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

[Irda Ranger]

Nothing improves your popularity like fireballing your party while they are in melee with the enemy.

Au contraire, mon ami. Letting off a reflecting lighting bolt (2e-style) in a 10x10 room is far more popular.

 

[mmadsen]

It is the case for 4e Fighters though. Especially with Full Attack removed, and expected 1:1 ratios in monster encounters, the only way a Fighter approaches one:many is with Cleave or a Grenade weapon (or Whirlwind Attack, if that still exists). However, you still don't get true many:many, in the way that wizards-with-wands do.

All Lanchester's Square Law assumes is that Side A's casualties are a function of how many units are left on Side B, and vice versa. Each tank or warship may only target one other tank or warship on the other side, but when that target goes down, it's no longer a target, and it no longer draws fire.

This is in contrast to hand-to-hand combat in a narrow pass, where the larger force cannot bring all its forces to bear.

This is also in contrast to indirect artillery fire, where casualties are not purely a function of many guns are on the other side, but also how many units we have on our side. The more units we have suffering the barrage, the more casualties we take, and as we lose casualties we do not take casualties at a higher and higher rate, as we would under direct, or aimed, fire.

As long as every combatant in a D&D battle can find a (single) target, Lanchester's Square Law should hold.

 

[mmadsen]

It doesn't really change your tactics though. [...] In a 'Bloodied' world, spreading damage around makes even less sense - but since the quantum outcome (choice of tactics) remains the same, it really doesn't change anything.

Exactly. I don't think a "bloodied" condition changes the big picture; it just changes some of the tactical details. I'm mildly concerned that such rules will add complexity without a big payoff.

 

[mmadsen]

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.

I thought I'd expand on this a bit, because it plays a large, but hidden, role in the game, and it could play a larger role in a new design.

If attack bonuses and defense bonuses increase in lock step, then character will find themselves hitting and being hit "reasonably often" at every level. Large differences in bonuses cause inordinate differences in outcome though -- in one direction, but not the other.

If your attack bonus outclasses your opponent's defense bonus, it's no big deal. Instead of hitting 50 percent of the time, you might hit 55, 60, 65, ..., up to 95 percent of the time. That is, if you totally outclass your opponent, you'll hit twice as often as against an equal.

If your defense bonus outclasses your opponent's attack bonus though, you'll defend not just 50 percent of attacks, but 55, 60, 65, ..., up to 95 of attacks. That seems parallel, but it's not. Instead of getting hit by one attack in two, you get hit by one attack in 20, or one tenth as many attacks. In fact, just going from defending 90 percent to 95 percent of attacks, an additional +1 bonus, doubles your expected lifespan.

Once you have a decent defense bonus, each additional point is tremendously valuable. Again, if your chance of defending is 50 percent, then you expect to get hit once per two rounds. If your chance of defending is 75 percent, then you expect to get hit once per four rounds -- doubling your defense, but still reasonable. If your chance of defending is 95 percent, then you expect to get hit once per 20 rounds -- which is a lot like having 10 times as many hit points as someone who gets hit every other round:

50% -- 02.00 [expected rounds between hits]
55% -- 02.22
60% -- 02.50
65% -- 02.86
70% -- 03.33
75% -- 04.00
80% -- 05.00
85% -- 06.67
90% -- 10.00
95% -- 20.00

 

[Mustrum_Ridcully]

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.

They seem to look strong, but that might just be because they miss the "classic" D&D 3 breakup of damage and defense.

Instead of 1024 hitpoints, a CR 20 equivalent might have Damage Reduction (good and silver or -) and Fast Healing/Regeneration.
Instead of a single attack, he would probably have two primary attacks and several secondary attacks, or some spell-like abilities that deal damage.

You know, I really wonder if this list is actually what the designers have written up, too?

And I feel the urge to check the MM to compare creatures of the various CR and check if the numbers already fit...

I use two creatures as examples (none of them Ogres, unfortunately, and average some of their values.)
- Xill (CR 6): +5 attack, Damage 18, AC 20, 32 hp
- Stone Giant (CR 8): +17 attack Damage 30, AC 25, 119 hp
Okay, the stone giant doesn't fit in the damage department...

 

[Cheiromancer]

Excellent points, mmadsen! Your description of the AC issue is very clear. I suppose it is no accident that three of the "big six" are AC boosters (armor and shield; amulet of natural armor; ring of protection... oh, and Dex boosters. So 4, actually). AC is super important to survival.

Anyway, I was just reading this quote from Andy Collins:

It's true that there won't be *as* much difference in power between any two monster levels as there is now--we're aiming for a slightly shallower power curve overall, so that monsters and PC abilities stay relevant across more levels.

That's not the same as saying there won't be much difference between levels (which suggests that level 1 and level 20 monsters will be basically the same--completely untrue).

It's a lot more fun (and useful) if a given monster is interesting over a spread of, say, 6 or 8 levels than if it's only viable in a spread of 3-5 levels (a generous description of the 3E model).

The fact that any given monster is only 20-25% of an encounter also means that cranking up the power of one monster (by including a monster of, say, PC level +4) won't alter the encounter nearly as much as if that were a one-on-one fight. You'll definitely notice that monster's presence, but it doesn't suddenly become a party-killah.

Do you suppose that quadrupling a creature's power will now happen over 4 levels instead of 2? That seems to be the easiest way of doubling the interval in which a monster is viable.

Oh, and it seems clear to me that monster levels are weaker than PC levels. If four fifth-level monsters fight a party of four fifth-level characters and challenges them moderately, then the monsters must be weaker than the characters. Or am I missing something?

And this reminds me of something that I've forgotten; when the PCs are fighting a group of weaker monsters, they are, on average, fighting only half of them. At the beginning of the fight they are fighting all of them, and at the end of the fight they aren't fighting any; at the mid-point of the fight half of them are gone. (I suppose the true average is more like 2/3, since everyone can't focus all their attacks on the same monster.) It's like the death spiral that heralds a TPK; as PCs drop, there are fewer PCs to defeat the remaining opponents, and the opponents attacks can be focussed on the PCs left standing.

I suspect that in multi-monster encounters a MonN will be about 1/2 a PC(N)'s power. If they are just changing the rate of exponential increase, that will be the power of a PC(N-2). Or maybe PC(N-3), if it turns out to be impractical for the party to focus their efforts on one opponent at a time.

It does seem to me that monster level is different than PC level. In other words, a group of 4th level PCs might be considered 6th level monsters if encountered as antagonists.

edit

If they are stretching out monster CRs (so a +2 CR gap is now +4 monster levels), I imagine that the same thing would have to happen to PC levels. I wonder if PCs will start at what was 4th level, and will end their career at what was 18th level? Or thereabouts.

 

[Wulf Ratbane]

Do you suppose that quadrupling a creature's power will now happen over 4 levels instead of 2? That seems to be the easiest way of doubling the interval in which a monster is viable.

Oh, and it seems clear to me that monster levels are weaker than PC levels. If four fifth-level monsters fight a party of four fifth-level characters and challenges them moderately, then the monsters must be weaker than the characters. Or am I missing something?

Argh, Xp, I have been saying this for 2 pages.

You have no idea how frustrating that is for me since I rely on you so heavily.

If they are stretching out monster CRs (so a +2 CR gap is now +4 monster levels), I imagine that the same thing would have to happen to PC levels. I wonder if PCs will start at what was 4th level, and will end their career at what was 18th level? Or thereabouts.

Errgh, it's like you rebooted.

From what I understand, and I apologize if I didn't say it explicitly before, the 4e power curve from 1-30 will supposedly look like the 3.5 power curve from 4-14.

Scroll back to the first post and look at the second, third, and fourth series. The reason I used the numbers I did in those examples is because of that specific rumor.

I believe that at 1st level, any single PC will be 4x to 16x the combat power of a single Level 1 monster.

 

[Cheiromancer]

Sorry Wulf- that's not what I was interpreting you as saying.

I have spent many of my posts amplifying and exploring the notion that monster power in 3.5 is basically an exponential function; that a four-fold increase in a monster's power is reflected by a +2 CR. This isn't true for a quadratic power curve; then a four-fold increase in a monster's power would be reflected by a doubling of its CR (more or less- the constant terms complicate things). I thought we should get the 3.5 situation straight before we started talking about 4e.

Then I noticed that the terminology in 4e seemed to be that monsters had levels. I wanted to make sure that people would not confuse monster levels with PC levels. In the 1 monster vs party system of CR (which is how I understand 3.5), a PC's level is higher than their CR - a 6th level PC is as powerful as a CR 4 monster. But in the 4E paradigm (with as many monsters as PCs) a PC's level is lower than the equivalent monster level. A 6th level PC would be an 8th level monster. (Maybe 9th) That's because a party of 6th level PCs would be an appropriate challenge for an 8th or 9th level party, not another 6th level party.

There is lots of variation in the use of "level" and "CR" - it can be very confusing. My own use of terms like Ogre4 contributes to the problem, since I meant the suffix to indicate CR, not monster level or (equivalent to) PC level.

As for your series in the first post, I didn't realize that you meant their importance to be the scale of the power curves. At that time I thought we were talking about what kind of formula expresses the power curve. (The now forbidden question of quadratic vs exponential functions )

Anyway, I think that a 1st level character will be between x2 or x4 the power of a 1st level monster. The PCs who are most effective against a monster will swiftly down their opponent and go to the aid of the other party members; thus the monsters will fall faster than they would if all the combats were completely separate. If the combats were all separate and one on one, then you'd need the PCs to be x4 the power of the monsters.

 

[gizmo33]

No, Wulf just threw you a bit of dimensional analysis.

If that's what you call using synonyms.

You know that combat power equals attack potential times staying power because that is the only way to get (damage) from (damage/round) and (rounds).

Make sense now?

Yes, that answers my original question of why multiply.

 

[mmadsen]

In the 1 monster vs party system of CR (which is how I understand 3.5), a PC's level is higher than their CR - a 6th level PC is as powerful as a CR 4 monster.

In 3E, a PC's level is equal to its CR -- assuming that the PC has level-appropriate equipment. The guideline though is that four PCs face one monster of their individual power level; an EL-N encounter consists of one CR-N opponent, but is appropriate for four Nth-level PCs.

If we take into account Lanchester's Square Law though, four PCs facing one monster should have 16 times that monster's combat power.

Edit: Ignore this bit about except that Lanchester's Square Law doesn't really hold against a single monster that doesn't lose any offensive power as it takes damage.