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

[wgreen]

Can we go play HYBRID now?

 

[Wulf Ratbane]

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.

I think most folks (the main contributing ones, at least) are hip to that.

Then I noticed that the terminology in 4e seemed to be that monsters had levels.

My understanding of the usage in this case is that a Level N monster is appropriate for a single Nth level PC, so you can use X Level N monsters for a party of size X.

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.

Correct-- hence my off-hand comment a few posts back about the Mirror of Opposition.

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.

Each of those curves is derived from the same formula, with the constants tweaked in different ways. The purpose of the thread is to try to predict

a) the starting power of 4e 1st level characters (constants a and b)

b) the rate of advancement of 4e characters (constants d and m).

And I believe that those constants are relative to each other. For example, if 4e 1st level characters start with 4 HD, and we want them to gain 1 HD per level advanced, then a=4 and d=.25. (But check me on that.)

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.

I believe we will see the latter case. I don't think we would see the design assuming anything about any individual contest. If the PCs start whittling away the enemy, that's all well and good (we can accept this scenario as simply "good for the game"), but I think the formulas will primarily take into account the relative combat power at the time the battle starts.

To try to anticipate any relative combat power change over time would move us into calculus, which would be impressive, but I think unlikely-- and again, probably an exercise in unnecessary precision for little increase in accuracy.

So I suppose it will be a 4x power difference, and I believe we'll see it implemented just by increasing the starting HD.

Someone with SAGA edition could tell us the starting HD of a 1st level character to see if we're in the ballpark. 4HD?

 

[mmadsen]

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.

Ah, but the kicker is that AC isn't simply important to survival, but that extra AC bonuses show increasing returns, not diminishing returns, as you heap bonuses on bonuses.

If your AC is mediocre, and you're getting hit half the time, which do you want, a +1 Dex bonus to AC or a +1 Con bonus to hit points per hit die? It's not immediately clear, but the AC bonus will increase your survivability by about 10 percent, while the hit-point bonus will probably increase your hit points by something like 20 percent. (For a Wizard with Con 8, averaging 1.5 hit points per level, it'll increase hit points by 67 percent. For a Fighter with Con 14, averaging 7.5 hit points per level, it'll increase hit points by 13 percent.)

If your AC is high, and you're getting hit 10 percent of the time, you almost certainly want the additional AC bonus. It will increase your survivability by 100 percent, doubling it.

Granted, there's a steep drop-off once you reach "hit only on a natural 20", but up to that point, each extra point of AC is worth more than the previous one.

We could sidestep some of this if fewer things were clumped into AC and we spread what are now AC bonuses across, say, defense and toughness. For instance, if armor bonuses were treated more like Con bonuses to hit points -- not that I'm suggesting that particular solution -- then there would be fewer bonuses stacked on top of one another for defense.

 

[Cheiromancer]

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 -- 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.

The assertion that a PC's level is equal to its CR is inconsistent with the assertion that a moderate encounter for an Nth level group is a creature whose CR is N. I prefer to accept the latter and reject the former.

And why wouldn't Lanchester's square law hold against a single monster? Imagine your PC was faced with a super-duper mirror of opposition that produced 4 duplicates. Fighting the horde you get hit 4 times for every hit you land. By the time you are killed you've whittled down one of your opponents to 3/4 their starting hit points. In other words, you used up 1/16 of the group's resources.

Ah, but the kicker is that AC isn't simply important to survival, but that extra AC bonuses show increasing returns, not diminishing returns, as you heap bonuses on bonuses.

Yeah- I think I alluded to that in post 4 of this thread. It's a good point, though. Worth repeating.

 

[Wulf Ratbane]

If that's what you call using synonyms.

First of all, your inability to grasp what others have described as "obvious" is not a reflection on the people struggling to explain it to you.

"How much damage can he do and how long can he do it?"

That is a simple, tangible, "real" expression of combat effectiveness that is completely independent of any rules system.

You're the only one to express any trouble with it so far. I hold out the possibility that you are the only sane one in the discussion but you will have to produce something to keep the discussion moving forward.

If you believe that you have a more applicable method for describing combat effectiveness, by all means, elucidate. Contribute to the discussion instead of just repeating, "I don't get it!"

Any further snarky posts from you would appear to be trolling a thread that has already attracted the interest of three different moderators.

 

[mmadsen]

The assertion that a PC's level is equal to its CR is inconsistent with the assertion that a moderate encounter for an Nth level group is a creature whose CR is N.

No, it's not. A "moderate" encounter for four 1st-level characters is one 1st-level character. If you pit four 1st-level characters against four other 1st-level characters, it's no longer a "moderate" encounter; it's even odds of a total party kill.

And why wouldn't Lanchester's square law hold against a single monster? Imagine your PC was faced with a super-duper mirror of opposition that produced 4 duplicates. Fighting the horde you get hit 4 times for every hit you land. By the time you are killed you've whittled down one of your opponents to 3/4 their starting hit points. In other words, you used up 1/16 of the group's resources.

Ah, my bad. Now I have to figure out what I was thinking... :\

 

[Wulf Ratbane]

No, it's not. A "moderate" encounter for four 1st-level characters is one 1st-level character. If you pit four 1st-level characters against four other 1st-level characters, it's no longer a "moderate" encounter; it's even odds of a total party kill.

Correct!

To move the discussion back to monsters, one CR-N monster was a "moderate" 3e encounter for four PCs. They out-numbered it 4:1, and so the ratio of total power to total power was 4:1.

In 4e, because the ratio of monsters to PCs is now 1:1, it must mean that 4e characters are 4x as powerful as before-- assuming that the definition of "moderately difficult" hasn't changed.

But personally, I'd like to see moderate difficulty actually tweaked upwards a bit: first, because it's just more fun; and second, because "per encounter" abilities are going to mean that characters can consistently handle tougher encounters.

I'd like to see the new "moderate" encounter fall somewhere between the current "moderate" (a 4:1 total power ratio, which is too easy) and "50/50 TPK" (a 1:1 total power ratio).

 

[mmadsen]

They out-numbered it 4:1, and so the ratio of total power to total power was 4:1.

They out-numbered it 4:1, and so the ratio of total power to total power was 16:1.

 

[Wulf Ratbane]

They out-numbered it 4:1, and so the ratio of total power to total power was 16:1.

The ratio of total power was 4:1.

The ratio of force projection was 16:1, as you correctly note.

Quadratic force projection is always going to be an issue. Drop it out of consideration for a moment. Just hold the thought.

How much more powerful is any single 1st level PC going to be when compared to a single 1st level monster?

So I task you again:

1a) Define the prototypical 1st level monster (the Orc brute, for example).

1b) Based on his stats, you should therefore be able to derive the stats of the typical 1st level PC "brute" (our Fighter). You can derive the stats of the Fighter from the fact that he must be more powerful than the Orc brute-- powerful enough to make a man-to-man combat feel "moderately difficult" as opposed to "a coin toss."

2a) Advance the brute to 2nd (gnoll), 3rd (bugbear), 4th level (ogre).

2b) Advance the Fighter to 2nd, 3rd, 4th level so that the individual combatant power ratio is preserved.

 

[Cheiromancer]

No, it's not. A "moderate" encounter for four 1st-level characters is one 1st-level character. If you pit four 1st-level characters against four other 1st-level characters, it's no longer a "moderate" encounter; it's even odds of a total party kill.
Ah, my bad. Now I have to figure out what I was thinking... :\

A moderate encounter for four 1st-level characters would be one CR 1 monster, or two 1st-level characters. Four 1st-level characters would be even odds of a TPK, as you note; two 1st-level characters would represent the loss of one quarter the resources of the party.