D&D 5E The mathematics of D&D–Damage and HP

[FrogReaver]

Its all relative and depends on context. The problem, though, is that DPR is isolated from other analysis types and its often used as the sole determinant for whether an option is good or not.

If the assertion you are making is that DPR isn't a "complete" metric then we all agree.

But if you are asserting that DPR isn't a damn good heuristic for evaluating options in the game then I'd say you need another look.

I've brought up Greatswords vs Greataxes and came to a conclusion that while Greatswords is a safer option, Greataxes are good for quickly finishing off enemies in more desperate situations.

Counterexample: consider a 35 hp enemy and you are doing 1d12+5 vs 2d6+5 on hit. You'll need at least 3 hits to kill (ignoring crits) and on average you will need 3 hits to kill. In this scenario the Greatsword will kill the enemy faster than the Great Axe.

 

[fearsomepirate]

you suggested a caster also prepare ten different mostly concentration almost good buffs

I did no such thing. You asked for a list of spells I would consider good, and I gave you a list. At no point did I say you should prepare or even learn all of them. Which spells you actually learn, prepare, and cast is contingent on a variety of factors in a real-world game that can neither be assumed away nor simplified.

edit: Yes WoW is very different from d&d, those differences are what makes the cold logic of pure math & "what do you bring to the table" used in things like WoW raid slot selection perfect for highlighting the problems in this aspect of 5e design

The problem with WoW-style analysis is D&D isn't a pure DPS/HOT game. Affecting chance to hit and action economy are huge parts of the game. Action denial, giving allies advantage, and imposing disadvantage on enemies aren't things you can't be dismissive about, and you to this point have been entirely dismissive about them. If you're not incorporating them into your analysis, you're not providing useful math.

Counterexample: consider a 35 hp enemy and you are doing 1d12+5 vs 2d6+5 on hit. You'll need at least 3 hits to kill (ignoring crits) and on average you will need 3 hits to kill. In this scenario the Greatsword will kill the enemy faster than the Great Axe.

Ignoring crits, the greatsword has a higher chance to kill monsters with 39 hp or less within 3 hits; the greataxe fares better in the 40-51 range. If you have the Great Weapon fighting style, however, the crossover point is 46 hp.

 

[pemerton]

Affecting chance to hit and action economy are huge parts of the game. Action denial, giving allies advantage, and imposing disadvantage on enemies aren't things you can't be dismissive about, and you to this point have been entirely dismissive about them. If you're not incorporating them into your analysis, you're not providing useful math.

As I already posted, my experience in these matters is 4e D&D not 5e D&D. But what you say here is absolutely true for 4e.

The weakest damage dealer in the 4e game that I GMed was the invoker/wizard. He was probably the weakest combat character overall, too - he was also the party "skill monkey"/ritualist.

But at low levels (when he was mostly wizard) his effects like AoE daze (Colour Spray) or AoE hostile teleport (Twist of Space) and at high levels (where he's mostly invoker) his effects like AoE blindness (Glyph of Radiance) and AoE domination (Compel Action) were super strong. Even Thunderwave (AoE push) is pretty good.

At least in 4e, another relevant consideration in combat maths is who takes the damage? In our 4e game the fighter and paladin had enormous depth in both healing surges and the ability to trigger those surges during combat, and it wasn't necessarily their lack of hp/surges that would drive the rest cycle. I know that 5e uses different healing mechanics, but an important part of battlefield control isn't just action denial but also controlling who is exposed when to what sorts of attacks.

 

[FrogReaver]

Ignoring crits, the greatsword has a higher chance to kill monsters with 39 hp or less within 3 hits; the greataxe fares better in the 40-51 range. If you have the Great Weapon fighting style, however, the crossover point is 46 hp.

Technically:
The Greatsword will kill faster in hp ranges of (7-12), (18-26), (35-39), (52-53).

That is, for those hp values it is more likely to actually kill an enemy on the first possible round to kill the enemy than it is for the greataxe to do so.

Anything about 53 Damage the great axe is more likely to kill on the first possible turn. Albeit, the chance that occurs pretty rapidly drops off. For example on 5 attacks - when the great axe player can first do 69 damage, he has a 8% chance of dealing at least 69 damage. Meanwhile the Greatsword Fighter has a 5.8% chance of dealing at least 69 damage. Going 1 turn longer the greatsword player now has a 72.09% chance to have done at least 69 damage. The Great Axe player only has a 52.3% chance of doing at least 69 damage. Even if I wanted the enemy dead as fast as possible, gaining a 3% chance for a 5 hit kill vs gaining a 20% chance for a 6 hit kill still makes me prefer to greatsword from an optimization perspective - even when optimizing for fast kills.

 

[pemerton]

On Great Axe vs Great Sword:

Chance of a 12: 1 in 12 vs 1 in 36
Chance of 11+: 1 in 6 vs 1 in 12
Chance of 10+: 1 in 4 vs 1 in 6
Chance of 9+: 1 in 3 vs 5 in 18
Chance of 8+: 5 in 12 for both
Chance of 7+: 1 in 2 vs 7 in 12​

So it's a pretty quirky range of opponents where the one-round kill chance is better with the Great Axe (eg cultists, bandits, guards, hobgoblins), And then once it gets into multi-round kills as @FrogReaver has posted the expected damage starts to loom more significantly.

And of course the variance cuts the other way too - the chance of not killing in two rounds with a Great Axe is going to be greater for those enemies than with a Great Sword.

 

[tetrasodium]

You said that martials can do things with skills when I suggested that the high level casters are mass suggesting, teleporting, plane shifting, reviving the dead, miraculously curing curses and diseases, transforming into dragons, conjuring elementals/celestials/etc...

You also should go back to review what you said next time you rush to roll out the snark like when I asked for details on "things". That is significantly more detailed than your original list of "things"

IMO. High level casters are already generally stronger and more versatile than martials in combat. And they have the ability to actually do things out of combat.

While still not enough to bridge the gap & badly contrived or depending on system differences no longer present in 5e to manufature value in many ways it's at least some level of detail that is capable of being responded to.

• teleport This one is a complex array of issues that range from only being useful if the GM makesit so to depending on edition differences no longer present in 5e
  • First & foremost trying to teleport to an area you are "very familiar with" has a 24% chance of not getting where you want ranging from a mishap to going somewhere else. The odds quickly get worse from there.
    • Even if we assume that one can teleport without error every time it runs into a more significant problem. Specifically that there is no point unless the GM makes it a point. In past editions when you recovered hp slowly while resting in the field & slightly less slow while resting under the right conditions it was a serious benefit to simply teleporting back to town to rest . Firstly that was still a thing generally of dubious value in those older editions though because the person needing the heavy duty recovery was unlikely to be the squishy caster so the caster recovering faster than their crunchier allies is a meaningless hurry up & wait benefit. Secondly even if we assume there was some tangible benefit to doing it the caster still needs to somehow return & doing so is unlikely to be easy or worth the risk unless the gm places a teleport circle where the party is now
• planeshift: This one now has two massive elephants in the room & both of them left a pile on the floor .
  • The first elephant in the room here is that this 7th level spell requires a "forked metal rod worth 250gp, attuned to a particular plane of existence." This spell literally can not even be cast unless the GM gives you something specific to cast it with or something specific to craft the required component needed to cast it.
  • The other is of course Descent into Avernus where the players along with an entire city are dragged into another plane without the use of a player casting such a spell & it eventually ends with players returning from a hardcover adventure where nearly every single creature has some combination of energy resists energy immunities and magic resistance long before anyone is capable of casting it.
• revive the dead: This one is mostly divine specific but I'm not dismissing the possibility of a arcane raise dead type spell existing & caster focused divine class/archetpes exist so it doesn't go away at that. The critical second point is that bringing Bob's body (or some piece of it) back to a town/city & paying a local cleric to bring him back has always been an option to the point of that kind of thing occasionally even getting mentioned in modules & such simply because Bob can't cast raise dead on himself if he's dead if no other reason. Also there are a wide array of ways that a GM could have something else bring bob back, Keith Baker wrote about several here & some of he ravenloft/vanrichten previews seem to imply similar things while talking about dark gifts. I'm not sure why you'd bring up a spell the caster can use to bring an ally back from death but not themselves as such a massive feather in the cap for casters.
• curing curses & diseases.
  Spoiler: xge relaxation

  
  In 5e bestow curse is a concentration spell with a 1 minute duration , trog stench lasts 1 turn, wight life drain lasts until a long rest... While most of these effects allow regular saves or automatically go away after a long rest there are still rare exceptions like mummy rot & the clay golem thing a group without a caster can hire an NPC to cure it just as they could if bob was the one who needed to cast raise dead but was also the one who was dead. "saved the party from needing to hire an npc to cast a spell" is lightyears away from justifying all of the cards in the deck stacked elusively against casters
• transforming into dragons: The only way that even google seems to think this might be doable is with true
  Spoiler: true polymorph

  
  As a 9th level spell this is only possible from level 17 on and of such dubious value & even my best effort from google was quick to point out the various downsides of tilting at this windmill that include but aren't limited to "What'd be the reason for them to stick with the party?" "retire the character" and my persona favorite "High level D&D is naughty word BONKERS ... I promise you the other players will be doing bonkers naughty word too, and at that point the campaign will be almost over anyway.".
• conjuring elementals/celestials/etc... Really?... No seriously... This is getting into territory on par with holding up how well sidewalk support using a unicycle or pogostick in a discussion about the state of bike lanes. You think that all of these strings red tape and hurdles were to proactively offset the game crushing powerhouse known as the shepherd circle druid almost nobody has ever seen played since it was released in XGE? You do know that magic resist energy resist/immune legendary resist & so on don't affect conjured creatures right? While casters other than the shepherd can conjure creatures, they are rarely worth conjuring. Tasha's introduced some new spells to summon useful creatures, but again we are talking years into 5e & concentration spells.

 

[tetrasodium]

I did no such thing. You asked for a list of spells I would consider good, and I gave you a list. At no point did I say you should prepare or even learn all of them. Which spells you actually learn, prepare, and cast is contingent on a variety of factors in a real-world game that can neither be assumed away nor simplified.



The problem with WoW-style analysis is D&D isn't a pure DPS/HOT game. Affecting chance to hit and action economy are huge parts of the game. Action denial, giving allies advantage, and imposing disadvantage on enemies aren't things you can't be dismissive about, and you to this point have been entirely dismissive about them. If you're not incorporating them into your analysis, you're not providing useful math.

That's a bit off. You said "There are plenty of things a wizard can do if a monster has good saves" and were asked to be specific. When you had it displayed how bad much of that specific list is you want to change your tune from "plenty of things " to something but not something that your willing to suggest or stand behind as a good option when a monster has good saves. That last condition is critical because there are a ton of monsters with energy resistance/immune along with good or great saves and/or magic resistance to give advantage on the saves.

The sort of purpose built quantum adventurer you are advocating for now is exactly the reason why having every card in the deck stacked against a allowing a caster hyperoptimized for any specific encounter encounter is such a problem for casters. The caster needs to be functional to a meaningful degree in a wide enough variety of encounters throughout the adventuring day or they need to be absurdly functional in a few. Taken as a whole the availability differences & impact of +N weapons vrs focus items, ac vrs saves, actual impact of resistant to nonmagical b/p/s vrs energy resist/immune, magic resist/legendary resist vrs almost every creature in 5e having easy to hit AC is a massive overcorrection from the old days of LFQW. The fact that many of those creature specific things combine so frequently while rarely if ever wind up set in a fashion that makes casters shine makes the problem worse.

D&d is indeed not a game of pure dps/hot, however the framing & sort of metrics used to rate the relative value of class A vrs class B in a raid group from games like WoW makes an excellent lens to view when a class misses the mark due to a combination of both class/spell design and creature/system design. The fact that a venn diagram of d&d players WoW players & MMO players is going to have significant overlap makes it even more relevant due to players already building the mental pathways to notice such things at a casual eyeball level during the course of a campaign without the need for detailed statistical analysis,

 

[FrogReaver]

That's a bit off. You said "There are plenty of things a wizard can do if a monster has good saves" and were asked to be specific. When you had it displayed how bad much of that specific list is you want to change your tune from "plenty of things " to something but not something that your willing to suggest or stand behind as a good option when a monster has good saves. That last condition is critical because there are a ton of monsters with energy resistance/immune along with good or great saves and/or magic resistance to give advantage on the saves.

The sort of purpose built quantum adventurer you are advocating for now is exactly the reason why having every card in the deck stacked against a allowing a caster hyperoptimized for any specific encounter encounter is such a problem for casters. The caster needs to be functional to a meaningful degree in a wide enough variety of encounters throughout the adventuring day or they need to be absurdly functional in a few. Taken as a whole the availability differences & impact of +N weapons vrs focus items, ac vrs saves, actual impact of resistant to nonmagical b/p/s vrs energy resist/immune, magic resist/legendary resist vrs almost every creature in 5e having easy to hit AC is a massive overcorrection from the old days of LFQW. The fact that many of those creature specific things combine so frequently while rarely if ever wind up set in a fashion that makes casters shine makes the problem worse.

D&d is indeed not a game of pure dps/hot, however the framing & sort of metrics used to rate the relative value of class A vrs class B in a raid group from games like WoW makes an excellent lens to view when a class misses the mark due to a combination of both class/spell design and creature/system design. The fact that a venn diagram of d&d players WoW players & MMO players is going to have significant overlap makes it even more relevant due to players already building the mental pathways to notice such things at a casual eyeball level during the course of a campaign without the need for detailed statistical analysis,

A level 15 wizard with 20 spells prepared is hardly a quantum adventurer.

 

[TwoSix]

D&D is nothing like WoW in this regard. You don't build your character and then go hang out in a lobby, waiting to get chosen for a raid by persons of unknown composition, hoping to find a party that matches up with you. You build your character along with the rest of your party over months or even years of play. You should be choosing spells that synergize with your allies' abilities, not basing them off some build you found online.

Heh...I thought you were being sarcastic for a second. Outside of absolute top-end guilds, modern endgame WoW is literally waiting in a lobby to get chosen for a group (normally a Mythic+ dungeon) of unknown composition.

 

[TwoSix]

A level 15 wizard with 20 spells prepared is hardly a quantum adventurer.

Well, if they've prepared stone shape, they could tunnel.