Sword or Axe? Some DnD 5e examples

I’ve discussed previously how the differences between the damage from a greataxe and greatsword (or maul) can impact decision-making in tabletop RPGs like Dungeons and Dragons. Things get even more interesting when you consider class bonuses and feats that adventurers can take. After all, not many folks swing their weapons as simple commoners. They are heroes! Let’s explore some examples from D&D 5e.

This discussion was inspired by some great interesting comments from Jeremy Crawford. See his Twitter here: https://twitter.com/JeremyECrawford
Thanks Jeremy!

Review the facts

https://i.warosu.org/data/tg/img/0310/04/1395537197976.jpg
We’ll need a lot of dice to test these theories

In Dungeons & Dragons 5e, the greatsword and greataxe have different damage dice. When you hit with these weapons, you roll the following damage dice:

Greatsword: 2d6 (two 6-sided dice)
Greataxe: 1d12 (one 12-sided die)

As a summary of a previous post, the greatsword has more damage on average (7.0 compared to greataxe’s 6.5). However, there are many occasions where the greataxe could be the better choice (enemies with high damage reduction, for example).
The greataxe has an equal chance of dealing damage between 1 and 12. The distribution of the greatsword’s damage, however, is more concentrated near the average value. That is, the damage is more likely to be between 5 and 9, and less likely to result on the extreme ends like 2 and 12. See the odds of each damage result for the greatsword below:

2d6 Probability Distribution

So, you can consider the greatsword as “more reliable/consistent” and it has higher average damage, but the greataxe has a better chance to land the big numbers. Either choice is great.

Great Weapon Fighting: reroll 1 and 2

In D&D 5e, Fighters with two-handed weapons can gain the ability to reroll damage dice that land on 1 or 2, but you must keep the second result. How fun!
So, how does that impact the distribution of damage for each of these weapons?

For both weapons, this ability should reduce the odds of getting a very low damage result. As a guess, I would say it should help the greatsword more, since you’ll probably roll more 1s and 2s when rolling 2d6 than when rolling a single d12. Let’s do the math and find out. (Let’s assume a player always chooses to reroll all 1s and 2s)

Greataxe (normal)
1d12
Average damage 6.5
even chance of 1,2,3,…11,12

Greataxe with Great Weapon Fighting
1d12 reroll 1,2 and take second result
Average damage 7.333
low chance of 1,2 and higher chance of 3-12

As expected, the damage of the greataxe increases, and it’s very unlikely to yield 1 or 2 damage (the odds of that are 2/12 * 2/12 = 4/144)
With Great Weapon Fighting, the average damage of the greataxe increased from 6.5 to 7.333 (an increase of 12.8%)


Greatsword (normal)
2d6
Average damage 7.0
Higher chances of average damage results

Greatsword with Great Weapon Fighting
2d6 reroll 1,2 and take second result
Average damage 8.333
low chance of 1,2 and higher chance of 3-12

With Greater Weapon Fighting, the greatsword maintains most of the essence of its damage distribution, just shifted toward higher values. It’s average damage climbs even more than the greataxe, with an increase from 7.0 to 8.333 (that’s a 19% increase – nice!)

Savage Attacker Feat

If you are a dice goblin, get excited! There is yet another way to reroll damage dice in D&D 5e. The Savage Attacker feat lets you reroll damage once per turn and use either result. Awesome!

Let’s look at how this feat impacts both the greataxe and greatsword. First, the greataxe:

Wow! This ability completely changes the shape of the damage distribution for the greataxe. Now, it’s very rare to deal very low damage. Instead of having very even odds for many damage values, the chance of a damage value steadily increases as that value gets higher.
This feat increases the average damage of the greataxe from 6.5 to 8.49. That’s 30.55% more!

Now let’s check out this feat’s impact on the greatsword:

The Savage Attacker feat also increases damage for the greatsword, and makes it unlikely to end up with less than 4 damage. However, the increase is not nearly as significant as it was for the greataxe. The greatsword’s average damage increases about 19.6%, from 7.0 to 8.37

So, if anyone ever tells you how the greatsword is the “optimal” choice, not only can you remind them how various situations give the advantage to the greataxe, but now you can also say that with the Savage Attacker feat, the greataxe has more damage on average.

D&D 5e is a master class in designing interesting choices for players. As a player choosing weapons, feats, etc., it would not feel great if there were choices that were “always better”. The fact that many flavors of hero can contribute meaningfully to challenges like combat, and perhaps shine in different scenarios, really is a great thing.

Why not BOTH?

Okay, what if we combine the effects of both Great Weapon Fighting and Savage Attacker?
In this case, 1s and 2s can be rerolled on both damage rolls. (source: https://twitter.com/JeremyECrawford/status/679830252005101568)

If you love rolling dice, and you hate getting low results, then this is the path for you. Think about how unlikely it is to deal only 2 damage with 2d6 in this scenario. You’d have to roll two 1s or 2s (4/36 chance), then reroll each of those and get 1s again (1/36 chance), then do it all over again (another 4/36 chance and 1/36 chance)… that’s a chance of 16 in 36*36*36*36.

Final odds: 1 in almost 105000
Even then, at least you’d get to roll 8 weapon dice on that attack before the heartbreaking disappointment.

So, let’s put these combined effects toward the greataxe and greatsword to see how things shake out.

Greataxe:

The greataxe gets bumped to an average damage of 9 (an increase of 33% over it’s original average value of 6)
Its damage distribution combines the effects of both Savage Attacker and Greater Weapon Fighting, to the surprise of absolutely nobody. It’s pretty impressive, though!

Greatsword:

The greatsword has only a tiny chance of doing low damage, and gets improved to an average damage of 9.46, which is 35.2% more than its original average of 7.0

Final Notes

These examples are a bit simplified, since they only deal with a single attack, no damage reduction or critical hits are considered, and no other bonuses (like with half-orcs and greataxe crits) are applied. However, I hope the above examples show how feats and abilities can enhance and reshape the expected damage from your weapon in Dungeons and Dragons 5e. Thanks again to Jeremy Crawford for the insightful comments that inspired this.

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