# 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 Apr 17 '18 at 1:49

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 Apr 17 '18 at 22:05

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.

• Comments are not for extended discussion; this conversation has been moved to chat. – mxyzplk Apr 17 '18 at 22:05

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.