was Fighting styles, I though reducing the chance of a 1-2 result would go a long way, reducing crappy rolls. Yet if we look at the graph below, were the impact of Greatweapon fighting is shown, we see that the Great Sword benefits more from this fighting style as it let's you re-roll all 1's and 2's from a roll. (IMHO the better way would be to grant one re-roll per damage roll).

I have connected the data points with lines for a more visual representation. So when one 'curve' is above the other, those result are more likely to occur than those beneath it. This shows that on a natural roll a great axe has higher probability to roll 11-12 than 2d6, yet with GW fs this is reduced to only 12.

If we translate this to expected results. For 2d6 we get the following:

83,33% falls between 4-10 for a natural roll, 86,42% falls between 6-11 with GW fighting style. With the minimum and median boosted +2 and the maximum +1, this is a significant increase and the average increase of 1,33 is somewhat misleading here as the floor goes up more than the ceiling, this fighting style makes the Great Sword even more dependable with results of <=4 having only a probability of 3,7%!

The 1d12 Great Axe has the following increases:

83,33% fell between 2-11 on a natural roll, with GW fs this becomes 77,78% between 4-11 or 97,22% between 3-12. This does improve the floor by +2 but the ceiling doesn't really move. Which is confirmed by the average increase of 0,83. So this fighting style does reduce the chance of rolling <=2 to 2,78% yet the minimum isn't increased all that much. So the variability isn't reduced and thus the reliability of the Great Axe is still lacking.

Next stop: Savage Attacker feature

By now most people know this feature to be a trap feature but I still went to see what it's impact is, because a re-roll is always useful if you are looking for a minimum result.

So let's take a graphic representation of this: This is the chance for one attack, which is of course the weak spot of this feature: it only helps for one bad roll, if you roll twice bad for damage, you are going to be stuck with the second bad roll. Also if you don't manage to roll higher than the previous roll, there is nothing gained by this feature. This is why I came up with a homebrew version of it, which grants 3 advantages:

1. Half ASI STR or DEX
2. One reroll per round for melee weapon damage, but if the re-rolled result <= the initial result you can add half max damage die to it. So with 1d12 you add 6 and with 2d6 you add 3 to the re-rolled lower result.
3. You get one critical melee weapon damage re-roll per round.

As we can see in the graph, once again 2d6 tends to gain more from a damage re-roll as the lower parts of the rolls get ignored for the more average or higher roll. 1d12 Does keep it's advantage now for rolling more times 11-12 but naturally still ends up more with low rolls <= 5. So if you would use the stock Savage Attacker feature, I would only re-roll any results <=4 on the first damage roll of the turn.

Let's have a look on the expected results for 2d6:

Note that the expected ranges are 4-10: 83,33% and 6-11: 86,61% respectively

• Minimum moves from 4 to 6: a gain of +2
• Median moves from 7 to 8: a gain of +1
• Maximum moves from 10 to 11 a gain of +1

On average 1,37 more damage but this clearly doesn't tell the whole picture as the lower results become far less frequent.

For 1d12 we see the following changes:

Note that the expected ranges are 2-11: 83,33% and 6-12: 82,64% respectively

• Minimum moves from 2 to 6: a gain of +4!
• Median moves from 7 to 12: a gain of +5!
• Maximum moves from 11 to 12 a gain of +1

On average the 1d12 roll only gain 0,99 damage yet we finally get the chance to roll <=4 below 5%! So one could say that this Savage Attacker feature justifies the use of a Great Axe for some extend. It helps you mitigate those low results, somewhat.

It would be interesting to see how both Great Weapon fighting style and Savage Attacker would combine statistically. Yet since the edge from savage attacker for 1d12 is rather low and the advantage from GW fs is in favor of 2d6, I would expect to 2d6 to be still ahead. (Let me know if you want this math done)

So the only thing left to look at is the critical hits As pointed out in previous answers the 1d12 great axe only real redeeming qualities lie in the benefit of added critical hit dice and of and expanded critical hit range.

I'll first give the results and I'll include some graphs to show how small the differences are on average.

With normal critical range and no advantage you need to add three critical hit dice to have some advantage from using a great axe.

With either Improved Critical or Advantage on the attack roll, the great axe becomes beneficial from +2 critical dice.

If you combine Improved Critical and Advantage on the attack roll, the great axe becomes beneficial from +1 critical dice.

Yet one must understand that these are average results, which means that they rely on the damage spike of the critical hit to increase the average damage dealt. Yet all damage done beyond the HP left of your target, is wasted. So having a better potential for dealing more spike damage only is relevant when you have enemies with enough HP for it to count.

My personal experience has been so far that my Improved Savage Attacker Feature as allowed my character to one-hit mooks more reliably, which is really the benefit you are looking for: increasing your action economy in combat. Without any ways to reduce the chance of rolling low, a great axe isn't a reliable weapon if you want to take out enemies consistently.

• Err... how is Savage Attacker a trap feature? For a Greataxe, it gives you a decent increase in average damage, and more importantly minimises your chances of completely whiffing an attack. +2 Strength is often better, but that's assuming you're not already hitting 20 Strength anyway (in which case what are you doing playing a barbarian lol). – Cubic Jul 18 at 13:18