Damage types in D&D have no inherent rules attached to them. Technically slashing, fire, and necrotic are all just words. They all come with flavor, and describe what's happening in the world in different ways, but absent all content that goes with the rules system that D&D provides, they have no meaning.
But, of course, in any modular game like D&D, tags of this sort can wind up meaning quite a lot.
The biggest distinction is, of course, between the "magical" and the "physical" damage types. Bludgeoning, piercing, and slashing are the only damage types that non-magical, non-futuristic weapons can produce (and most magic weapons do as well). But then, some magical spells, like Cloud of Daggers or Catapult will deal these, and flames, frigid water, and literal acid that have no magical property will nevertheless do damage that is usually associated with magic.
I want to take a look at every damage type and see how likely they are to deal solid damage to a monster. I'm going to limit my categorization to resistances, immunities, and vulnerabilities, mainly for the purpose of keeping it easily searchable. Obviously, there are cases like radiant damage preventing a zombie's undead fortitude or fire/acid damage preventing a troll's regeneration that are going to fall through the cracks here, but I'll try to be reasonably thorough. I'll be searching through monster stat blocks, filtering for vulnerabilities, resistances, and immunities (and looking at conditionals, like whether the damage comes from a magic weapon.)
(Also, this post is from between the releases of Candlekeep Mysteries and Van Richten's Guide to Ravenloft, so these are always changing.)
The damage types in D&D are Acid, Bludgeoning, Cold, Fire, Force, Lightning, Necrotic, Piercing, Poison, Psychic, Radiant, Slashing, and Thunder.
Acid:
Vulnerabilities: 1
Resistances: 48
Immunities: 43
Notably, all Yugoloths are immune to acid damage. I guess Gehenna has a lot of acid?
Bludgeoning:
Vulnerabilities: 16
Resistances: 24 (unconditional) 204 (conditional)
Immunities: 1 (unconditional: only the artifact Mighty Servant of Leuk-o) 82 (conditional)
As one of the "physical" damage types, it's not surprising to see all the resistances and immunities to non-magic damage. Bludgeoning is particularly good, though, when dealing with many skeletal monsters, as well as some made of glass or ice.
Cold:
Vulnerabilities: 7
Resistances: 163
Immunities: 62
As one of the more common "environmental" damage types, it's not a surprise to see a lot of resistances and immunities here. The vulnerabilities are all for fiery or lava-like creatures. Actually, I had sort of lied about inherent rules attached to damage types - creatures (including player characters) who are resistant to cold don't need to worry about getting exhausted due to extreme cold.
Fire:
Vulnerabilities: 24
Resistances: 127
Immunities: 99
Again, like cold, fire resistance can prevent exhaustion from extreme heat. Also, anything in water gets resistance to fire damage (which makes me wonder then, if RAW, falling in boiling water inherently does half the damage it should). Fiends generally are resistant to fire and all devils are immune to it. Fire does get a lot of vulnerabilities from both frozen things and also any dry things like a scarecrow stuffed with straw.
Force:
Vulnerabilities: 2
Resistances: 0
Immunities: 5
So far (and likely to stay that way) the least interactive of the damage types, Force sort of represents a generic "it's magic" element. Helmed Horrors, interestingly, are immune to it (along with some other types) and most of the things immune to Force are variants on those. Still, a mostly safe bet (which is good news for Warlocks).
Lightning
Vulnerabilities: 1
Resistances: 115
Immunities: 58
Another classic damage type, all demons get resistance to this (along with fire and cold).
Necrotic:
Vulnerabilities: 2
Resistances: 66
Immunities: 54
Necrotic is sort of the opposite of radiant, but a lot more things (I believe) are resistant to necrotic than radiant. Notably, I think all incorporeal undead (like ghosts, specters, etc.,) are immune to this.
Piercing:
Vulnerabilities: 3 (conditional)
Resistances: 33 (unconditional) 208 (conditional)
Immunities: 82 (conditional)
Another "physical" damage type, magic piercing weapons should always get the job done. Notably, Rakshasas and their variants are actually vulnerable to piercing damage from good creatures, which is apparently a simplified version of earlier editions where it was specifically from crossbow bolts fired by good characters.
Poison:
Vulnerabilities: 0
Resistances: 46
Immunities: 414
Damn, poison's got some real downsides. I guess it doesn't help that almost all constructs, almost all fiends, any Yuan-ti, and probably a lot of oozes are totally unaffected. I don't know about best, but poison damage might turn out to be the least effective damage type, with over four times as many immunities as the next damage type. But then, let's hold off, because Psychic's next.
Psychic:
Vulnerabilities: 1 (poor Flumphs!)
Resistances: 18
Immunities: 79
This is kind of interesting. Like poison, there are more immunities than resistances. Just as poison can't affect non-living things, psychic can't hurt mindless things. (And there's usually a good overlap.) Still, this is clearly better than poison by the numbers.
Radiant:
Vulnerabilities: 9
Resistances: 15
Immunities: 7
You might be surprised to see so few vulnerabilities to this holiest of damage types (though it can simply be from literal light, like a laser pistol, or other forms of radiation like sickening radiance.) Often, though, it's not that a creature is vulnerable to radiant, but that it's resistant to so many other types. Still, with so few things that won't take full damage, radiant's a very powerful damage type, and might win out.
Slashing:
Vulnerabilities: 0
Resistances: 20 (unconditional) 210 (conditional)
Immunities: 9 (unconditional) 82 (conditional)
Yep, lots of oozes just don't mind sharp things passing through them - though I don't really know why any other physical weapons wouldn't similarly fail to affect them. This is, I think, the most common weapon damage type (though given that non-futuristic ranged weapons all do piercing, I could be wrong) but also I think the one that runs into the most problems.
Thunder:
Vulnerabilities: 3
Resistances: 36
Immunities: 6
Thunder is one of the harder damage types to come by, but also seems to be pretty broadly effective. Did you know that Earth Elementals are vulnerable to it?
Ok, now let's try to score these. Because vulnerabilities double the damage the target takes (like adding one more instance of that damage) and immunities eliminate all the damage (like subtracting your one instance of the damage) I'm going to value them as opposites, while resistances will be half as much, as they only subtract half the damage. Because resistances and immunities are going to be more common, we're going to count them as the positive values, and the best damage type will be the one with the lowest score.
So, a vulnerability grants a type -2 to their score. A resistance adds 1. An immunity adds 2.
We're going to handle bludgeoning, piercing, and slashing damage a little differently: using a nonmagical weapon will significantly decrease their effectiveness, so we're going to talk about them as two separate damage types each. I'm including the "good piercing damage hurts Rakshasas" in the calculations here.
Ranked from worst damage type to best:
Poison: 874
Slashing (nonmagical damage): 412
Piercing (nonmagical damage): 399
Bludgeoning (nonmagical damage): 362
Fire: 277
Cold: 273
Lightning: 229
Psychic: 174
Necrotic: 170
Acid: 132
Thunder: 42
Slashing (magical): 38
Piercing (magical): 27
Radiant: 11
Force: 6
Bludgeoning (magical): -6
So there we have it: I highly recommend avoiding poison as a primary source of damage, as you're going to run into resistances and immunities to an absurdly higher degree than any other damage type. Meanwhile, on the flip side, once you can get magic weapons, bludgeoning damage is going to be fantastic - you're more likely to encounter things vulnerable to your strikes than immune, and only a handful of things are resistant to magic bludgeoning damage.
Given that bludgeoning's most of what a Monk will do, that's good news for them.
For you firebugs out there, I've got bad news for you: once magic weapons become easy to get, you're second only to poison in ineffectiveness. Though other classical magical elements like cold and lightning are not far ahead of you.
Among magic damage types, force and radiant are both quite good options, largely due to a lack of resistance or immunities. Likewise, consider that most things that are resistant to radiant damage are good-aligned things like celestials, so unless you're playing an evil campaign or your DM is being very subversive, you're likely not to have to worry about this all that much.
Radiant damage tends to be limited to Clerics and Paladins, though Force is a great option here as well (again, good news for Warlocks.) Among the more easily-accessed damage types, acid seems like a pretty good option. I'd recommend Thunder, but there aren't a ton of spells that do that.
I was pleasantly surprised that psychic pulled out so far ahead of poison, which makes my desire to play a Soulknife feel surprisingly more viable.
I think there's also something to be said for analyzing the ease of access to these various damage types, though that's a whole complicated process that I'm not eager to get into right now. I suspect the reason we see so much resistance and vulnerability to fire, cold, and lightning is that I'd bet these are also the easiest elements to get your hands on as a spellcaster. Still, maybe consider focusing on acid! (Again, as long as you don't expect to be facing a lot of yugoloths.)
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