5E D&D Blogcast: Bow vs. Axe

“Can I Axe You A Question?”

by Steve & Matt (feat. Tom)

In many of our previous posts, we’ve discussed in very general terms how good certain abilities or bonuses are for characters. More recently in the Max Damage blog series, we have taken a closer look at the specific contexts in which some of those abilities are beneficial. We’ve also taken a stab at backing up some of our analyses with numerical approximations of expected damage, but it’s never been terribly precise.

Until now, that is. (Pretty charts after break!)

One of the recurring debates that you’ll see within a game like D&D is whether it is better to go with high damage in melee or weaker damage from afar. The game can accommodate either play style, and there are arguments to be made for both. The Archery Style, for instance, makes it more likely for a bow-wielding Fighter to actually connect with their attacks, which on the macro scale should yield a damage increase compared to a character without that bonus to hit.

But how much of a difference does that really make? After years of playing earlier editions like 3.5E and Pathfinder, it’s easy to forget that critical hits no longer need to be confirmed, so high bonuses to hit, even absurdly high ones, are less important in 5E. Additionally, it’s much harder to stack flat damage bonuses onto your attacks than it was in earlier editions, so a modest bonus to hit (such as from the Archery style) isn’t going to increase your average damage per swing the way it might have in the days of old.

So, keeping in mind that 5E is new and unfamiliar statistical terrain, with an abundance of bounded accuracy, class-determined damage potentials, and a limited range of ACs, how much does a character’s attack bonus and an enemy’s armor class affect the damage differential? Resident math wizard and rules guru Steve took the time to do a side-by-side comparison of a half-orc Fighter (Champion) with a great axe and a human Fighter (Champion) with a longbow, with solid evidence produced by actually crunching the numbers and seeing what the data show. 

THE NUMBERS 

Since the effectiveness of different combat strategies is relevant from Level 1 onward, especially for a character like the Fighter who is typically combat-focused, our analysis begins with a Level 1 character. For each build, it is assumed that the character has a 16 (+3 bonus) in their primary ability score (Strength for axe, Dexterity for bow), the relevant fighting style for their attacks (Great Weapon Fighting for axe, Archery for bow), and no external influences on their combat abilities. Average damage output is per attack, which should be the same as output per round if the character attacks every round.

As you can see from the graph, the bow is almost always the better choice for delivering damage at Level 1, assuming your character is human and gained the Sharpshooter feat at character creation. Only from AC 19 to 21 is the axe ever-so-slightly better. For an enemy armor class of 18 or lower, the damage bonus provided by Sharpshooter outweighs the accuracy penalty; for an enemy armor class of 22 to 25, higher damage is achieved by relying on a regular bow attack’s greater accuracy. At even greater ACs, Sharpshooter’s damage bonus wins out again because nothing short of a critical hit will even connect with the opponent (at that point, however, your DM has clearly proven him/herself to be a sadist who delights in murdering Level 1 PCs). 

But what if there IS an external influence on your likelihood of hitting, or even critting? When you attack with disadvantage, the bow’s supremacy at Level 1 is undisputed. 

Basically, use Sharpshooter against anything with an AC of 13 or lower, and regular bow attacks against anything with an AC greater than 13, and you’ll be doing the most damage possible, on average. 

On the other hand, attacking with advantage only improves the axe’s performance slightly–from AC 19 to 22, you’re better off attacking with the axe. Otherwise, the breakdown of optimal attack type is no different from normal circumstances.

TL;DR: At Level 1, the Sharpshooter/Archery Fighter readily outstrips the Axe Fighter in damage output.

NOTHING LASTS FOREVER 

As your Fighter gains levels and goes into the Champion Archetype for those sweet, sweet crits, the equation begins to change. After all, crits are much more relevant for a great axe-wielding half-orc than they are for a longbow-wielding human.

At Levels 3, 4, and 5, the axe’s damage potential starts to catch up to the bow’s, and then surpasses it.  At Level 3, the Fighter gains the Improved Critical class feature.  Suddenly, the half-orc’s extra crit damage die will matter twice as often–even more if he’s able to get advantage.  This is not enough to close the gap, but at Level 4, when the half-orc gains his first feat, the contest is all but over.  With Great Weapon Master, the half-orc is able to considerably out-damage the archer, ending her early advantage.  Another nail in the coffin comes at the very next level, when fighters gain access to a second attack.  Now, in addition to a significantly higher base damage potential, the half orc has a much higher possibility of scoring a critical hit in a given round, thus granting him the bonus attack from his feat.  Since a player may only take one bonus action per turn, the total chance of getting at least one critical hit on any given turn becomes an even greater concern than the average damage per hit.  Having a possible third swing of a greataxe at Level 5 (along with the already higher base damage) will turn a slim advantage into an overwhelming one.  Action Surge compounds this effect, first by multiplying the total damage output for the round, and then by further increasing the chances of getting that bonus swing.  By Level 20, well… the numbers speak for themselves.

 By late levels, the melee attacker clearly exceeds the ranged attacker in terms of raw damage output. For an opponent AC of 22 or lower, you’re best off using Great Weapon Master to inflict the greatest possible damage per hit. For an AC of 23 to 33 (even the Tarrasque has only a 25 AC), your best damage output will come from just swinging that great axe without the penalty to hit. Additionally, it should be noted that the Great Weapon Master feat grants a bonus attack when you score a critical hit or manage to drop an opponent. Even when he’s not fighting hordes of weak enemies, a 20th level Champion has a 47.8% chance to roll at least 1 critical hit when he makes all four attacks under normal circumstances, so has a decent chance to get his bonus attack every round of continuous attacking. As such, you can expect the gap between the axe numbers and the bow numbers to widen in a typical round of ideal combat. This puts the half-orc with his great axe well ahead of the competition. 

We can also infer heuristically that advantage and disadvantage will have a tremendous impact on the great axe wielder; not only does he get extra attacks if he crits, but the half-orc racial feature Savage Attacks also significantly increases damage upon scoring a critical hit. Remember, the average chance to crit per swing for a Champion is 15% (a roll of 18-20) as of Level 15. With disadvantage, that chance drops to 2.25%, but with advantage, it soars to 27.75%. In a full round of attacking at Level 20 with Action Surge and advantage, your chance of scoring a crit over those 8 attacks is a staggering 94.78%, almost guaranteeing a critical hit and bonus attack even against a lone BBEG. 

TL;DR: The Great Weapon Master half-orc’s damage potential (with a great axe) surpasses puny humans’ (with bows) after reaching Level 4.

THE TAKEAWAY 

Finally, while Archery does seem to disappoint now that the numbers are in, it behooves us to take a qualitative look as well as a quantitative one. With the Sharpshooter feat’s passive benefits, the archer can effectively damage targets at a range that might as well be unlimited for all practical purposes. After all, the sharpshooter feat negates the disadvantage normally incurred by shooting at long range and also allows the archer to ignore cover, which can add up to 5 AC for the target. More importantly, though, none of these analyses take into account the tactical considerations of battle. The axe wielder may not be able to reach a second foe in a round after killing his first target. This will rarely be an issue for the archer.  Aside from combat, the archer has the distinct advantage that he or she will have a very high Dexterity score and the ability to select the Medium Armor Master feat, for great stealth abilities as well as a significant boost to the crucial Dexterity saving throw, which is otherwise a weakness of the Fighter.