D&D 4E The Quadratic Problem—Speculations on 4e

[Wulf Ratbane]

Maybe I'm missing something, but why do people keep referring to Lanchester's Square Law when describing Brute combat in D&D? Wasn't his point that ancient warfare (swords and formations) was linear, while only modern artillery made combat non-linear?

That is a good observation, but I don't think it's totally applicable.

His point was that ancient combatants could only ever fight one-on-one-- clearly that's not the case in D&D (and I rather dispute the fact that it was actually the case in ancient warfare either, but let's not digress...)

There is a practical limit to how many combatants can attack a single foe in D&D (eight? hmmm?), but it is certainly not one-on-one.

Wouldn't that mean that Brute monsters and Artillery monsters (two "roles" that Mearls has described as being used in the 4e MM) would have to have different rates of advancement for different qualities? This is perhaps the driving reason for breaking up the MM into roles in the first place. Mearls has explicitly stated there will be a "brute" advancement and a "artillery" advancement (among other roles), and I expect those rates will be informed by this thinking.

That is a VERY good observation, and certainly much more applicable.

Lastly, I'm surprised I haven't see more discussion on how the limitations of using a single 20-sided die effects outcome resolution. I can barely follow the algebra, so probability theory is right beyond me, but it seems to me that the lack of granularity of outcomes and the lack of any kind of probability curve have a huge impact on D&D's ability to scale with level.

No, no, that concern is definitely out there-- the WoTC designers have certainly named it specifically with regards to the sweet spot, and it is definitely at the top of my mind. Looking at the way that bonuses are scaling, any proposal that puts the BAB at 30th level outside the bounds of the d20 is, in my opinion, a problem. (Personally I like a 2/3 rate of advancement on BAB compared to 3e.)

 

[Wulf Ratbane]

I start with a different set of assumptions. I'm assuming that when they find a monster that is a moderate challenge (25% resources) against four Nth-level PCs, they say it is a MonN. (Thanks for the improved notation, btw).

I don't think so. I believe that in the 4e notation, MonN means, "Five of these guys will give five of your Nth-level PCs a moderate challenge."

If your average party level is 3rd, you want to open the MM to the Level 3 monsters and give them five of them to fight.

I do believe that's the plan.

If a party of Nth level comes across a single MonN, they will have a very easy time of it.

And it's much more intuitive:

"Can we take this guy?"

"Why not? He's the same level as us. There are five of us and only one of him! We'll wipe the floor with him!"

And they will.

That's very different from 3e.

 

[mmadsen]

His point was that ancient combatants could only ever fight one-on-one-- clearly that's not the case in D&D (and I rather dispute the fact that it was actually the case in ancient warfare either, but let's not digress...)

His conclusion was important though, if flawed: In modern many-on-many combat, quality does not scale as quickly as quantity, where it had before, in ancient one-on-one combat.

If 300 Spartans are holding the pass against 10,000 Persian Immortals, they "only" have to be 33 times as good (6th-level), man for man, to fight to a draw. If those same 300 Spartans try to meet 10,000 Persians in the open field, they have to be 1100 times as good (11th-level) to fight to a draw.

One flaw in Lanchester's thinking, or the analysis based on it that I've read, is the assumption that quality is itself a simple linear measure, when a tank or warship can have better armor, better mobility, better accuracy, better penetration, better range, etc., and those things compound.

 

[mmadsen]

"Can we take this guy?"

"Why not? He's the same level as us. There are five of us and only one of him! We'll wipe the floor with him!"

And they will.

That's very different from 3e.

Um, that sounds exactly like 3E to me...

 

[Cheiromancer]

I don't think so. I believe that in the 4e notation, MonN means, "Five of these guys will give five of your Nth-level PCs a moderate challenge."

No, I am using the 3.5 notation. If we can agree on what the power curve is in the current system, and what exactly that means for monster and PC power, then we can speculate on how it might change in 4e. I have a suspicion that if they changed from exponential (the current system) to a quadratic system that it might go a long way to extending the sweet spot.

Incidentally, rycanada's DM's Best Friend Table could be helpful in determining what the key stats actually are for monsters of different CRs. It includes the stats for critters with special abilities, but its a starting point.

 

[Wulf Ratbane]

Um, that sounds exactly like 3E to me...

"Wipe the floor" wasn't specific enough.

 

[Driddle]

Nevermind.
PC already addressed the issue.

 

[mmadsen]

Wouldn't that mean that Brute monsters and Artillery monsters (two "roles" that Mearls has described as being used in the 4e MM) would have to have different rates of advancement for different qualities? This is perhaps the driving reason for breaking up the MM into roles in the first place. Mearls has explicitly stated there will be a "brute" advancement and a "artillery" advancement (among other roles), and I expect those rates will be informed by this thinking.

Very interesting point.

Further, Lanchester would have pointed out that surface area is different from number of combatants. 9 wizards, no two of whom are within 15' of each other, may be far more Survivable than 9 wizards squeezed into a 15'x15' room, depending on whether their enemy uses precision weapons (Finger of Death) or area weapons (DB Fireball).

Of course.

With unaimed fire (or area weapons), additional defenders don't diffuse the attacks against them, so such combat follows Lanchester's Linear Law -- despite the fact that it bears little resemblance to ancient, man-to-man combat.

Lastly, I'm surprised I haven't see more discussion on how the limitations of using a single 20-sided die effects outcome resolution. I can barely follow the algebra, so probability theory is right beyond me, but it seems to me that the lack of granularity of outcomes and the lack of any kind of probability curve have a huge impact on D&D's ability to scale with level.

The issue, which the designers seem to have recognized, is the spread between attack and defense bonuses, and between various characters' attack and defense bonuses. As long as those increase in lock step, everything works swimmingly. As soon as big enough differences show up though, then we get characters who effectively can't hit or can't be hit.

 

[Cheiromancer]

Maybe I've made a mistake with the numbers, but I get a series of OgreNs that seem to be awfully strong. Each is 4 times as strong as its predecessor- it can defeat two of them when they gang up on him. In theory each should be a moderate encounter for an Nth level group. But they look awfully tough. Maybe the exponential rule breaks down for high level brutes?

Ogre4:  Attack +8,  damage 16,  AC 19, hp 32
Ogre6:  Attack +8,  damage 16,  AC 24, hp 64
Ogre8:  Attack +13, damage 16,  AC 24, hp 128
Ogre10: Attack +13, damage 32,  AC 29, hp 128
Ogre12: Attack +18, damage 32,  AC 29, hp 256
Ogre14: Attack +18, damage 32,  AC 34, hp 512
Ogre16: Attack +23, damage 64,  AC 34, hp 512
Ogre18: Attack +23, damage 64,  AC 39, hp 1024
Ogre20: Attack +28, damage 128, AC 39, hp 1024

Or maybe this is the function of high level magics (dominate monster, etc.). To give the party the power to take on what, according to the exponential law, should be a moderate encounter.

 

[DarkKestral]

Maybe I've made a mistake with the numbers, but I get a series of OgreNs that seem to be awfully strong. Each is 4 times as strong as its predecessor- it can defeat two of them when they gang up on him. In theory each should be a moderate encounter for an Nth level group. But they look awfully tough. Maybe the exponential rule breaks down for high level brutes?

Ogre4:  Attack +8,  damage 16,  AC 19, hp 32
Ogre6:  Attack +8,  damage 16,  AC 24, hp 64
Ogre8:  Attack +13, damage 16,  AC 24, hp 128
Ogre10: Attack +13, damage 32,  AC 29, hp 128
Ogre12: Attack +18, damage 32,  AC 29, hp 256
Ogre14: Attack +18, damage 32,  AC 34, hp 512
Ogre16: Attack +23, damage 64,  AC 34, hp 512
Ogre18: Attack +23, damage 64,  AC 39, hp 1024
Ogre20: Attack +28, damage 128, AC 39, hp 1024

Or maybe this is the function of high level magics (dominate monster, etc.). To give the party the power to take on what, according to the exponential law, should be a moderate encounter.

Actually, I think that's about right. Looking at say a dragon, they'll usually have an attack bonus in the high 20s to low 30s, can do 60 to 100 damage a round, have ACs in the low 40s to mid 50s, and about 800-1000 hps. Since they have so much AoE and a bunch of attacks, we can probably drop about 200 HP and some damage.. which means that perhaps the formula's right on target or thereabouts.

And heck, look at the combat posted for 4e.. it might be approximately there, because we know it had about 1000 HPs, probably a bonus of 28 or so, and was doing about 60-100 damage around to the party.