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

[Wulf Ratbane]

I don't think anyone's arguing that the designers want every fight to be a coin flip; they're simply changing their nomenclature.

Currently, a creature is CR-N if it's as powerful as an Nth-level character, and one CR-N creature comprises an EL-N encounter, which is an appropriate challenge for four Nth-level characters.

If we wanted to re-normalize CR and EL so that CR-N and EL-N implied that four monsters were an appropriate challenge (and not a fair fight) for four Nth-level characters, we'd simply subtract four from all CRs and ELs, since the current system adds two to EL for each doubling in numbers.

Hey "M"--

I think you're just restating what I saying.

I believe it would be helpful to look at the absolute baseline and work forward.

1) First, design a Level 1 "brute." What is his BAB, AC, avg. damage, and hps? (We'll stop using CR, as apparently so will WOTC, reverting to the older "level" nomenclature.)

2) Now, we know that in 4e, 5 of these Brutes are an appropriate encounter for FIVE PCs.

3) A 1st level PC must be more powerful than this "baseline" Level 1 brute. If a given PC was equal in power to this brute, then the whole matchup would be a 50/50 coin flip.

Aside:[sblock]As an aside here, I'd really much rather be using a 4 PC party. Not because it may or may not be the typical size, but because "4" is going to work out much smoother for our math. With everyone's agreement, we can switch to a 4:4 match-up.[/sblock]

4) How much more powerful does the 1st level PC have to be than a Level 1 brute? What level of difficulty do we want to solve for? Although I think 50/50 is too tough, I think the default "moderate" of 3e was actually too easy. Somewhere in between would be my guess.

5) Working forwards, what are the stats of a 1st level Fighter (our "brute")?

6) Working farther forwards, what are the stats of a Level 2 brute? And of a Level 2 fighter, such that the relationship is preserved?

 

[Nonlethal Force]

mmadsen, I think the confusion comes in terminology. The poster states they are increasing the BAB probablity, but the equation seems to only address pure BAB. Thus, ability to hit an opponents defense (and thus the probability angle) is not addressed in the equation.

I think what the poster was trying to derive is the fighter's increase with respect to the prior level's total. In other words, from level 1 to level 2 there is a 100% increase. That is followed by a 50% increase from level 2 to three. That is followed by a 33% increase, etc.

 

[mmadsen]

I think you're just restating what I saying.

Definitely, but I think we need a bit of that, to make sure we're all on the same page.

As an aside here, I'd really much rather be using a 4 PC party. Not because it may or may not be the typical size, but because "4" is going to work out much smoother for our math. With everyone's agreement, we can switch to a 4:4 match-up.

Definitely.

How much more powerful does the 1st level PC have to be than a Level 1 brute? What level of difficulty do we want to solve for? Although I think 50/50 is too tough, I think the default "moderate" of 3e was actually too easy.

Under the old system, a single CR-N monster was supposed to be a moderate challenge for four Nth-level PCs, but I think they forgot Lanchester's Square Law there, because four PCs should be 16 times as powerful as one.

Under the new system, a MonN should be one-sixteenth as powerful as a PCN, if we want to maintain the old, easy standard for a "moderate" challenge. Given the exponential nature of levels, that would set MonN+4 = PCN. So a single Mon5 would be a moderate challenge for a single PC1.

I don't think they'll go that far.

 

[Wulf Ratbane]

I think they forgot Lanchester's Square Law there, because four PCs should be 16 times as powerful as one.

It makes one monster very hard to balance against a party, no matter what level of difficulty you want it to present.

If five Orcs are appropriate for five PCs, what ONE monster is appropriate for those PCs? What will its stats look like? And will it really have a 50/50 shot against five orcs? (Same power...)

Under the new system, a MonN should be one-sixteenth as powerful as a PCN, if we want to maintain the old, easy standard for a "moderate" challenge. Given the exponential nature of levels, that would set MonN+4 = PCN. So a single Mon5 would be a moderate challenge for a single PC1.

I don't think they'll go that far.

And yet... "4th is the new 1st."

 

[Wulf Ratbane]

(And we haven't even started talking about using equivalent NPCs as adversaries, and what that will do to encounter design. The Mirror of Opposition is a sacred cow!)

 

[zachKS]

I have no problem with colloquial use of exponential as "Growing Fast".

It's inconsistent colloquialism that irks me. You used quadratic, a non-colloquial term, with Exponential used colloquially.

This is the problem with us nerds, we can never get past our own intellect to have a discussion about anything other than "I'm smarter than you, na-na-na-boo-boo."


A quadratic IS an exponential function ( f(x)=a^x + b ) where x = 2.

 

[mmadsen]

It makes one monster very hard to balance against a party, no matter what level of difficulty you want it to present.

Not really. If you want a creature 16 times a powerful as another, you can simply give it 16 times as many hit points. (This is assuming we're talking about brutes fighting other brutes, of course, with no way around hit points.) Or you could give it +4 to-hit and +4 AC, assuming it was already in the range where it hit half the time and got hit half the time.

Once you've laid it all out, the math's pretty straightforward.

If five Orcs are appropriate for five PCs, what ONE monster is appropriate for those PCs? What will its stats look like? And will it really have a 50/50 shot against five orcs? (Same power...)

A monster 25 times as powerful as a single orc should be easy to design. (See above.) Will it really be an equal match for for five orcs? More or less. We still have to keep our eyes open for things that should work in general but which don't work in this case.

For instance, a monster that does 25 times as much damage should be 25 times as powerful, but most of that extra damage will go to waste against one-hit-die orcs.

Or a +9 bonus to AC might mean that a monster that was getting hit half the time (50 percent) now gets hit one-tenth as often (5 percent), but, if it was getting hit just a bit more often, 60 percent of the time, a +9 bonus means it's now getting hit one-fourth as often -- nowhere near as big an improvement as we'd planned.

 

[mmadsen]

This is the problem with us nerds, we can never get past our own intellect to have a discussion about anything other than "I'm smarter than you, na-na-na-boo-boo."

A quadratic IS an exponential function ( f(x)=a^x + b ) where x = 2.

Making an honest mistake is one thing, but why would you jump in to volunteer the wrong answer and contradict people who know what they're talking about? A quadratic function is a polynomial of degree 2. For instance, x² is quadratic, while 2^x is exponential.

 

[BryonD]

Making an honest mistake is one thing, but why would you jump in to volunteer the wrong answer and contradict people who know what they're talking about? A quadratic function is a polynomial of degree 2. For instance, x² is quadratic, while 2^x is exponential.

See, that is kinda the point.

You are exactly right.

But getting hung up on this is beyond much of the audience who have zero NEED to get the precise labels in order to understand the real focus of the conversation (thus my calling it niche within this audience). And making a show out of it for ego's sake has only served to add confusion that was not present before, without actually helping the people who do know the difference understand the real point one lick better.

Can we please drop it and move on?

 

[mmadsen]

And we haven't even started talking about using equivalent NPCs as adversaries, and what that will do to encounter design. The Mirror of Opposition is a sacred cow!

I think the current system, where CR-N is as powerful as Nth-level, makes far more sense than creating a second scale, so that five monsters of Nth-monster level are just strong enough to pose a moderate challenge to five PCs of Nth-level.