5e Weapon Creation Guide:
hokieboat's system for building statistically balanced weapons
The base weapon list in the 5th edition is intentionally simplified. If one assumes that the selection of weapons (excluding the blowgun and the net) is 'balanced,' then it is possible to reverse engineer a formula for a weapon's efficacy using statistical optimization techniques. One can then use this formula to build custom weapons with new combinations of damage and properties, and know that these new weapons are mathematically proven to be equivalent in power to the existing weapons in the game.
The Process
Weapon balance is calculated using 'damage factor,' which is a metric that is used to quantify the value of each weapon property. To create a new weapon, you choose the properties you want, which then gives you a 'budget' to determine what damage die to use.
Step 1: Simple or Martial
| Property | Initial Damage Factor Budget |
|---|---|
| Simple | 3.45 |
| Martial | 4.45 |
Step 2: Add General Properties
Keep in mind that some combinations are incompatible - like Light & Heavy, or Light & Two-Handed. Add the modifiers to your initial budget.
| Property | Damage Factor Modifier |
|---|---|
| Finesse | -0.25 |
| Heavy | +1 |
| Light | -0.7 |
| Mounted* | +3.45 |
| Reach | -1.4 |
| Two-Handed | +1.35 |
| Versatile+ | -0.05 |
* Mounted replaces Special for Lance
+ The damage die you will pick is for the 1H damage
Step 3: Add Ranged Properties
Adding the Thrown property does not automatically make it a Ranged weapon - you can choose. Determine the base range of the weapon in 10 ft. increments, and add the corresponding modifier for each increment you add.
| Property | Damage Factor Modifier |
|---|---|
| Ammunition (range +10/+40) | -0.15 per 10 ft. |
| Loading | +0.45 |
| Thrown (range +10/+30) | -0.05 per 10 ft. |
Step 4: Find Damage Die
Using the damage factor that you have calculated so far, 'purchase' a damage die. If, after selecting a damage die, you are between -0.3 and 0.3, your weapon is statistically balanced! All the 5th edition weapons meet this standard, with the exceptions that handaxes and light crossbows are high, then the sling, dart, trident and blowgun are low.
| Dice | DF Cost |
|---|---|
| 1d4 | 2.5 |
| 1d8 | 4.5 |
| 1d10 | 5.5 |
| 1d12 | 6.5 |
| 3d4 | 7.5 |
| 1d6 + 2d4 | 8.5 |
| 1d8 + 2d4 | 9.5 |
| Dice | DF Cost |
|---|---|
| 1d6 | 3.5 |
| 2d4 | 5 |
| 1d6 + 1d4 | 6 |
| 2d6 | 7 |
| 1d8 + 1d6 | 8 |
| 2d8 | 9 |
| 1d12 + 1d6 | 10 |
| 3d6 | 10.5 |
Adding Custom Properties
If it is a property where the damage change can be calculated out (i.e. re-rolls dice under certain conditions), do that to determine the modifier. Otherwise, just make it up so that is falls roughly in line with the others.
Example
Say I want to make an insanely long ranged crossbow. First, I pick the Martial property to start, giving me an initial damage factor budget of 4.45. Next, I choose the Heavy and Two-Handed general properties, which modify my damage factor budget by +1 and +1.35, respectively, giving me a new total of 6.8. Then, I move on to picking ranged properties. I add Loading for +0.45, bringing me to 7.25. I decide to add 32 10 ft. increments for the base range, for a total range of 320/1280 and a total modifier of -4.8 (32 x -0.15). My budget for a damage die is now 2.45. Finally, looking at the table, I can purchase a d4 for the damage die, and the final sum (-0.05) will be within the -0.3 to 0.3 range.
How the Formula was Derived
I first created a table of the 5th edition weapons in Excel. Then, I calculated a damage factor for each weapon on the list. Next, I used the Non-Dominated Sorting Genetic Algorithm (NSGA-II) with continuous inputs for the values of each weapon property, rounded to the nearest 0.05, to minimize the standard deviation of the damage factor and minimize the number of weapons outside of 1 standard deviation. Final average and standard deviation were also rounded to the nearest 0.05.
Notes
- The Blowgun and Net were excluded from the analysis
- Javelin range was set at 35 because it's range is 30/120 instead of 30/90.
- Nonlinear interactions between properties were considered negligible
DMG Firearms
The same calculation process was applied to the firearms on DMG pg 267-268. Ammunition, Loading, Martial and Two-Handed properties keep their existing modifiers for commonality with the rest of the framework. The laser rifle and shotgun are underpowered using these metrics.
The Numbers
Standard Deviation: 1.5
Weapon Properties
| Name | Damage Factor Modifier |
|---|---|
| Firearm | +0.85 |
| Modern | +6.2 |
| Futuristic | +21.8 |
| Burst Fire | +7.85 |
| Reload (+1) | -0.35 |
Notes
- The Firearm property reduces the maximum range by 25% (changing the range scale to +X/+3X to fit the DMG weapons).
Gunslinger Firearms
This set is for Matt Mercer and Critical Role's Gunslinger Archetype. Ammunition, Light, and Two-Handed properties keep their existing modifiers for commonality with the rest of the framework. The Musket is low and the Bad News is high.
The Numbers
Standard Deviation: 1.35
Weapon Properties
| Name | Damage Factor Modifier |
|---|---|
| Firearm | -0.5 |
| Explosive | -3.1 |
| Misfire (+1) | +3.3 |
| Reload (+1) | -0.3 |
Notes
- The Explosive property reduces the maximum range by 50% (changing the range scale to +X/+2X).
- What's interesting is that making a weapon a firearm serves to effectively decrease the damage die.
Extra Details
The "damage factor" is not the actual damage of a weapon. It is a number used to quantify weapon efficacy, though it is described as a pseudo-damage because there is a 1:1 relationship between the average damage of a die roll and its contribution to the damage factor. Likewise, the damage modifiers represent approximately what the game designers decided each weapon property was worth in terms of contribution to average damage. This is different from the actual damage output of a property. For example, a 1d8 weapon with Reach and a 1d8 weapon without Reach do the exact same amount of damage - 1d8. However, implicitly, the designers decided that adding the Reach property to a weapon was equivalent to adding 1.4 points of average damage. This could be because weapons with Reach have more opportunities to attack, and thus will do more damage over the course of an adventure. Similarly, the Martial and Heavy properties both serve to increase the damage die by one size. In this case, it is likely that the designers explicitly decided to increase the damage of those weapons to maintain verisimilitude.
Additionally, there is zero correlation among damage factor, weight, and cost for the 5th edition weapons, so just make that stuff up. Damage type doesn't matter either.