Damage Modifiers in D&D: A Handy Graph
D&D damage multipliers are a curious thing. Looking at them, they are so simple, and yet underneath it all they can be quite complex.
This article today was born out of a curiosity and a deceptive question – what damage modifiers on which dice are equal to which other damage modifiers on which other dice?
Or, to put it simply – is a +4 Dagger better than a +2 Longsword?
Okay, so it is a bit of a random question, and it is funny where these things lead; however, it lead to a short analysis that actually created a somewhat useful reference tool. That tool is the graph below.
Damage Modifiers in D&D
There should probably be a bit of an explanation to the above graph. What the above shows is different weapon types (one per each type or pairing of damage die in the rules in the Player’s Handbook) and what their average damage is at various modifier levels.
The Y Axis is Average Damage, the X Axis is the size of the modifier.
The weapons were chosen based on the type of dice. In D&D, the base weapons (leaving aside blowgun) come in seven different varieties. Those are 1D4, 1D6, 1D8, 1D10, 1D12, 2D6, and 2D8. What this means is, since those dice cover every option in the basic game for normal weapon damage, we can actually graph the results at various different modifiers or proficiency levels.
We actually had a bit of a debate whether to do lowest, average, and highest possible damage per dice/modifier type, but decided there wasn’t a huge amount of point. The graph is the same – the only thing that changes is the scale on the Y axis.
By using the dice we can create a data set, and by utilising that data set we can create a graph like the the above to compare damage types. We can look at that graph and draw a line to say, definitively, what kind of weapon and what kind of modifier outdoes another. We can then ask questions like – do you attack with your Longsword for which you get your +6 modifier or do you attack with your +4 Glaive? Using a graph like this it is easy to see.
In fact, we can take that as a really life example by…wait for it…drawing a line.
In the graph above, the red dotted line rests at the top of a +6 Longsword. As we can see, it is equivalent to a +7 Short Sword or a +5 Glaive (not a +4). Alternatively, it is the same as a +4 Pike, or a +8 Dagger.
Of course, each weapon has its own perks and disadvantages. Pikes are great for damage, but if you are indoors you may prefer a Longsword. The graph is more of a reference than specifically for recommendations. Going around a dungeon with a Pike makes it really difficult to turn around corners. You can…err…take my word for that.
The Interesting Point With Damage Modifier Averages
There is a weird point with averages when it comes to rolling dice, and that is although the odds of rolling any face is even, the average isn’t just half the die faces. So, for 1D6 the average isn’t 3, and with 1D8 it isn’t 4.
Instead, the average is actually the sum of all of the numbers on a dice, divided by the number of faces. This is a cool little formula that can be used to work out the average of any dice based on the numbers (so if you had a D6 with weird numbers on the faces, this would still work).
What that formula means that with a D6 we have (1+2+3+4+5+6)/6, or 21/6. The answer to that isn’t 3, but rather 3.5. For a D8 we have (1+2+3+4+5+6+7+8)/8, or 36/8, which has the answer 4.5.
It’s one of those interesting quirks of numbers and dice. Math, amIright?
Recognising Patterns in Damage Modifiers
Whilst we’re geeking out over mathematics, there are a couple of other observations.
What is interesting is that we can see patterns emerging throughout the graph. 1D6+2 is the same as 1D8+1, as an example. This becomes incredibly prominent later on where we can see 1D4+8 is the same as 1D6+7, which is the same as 1D8+6, which is the same as 1D10+5, which is the same as 1D12+4. It’s not as clear cut when looking at the damage modifiers of the weapons where we are rolling two dice, but it is an interesting observation none the less.
A further quizzical point is that the minimum for all of the one dice weapons would be the same (one plus the weapon modifier). All of their averages are one apart, and all of their top ends are two apart. So the lowest number on 1D4+1 is 2, the average is 3.5, and the top is 5. With 1D6+1, the lowest number is 2, the average is 4.5, and the top is 7.
So there we have it – a quick debate, a slightly longer to draw graph, and a bit of an explanation to go with. Not bad for a Wednesday.
I’m going to keep this brief, but please let me know your thoughts in the comments below. Are there any specific D&D questions you would like me to graph moving forward? Alternatively, what are your thoughts on the damage modifiers?