D&D 5E Classes, and the structure of DPR

[clearstream]

A very specific situation can be analyzed with probability distributions (including crits). However, the analysis for this could change significantly depending on the specific damage, hit rate and number of attacks paramaters you use. IMO, that means that specific kind of analysis in regards to this question won't be generalized enough to be beneficial.

Ah well. Here is some of the argument on blur in another context. I've looked at it a few times since, and it is very efficient where a character has good AC to begin with. D&D 5E - Bladesinger - a criticism of its design [EDIT let's not get into bladesingers though! This is linked only to share with you where some previous discussion landed.]

This is only true if you are talking relatively. Absolute matters more given the number of hits we are talking about potentially receiving. +1 AC will cause the same number of hits to miss at 20AC as at 10AC.

Another way to model this is to consider the reduction to the number of hits you are taking. If your AC is such that monsters hit you on say 18+, then gaining +1 means that for every three hits you were going to take, you instead take two. An improvement of a third or 33%. Generally, it is more important to model defenses as reduction in incoming, than as change on base value, because it is the reduction on incoming that will be experienced at the table.

One character in my current campaign is an SnB battlemaster. The player isn't overly concerned with optimisation, but they did take commander's strike, which they can use to give the party rogue a second sneak attack each round. The battlemaster simply stands next to a target, and it will be in for two turns of sneak attack damage a round (presently +6d6 per sneak attack). The battlemaster has chainmail, a shield +1, and defense, for 20 AC. The character's weakness - as a dwarf - is their move.

In a recent encounter - in ToA - the monsters had +6 to hit, and there were nine of them with two attacks each. For every eight hits he would take at AC 19, he takes seven at AC 20. An improvement of 12.5%. Their damage was about 10 a hit, and due to specifics of ToA he has 144hp. On average it would take 41 of their attacks for them to kill him at AC 20, and 36 at AC 19. Again around a 12% improvement. More tellingly, if they dog-piled him they will on average kill him in two rounds, at AC 19, but will need three rounds at AC 20. If he had plate, the benefits of defense would be even more pronounced (about 17%, instead).

These kinds of considerations are not obvious, and I guess bring me back to my theme that defenses are typically undervalued.

 

[Shardstone]

Exactly, that's why I think it is best to think of this as the baseline or reference-structure. And - crediting other respondents - it is very important to call out that there is diversity. Think about it like this

1. The tiers are meaningful in 5E. Tier 2 characters will see a step (or steppy) increase in mechanical power over tier 1 characters. And tier 3 over tier 2, etc.
2. The simplest place that is visible is in fighter extra attack and warlock eldritch blast.
3. Each class has been consciously designed to have its own approach, but the approaches can be simplified to - A) I attack many times, B) I attack fewer times but do more damage, C) I attack and also defend. Fighters are A. Rogues are B. Rangers are C. Note that 'defend' is where you see even more diversity because it often spills over into explore (e.g. ability to hide).
4. This simplifies the task of design as it means a designer knows the approach a class is using, and they know how much power to build into its features at each level. You can observe this most easily I think in the designs for sub-classes such as fey wanderer, if you compare its features to other more straightforward classes.

The designers introduce enormous variation as offsets from those backbones, but the intents always ring through. Look at every ranger 11th level feature from PHB, XGE and TCoE and compare those to every fighter 11th level feature. Cost the barbarian d12 HD in ASIs, and consider that against the value of spell slots and spell levels. You will see underlying skeleton bringing cohesion everywhere!

How can I get you to do a full analysis on all this? This is amazing!

 

[HammerMan]

you may have struck on the main MATH problem of 5e. not all classes match for damage, and the classes that do are not even with out of combat abilities...

Wizards (any caster really but lets stick to basics) get up grades to cantrips at 5 11 and 17, so at will they keep up, but are a bit weaker then most martial classes... BUT each spell level is a HUGE boom of damage, and once we are talking 5-11th level they have enough slots to not need those cantrips... BUT they also have access to every movement/social/exploration ability in one way or another with those slots...

 

[UngeheuerLich]

This is only true if you assume there is never any advantage or disadvantage and everything is a straight roll with no modifiers.

Even when this is the case, when the numbers of hits is low already this dramatically changes the damage taken. For example, going from a 19 required to hit to a 20 required to hit will cut the number of hits in half and cut the amount of damage dice rolled against you by a full third. That is the difference between 100 damage and 67 damage on a series of attack rolls (and it would be less than 67 if some of that damage is a bonus and not from dice).

If you put disadvantage on top of that +1 it cuts the number of hits by 98% and the damage dice taken by 97%. That is the difference between 100 damage and 3 damage.

I think both perspectives are relevant.

In the 5e bounded accuracy, relative increases are the main factor if you are attacked often by creatures with low to hit values (many low level crossbow men or something).
If you are to be perforated by many bolts, being hit by 20% to 25% less means the difference between life and death, since your effective hp increases.

If you are facing one heavy hitter, probably with a status effect that takes you out of combat, effective hp are irrelevant and you just have a 5% better chance not to be taken out of combat.

 

[clearstream]

Disadvantage has the most absolute affect on reducing hits when you are at 50% to be hit. Why - because the difference between h and h*(1-h) is maximized on the scale of 0 to 1 when h = 0.5. *h=chance to be hit

Hopefully you'll see my post above, dealing with your other concerns. On this one, I can give a simple example of why the picture is not quite as you have it.

Consider when I am only hit on a 20. It's obvious that 20^2 = 400. So the reduction in hits is from 1:20 to 1:400.

To give an idea of what that means experientially, I run my campaign weekly and we probably miss a dozen or so sessions a year: call it 40 sessions per year. 'About 5 rounds' is a fair approximation for length of combats. They can be longer. Seldom shorter. Characters are high-tier 2 and a fighter like our dwarf is probably attacked at least ten times a combat, seeing as many foes have multiattack.

So it is quite plausible to say that over a year, a character in my campaign is going to be attacked 400 times. If they had sufficiently high AC and blur, they will have gone from being hit once each fortnight, to being hit once each year.

Of course, characters don't have that level of AC, however the point stands - and is hopefully illustrated above - that applying disadvantage to attackers when you have a high AC is really stronger than applying disadvantage when you have low AC. As can be understood by seeing that 10^2 = 100 and 20^2 is 400. If a creature misses a character on ten numbers out of twenty, disadvantage makes it 100 numbers out of 400. If they can hit a character on one number out of twenty, disadvantage makes it 1 number out of 400.

 

[HammerMan]

Hopefully you'll see my post above, dealing with your other concerns. On this one, I can give a simple example of why the picture is not quite as you have it.

Consider when I am only hit on a 20. It's obvious that 20^2 = 400. So the reduction in hits is from 1:20 to 1:400.

To give an idea of what that means experientially, I run my campaign weekly and we probably miss a dozen or so sessions a year: call it 40 sessions per year. 'About 5 rounds' is a fair approximation for length of combats. They can be longer. Seldom shorter. Characters are high-tier 2 and a fighter like our dwarf is probably attacked at least ten times a combat, seeing as many foes have multiattack.

So it is quite plausible to say that over a year, a character in my campaign is going to be attacked 400 times. If they had sufficiently high AC and blur, they will have gone from being hit once each fortnight, to being hit once each year.

Of course, characters don't have that level of AC, however the point stands - and is hopefully illustrated above - that applying disadvantage to attackers when you have a high AC is really stronger than applying disadvantage when you have low AC. As can be understood by seeing that 10^2 = 100 and 20^2 is 400. If a creature misses a character on ten numbers out of twenty, disadvantage makes it 100 numbers out of 400. If they can hit a character on one number out of twenty, disadvantage makes it 1 number out of 400.

We had a DM ask a player to lower there AC because it was so high that if the DM through a monster or what ever that could hit him on a 16, he would hit most of us on 7-8's and one of us on a 5 (yes the two PCs neither was me had an 11pt AC difference). That was one of the last times we played 3.5. It wasn't the worst AC difference either, but it was the time the DM just said "Look, I could give everyone 2-3 magic items, or you can do this... I see no reason to play the escalation game"
The PC gave his +2 ring of defense to the lower AC player, and traded his armor with the DM for a +1 less but having fire and acid resistance.... and still had the highest AC at the table...

in 4e I asked the swordmage and ranger to trade out weapon expertise. because in a game with a tactics warlord they were too high of attack... both did without question but both were in the above game too and we all kinda learned not to power game too much way back on that day.

right now we occasionally find cool synergies that power us up, by we try to keep the party mostly in parity... and we do so as PCs and DMs

 

[jgsugden]

There is a lot of White Room work here with cracks in the paint showing different colors.

If you're going to do this type of analysis, I suggest you prepare by doing the following exercise. When you run your PCs, track effective damage per PC. Effective damage is damage dealt to an enemy that brings their health lower down to 0, but disregards all damage dealt that goes below 0. Track it per round of combat. Be sure not to disregard any results when you do this - if your GWM doesn't get to attack in the last round, or if they find that they're just wrapping up individual weenies rather than facing a big threat, don't ignore those situations. It is enlightening to really pay attention to the details here.

GWM: The utility of GWM is highly variable from game to game. If you're fighting beasts all the time, then it is great against those low ACs. If you're fighting high AC enemies all the time, it can be nearly a waste of a feat. However, most people focus on DPR and assume a 'middle of the road' AC distribution. Even when you do so, they fail to account for several handicaps of GWM. First - overkill. If an enemy has 7 hps and you're doing either 2d6+5 or 2d6+15, GWM is not valuable to you - and people do not discount the value of the DPR of GWM attacks for the reality that it inflicts more overkill than lesser damage attacks. Second, reducing your chance to hit increases the variability in combat - which opens the door to more bad luck streaks. I've seen far too many big weapon fighters go down due to a 'run of bad luck' that would not have been so bad had they not been using GWM.

Monk Damage: Monks are not intended to stay up to speed with other classes in damage dealing. They're just not. They have other special abilities that allow them to be effective, like stun, but they're intended to deal less damage than other classes - when concentrating on one foe. Their ability to split up their damage into three or four pools early on will reduce the damage lost to overkill, and keep them effective combatants from a damage perspective, but they arenot intended to be high damage PCs.

 

[FrogReaver]

Another way to model this is to consider the reduction to the number of hits you are taking. If your AC is such that monsters hit you on say 18+, then gaining +1 means that for every three hits you were going to take, you instead take two. An improvement of a third or 33%. Generally, it is more important to model defenses as reduction in incoming, than as change on base value, because it is the reduction on incoming that will be experienced at the table.

That's the model I referred to when I said 'relative'. Having a relative 1000% increase sounds great - unless it's going from 1 penny to 10 pennies. Taking 33% fewer hits sounds great until you realize that in most circumstances it means taking around 1 fewer hits (or less).

IMO, it's not the relative reduction players experience at the table it's the absolute reduction in a given encounter/adventuring day that they experience.

In a recent encounter - in ToA - the monsters had +6 to hit, and there were nine of them with two attacks each. For every eight hits he would take at AC 19, he takes seven at AC 20. An improvement of 12.5%. Their damage was about 10 a hit, and due to specifics of ToA he has 144hp. On average it would take 41 of their attacks for them to kill him at AC 20, and 36 at AC 19. Again around a 12% improvement.

There's some important context missing. How many times did he actually get attacked in that encounter? My guess is that it was significantly lower than 36+ attacks. Probably only 20 attacks. (and maybe not even that many). In which case he would on average save 1 hit worth of damage (or less). 1 hit prevented from the enemies which you said would have been for about 10 damage. Preventing 10 damage in a single encounter on a 144 hp character isn't very impressive IMO. Still better than GWF but not particularly impressive.

 

[FrogReaver]

Hopefully you'll see my post above, dealing with your other concerns. On this one, I can give a simple example of why the picture is not quite as you have it.

Consider when I am only hit on a 20. It's obvious that 20^2 = 400. So the reduction in hits is from 1:20 to 1:400.

To give an idea of what that means experientially, I run my campaign weekly and we probably miss a dozen or so sessions a year: call it 40 sessions per year. 'About 5 rounds' is a fair approximation for length of combats. They can be longer. Seldom shorter. Characters are high-tier 2 and a fighter like our dwarf is probably attacked at least ten times a combat, seeing as many foes have multiattack.

So it is quite plausible to say that over a year, a character in my campaign is going to be attacked 400 times. If they had sufficiently high AC and blur, they will have gone from being hit once each fortnight, to being hit once each year.

So it's one encounter of 5 rounds per session that he gets attacked 10 times in that session. Even if you only got hit on a 20, that means you are being hit less than 1 time per session (about 1 hit every 2 sessions). How valuable is it really to go from being hit 1 time every 2 sessions to being hit 1 time every 40 sessions (due to advantage)? I don't think it's valuable at all.

Now consider the scenario where you are being hit on an 11+ (50% of the time). That means you get hit 5 times per session and instead you go to being hit 5 times per 2 sessions (with advantage). IMO that's particularly valuable.

Why? Because 5 hits a session means you are taking significant damage. Halving significant damage is a significant result. Taking 1/20th of very little damage still means you are taking very little damage.

Of course, characters don't have that level of AC, however the point stands - and is hopefully illustrated above - that applying disadvantage to attackers when you have a high AC is really stronger than applying disadvantage when you have low AC. As can be understood by seeing that 10^2 = 100 and 20^2 is 400. If a creature misses a character on ten numbers out of twenty, disadvantage makes it 100 numbers out of 400. If they can hit a character on one number out of twenty, disadvantage makes it 1 number out of 400.

I understand the math. I disagree with your analysis of what that math means in relation to D&D tactics because you are missing the 'absolute' context for the number of hits and amount of damage you are preventing. Thus, based on that context I expanded in this post (above) - I suggest that applying disadvantage to enemy attacks is most beneficial when you are in the middle AC ranges (50% chance to be hit give or take a bit)

 

[FrogReaver]

I think both perspectives are relevant.

In the 5e bounded accuracy, relative increases are the main factor if you are attacked often by creatures with low to hit values (many low level crossbow men or something).
If you are to be perforated by many bolts, being hit by 20% to 25% less means the difference between life and death, since your effective hp increases.

If you are facing one heavy hitter, probably with a status effect that takes you out of combat, effective hp are irrelevant and you just have a 5% better chance not to be taken out of combat.

Agree with much of this. I'd just add that PC's aren't dropping down to 0 hp all that often and if they aren't dropping down to zero very often then extra defense (AC or disadvantage to enemy attacks) is largely meaningless. It doesn't matter if you buff up to being able to take 1,000,000 eHP damage if you could take 200 eHP damage before and were never (or rarely) dropped to 0 at that eHP level.