With the Great Weapon Fighting fighting style, how does the double-bladed scimitar's damage evolve?

Question

Traditionally, the Greatsword, Maul and Greataxe are considered the strongest two-handed weapons (unless you take the Polearm Master feat, where Glaives and Halberds rock out). Barbarians and Half-Orcs benefit more from the Greataxe's 1d12, while others prefer the Greatsword or Maul's 2d6.

I want to compare the new Eberron's Double-Bladed Scimitar with other weapons.

A double-bladed scimitar is a martial weapon, weighing 6 pounds and dealing 2d4 slashing damage on a hit.

It has the two-handed property and the following special property:

• If you attack with a double-bladed scimitar as part of the Attack action on your turn, you can use a bonus action immediately after to make a melee attack with it. This attack deals 1d4 slashing damage on a hit, instead of 2d4.

For a Fighter or a Paladin with Great Weapon Fighting, I built a graph that compared the Greatsword with it (same analysis would work for Maul). Since Fighters have ASI at levels 4 and 6, they can usually reach a +5 STR modifier very early, and the Greatsword only becomes the strongest weapon at level 20, when the Fighter does 4 attacks per turn.

That being said, comments have pointed out the graph doesn't incorporate the Champion Fighter's expanded critical range, which would affect the damage calculations. Is my graph correct for non-Champion Fighters? How would Champion Fighter's affect it?

Answer 1

The scimitar is better until the Fighter can make 3-4 attacks with the Attack action.

Note that the following question already covers the expected damage gain from the Great Weapon Fighting Style, and so I will use it in my formulas. (A 1dX weapon gains an average of X-2/X damage from the Fighting Style). "How much damage does Great Weapon Fighting add on average?"

The following formula is the expected damage of a 2d6 weapon where A is the number of attacks we make and S is our Strength Modifier:

$$A\left(\frac{18}{20}\left[2\times\left(\frac{6+1}{2}+\frac{6-2}{6}\right)+S\right] + \frac{1}{20}\left[2\times2\times\left(\frac{6+1}{2}+\frac{6-2}{6}\right)+S\right]\right)$$

The 18/20 and 1/20 represent the chances of hitting and getting a critical hit. We also know that the average of 1d6 is (6+1)/2 and that the average from GWFS is (6-2/2). Both of these are multiplied by 2 because we roll 2d6, not just one. After all of that we add our Strength Modifier. And in the critical hit scenario we double all the dice rolled (which also doubles the expected gain from GWFS).

Similarly we can derive a formula for the Double Scimitar, but note that the second attack can only be made once, regardless of the number of attacks we can otherwise make. This means that our attack modifier A will only be multiplied by the 2d4 attacks, and not the single 1d4 attack:

$$A\left(\frac{18}{20}\left[2\times\left(\frac{4+1}{2}+\frac{4-2}{4}\right)+S\right] + \frac{1}{20}\left[2\times2\times\left(\frac{4+1}{2}+\frac{4-2}{4}\right)+S\right]\right) + \frac{18}{20}\left[\left(\frac{4+1}{2}+\frac{4-2}{4}\right)+S\right] + \frac{1}{20}\left[2\times\left(\frac{4+1}{2}+\frac{4-2}{4}\right)+S\right]$$

These formulas can be easily modified for any die size, number of dice, and critical hit chance by changing all the relevant numbers, but for readability and whatnot here are more simplified versions of the formulas:

2d6 Weapon:

$$A\left(\frac{18}{20}\left[\frac{25}{3}+S\right] + \frac{1}{20}\left[\frac{50}{3}+S\right]\right)$$

Double Scimitar:

$$A\left(\frac{18}{20}\bigg[6+S\bigg] + \frac{1}{20}\bigg[12+S\bigg]\right) + \frac{18}{20}\bigg(3+S\bigg) + \frac{1}{20}\bigg(6+S\bigg)$$

We can then graph these formulas for various values of A and S (I let A range from 1 to 4 and S range from 2 to 5):

Here the x-axis is the number of attacks and the y-axis is the expected damage. The purple lines use the Scimitar while the green lines use a 2d6 weapon. After a certain number of available attacks, the 2d6 weapon will always become better than the scimitar. These points are highlighted by the intersections of their damage lines, an approximating curve is shown in orange.

Solid lines are +2 Strength, dashed lines are +3, dotted lines are +4, and the black lines are +5.

Here is the same graph with much of the clutter removed and leaving only the orange line to represent the scimitar's expected damage. Again, where the green and orange lines intersect is when a 2d6 weapon becomes a better option than the scimitar.

Conclusions:

• If the Fighter can make 1-2 attacks with the Attack action, the Scimitar is better.
• If the Fighter can make 3-4 attacks with the Attack action, the 2d6 weapon is better.
• An exception: If the Fighter can only make 3 attacks with the Attack action and their Strength Modifier is +5, then the Scimitar is better.