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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.

Weapon Damage Amount D&D

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.

Weapon Modifiers in DandD Damage

 

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?

11 Comments »

  1. Nice post, Luke! With your first example (+4 Dagger vs +2 Long sword) the dagger yields a damage range of 5-8 pts, and the long sword ranges from 3-10 pts. While a number of people would opt for the higher damage potential of the long sword, you’re probably better off sticking with the more consistent damage of the dagger. Especially if your chances for hitting are low to begin with.

    I’m curious why they chose 1d12 for the Pike, but 2d6 for the Greatsword? It does give a small difference between the two weapons, but is less consistent overall. Then again, D&D has always been stuck by the huge gap between d12 and d20. You’d think after all these years, they would start manufacturing some d14, d16, and d18 dice? Which would likely create even more confusion amongst people on ‘what dice do I roll?’. Though I found for new people, ‘rainbow’ colored sets certainly help.

    Liked by 1 person

    • I actually wonder why no one has ever created a D14, D16 or D18, that’s a really great point.

      I mean, it has to be possible to make a D16 or D18, right? 🤔

      I completely take your point as well about the pike. No idea why that would do more!

      Agree with you on the damage potential. Personally, I always choose on guaranteed minimum rather than potential maximum, but I am sure there is a debate there. Which would you rather go for?

      Liked by 1 person

      • Guaranteed minimum. I would think I learned most of dice math from Blood Bowl, but really that particular lesson was from D&D.

        I always wanted to play a Magic-User and get them to higher level. Unfortunately, (at least back in the day) their hit points were 1d4 at 1st level. With 1 spell, I was typically thrown into combat with a 1d4 dagger. With a poor chance of hitting, you really, really, really hope you’re not rolling a 1 when you finally do hit. Not that it doesn’t happen with Fighters too, rolling a 1 on a d8 after several misses, can really make you frustrated.

        I’ve seen some odd dice, and I’m sure you can find them all. The new Blood Bowl set comes with a d16, to make it easier to randomly roll against the team (max 16 players per team). But for whatever reason, they just never made it into D&D. They might have been better spreading things out a bit. d6, d10, d14, d20?

        And if we’re really going to be talking about dice (haha!), why not get rid of the d4?! That’s the worst die to “roll”. I picked up some d8s numbered 1-4 at one point, and if I ever went back to D&D seriously, I’d be making great use of those.

        Liked by 1 person

        • Totally with you when it comes to Magic Users. It’s one of the reasons I didn’t hugely like the magic users in AD&D – they just fell apart so easily, and since they only had a few spells making them so not worth playing. At least Cantrips and a few more proficiencies make them worth playing again in later editions.

          Those D16 and D8 sound interesting – D4s – I feel your pain, and like the idea of getting rid of the D4!

          Liked by 1 person

          • I think it’s just one of those things where they are stuck with what came before. They would have to change a lot of charts, etc. if they change the die values.

            I kind of liked the challenge of trying to keep my Magic-User alive in 2nd edition. I had to shift to full on ‘survival’ mode, of course. Stay away from close combat. Use ranged weapons to stay somewhat relevant. Always make sure the fighters were inbetween any monsters and me. Try to remain on the party’s good side and retain super loyal NPCs.

            Liked by 1 person

            • Funny, I said “Guaranteed minimum.” earlier….and in some games (like Blood Bowl), that probably would be guaranteed. In a competitive game, I’m going to most likely look at stacking the advantages, etc.

              However, a lot of my role-playing was tied around characters and letting that dictate decisions. I’ve often done very silly things without regards to the best die rolls and min/maxing. It depends on the game/mood for me. I also really enjoy playing the character who shouldn’t be able to survive based on their stats, but somehow manages to beat the odds.

              Liked by 1 person

  2. interesting, as always. I do enjoy exploring some of the maths that lie beneath. That the minimum is the nearly the same (for a given damage modifier) follows from all dice having ones, and rolling two dice at most in this analysis. Maximums can be misleading, because rolling larger maximums is less likely than the lower maximums (e.g. I have a 25% of getting max damage with a dagger but only 10% chance with a glaive).
    Another way of looking at this could be calculating the probability of killing a (7hp) goblin with a single blow. A dagger with a damage bonus of +3 has a 25% chance of doing 7hp damage, while a short sword has a 50% chance. The Goblin Death Rate, it’s a stat waiting to happen.

    Liked by 2 people

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