The Mathematical Model of the d20 System

[Wulf Ratbane]

Wow, you went for the personal attacks fast.

Well the conversation was going like this:

"Prove the Pythagorean Theorem."

Now you can either get out your compass and ruler, and set about proving the Pythagorean Theorem, or you can just say, "Well, if I recall correctly, Pythagoras said the square of the hypoteneuse was equal to the sum of the squares of the other two sides, so I guess that proves it."

Okay. In my experience playing 3.5e, CR is accurate for 4-5 encounters per day. At one expected encounter per day, the listed CRs start out reasonable (below level 5), but starting at level 5 and increasing as the party's levels go up, the CR of an encounter which is expected to be the only encounter in a day is an underestimate. In other words: as PCs get higher in level, a fresh party who expect not to have to fight later can reliably take on higher EL encounters, the difference increasing as they increase in character level.

(Note that expect is emphasized for a reason.)

That is an accurate observation of the symptoms. CR starts to get less and less reliably predictive as CR increases. Partly this is because the number of asymmetric abilities increase as level increases, and partly it is because doubling the numbers to achieve EL+2 no longer holds true after about CR12 (though this is interrelated).

So much of the CR value of high-CR creatures is tied up in their special abilities that HD end up meaning less and less. High CR creatures are bloated with abilities that they simply won't ever have enough actions to use. Not only do they have to survive more asymmetric attacks (save or die), they also lack the HD to survive conventional attacks.

It's worth noting that 4e at least attempts to address this.

By

(a) removing a lot of those asymmetric abilities (even poison is a damage type, now!) and

(b) increasing hit points,

combat, especially high level combat, is a lot more ablative in 4e than it was in 3e.

It is also true that high level 3e characters have far greater means at their disposal to choose the time and manner of each encounter. If they only want to face one encounter per day, it's much easier for them to nip off to a pocket dimension if they like. This further exacerbates the problem.

I'd also like to point out that I am standing on the shoulders of giants here, and if you have a chance to read Upper_Krust's "Challenging Challenge Ratings," I recommend it.

 

[Nifft]

Well the conversation was going like this:

"Prove the Pythagorean Theorem."

Now you can either get out your compass and ruler, and set about proving the Pythagorean Theorem, or you can just say, "Well, if I recall correctly, Pythagoras said the square of the hypoteneuse was equal to the sum of the squares of the other two sides, so I guess that proves it."

Is that your excuse? I questioned your assumptions?

Or did I miss you proving that CR is only meaningful for fresh, fully rested PCs?

It's a trifle hypocritical to attack someone for citing outside sources, then later claim authority via "standing on the shoulders of giants".

I'd also like to point out that I am standing on the shoulders of giants here, and if you have a chance to read Upper_Krust's "Challenging Challenge Ratings," I recommend it.

Yep, U_K does good work.

-- N

 

[Wulf Ratbane]

It's a trifle hypocritical to attack someone for citing outside sources, then later claim authority via "standing on the shoulders of giants".

I'm not claiming authority by standing on the shoulders of giants. (It's called "attribution.")

I am pointing you to an outside source where you can read some actual work on the math behind the d20 system, instead of relying on your recollection of what the 3e designers said their intent behind the system was.

Deflecting you to Upper_Krust's work was my way of trying to be polite.

Because really, I can't be bothered bootstrapping you up to speed on the conversation. The fact that CR/EL is broken-- and that the designer's intent is shot to hell-- has been settled around these parts for at least 5 years.

And I know you know that, so your contrariness is doubly annoying.

I won't be "proving" that CR assumes a fresh party. For the record, I also won't be proving that the sky is blue, that water is wet, or that bunnies are cute.

I am eager to engage on this subject. If you have something interesting and insightful to say, I am all ears. I think my track record on this thread from the beginning is pretty good on that account, and I am not going to get dragged farther off topic.

EDIT: And if I want to appeal to authority, I'll appeal to my own authority. The thread was asking about MY PUBLISHED WORK. I'm up to my elbows in the guts of 3e.

 

[arscott]

Well the conversation was going like this:

"Prove the Pythagorean Theorem."

Now you can either get out your compass and ruler, and set about proving the Pythagorean Theorem, or you can just say, "Well, if I recall correctly, Pythagoras said the square of the hypoteneuse was equal to the sum of the squares of the other two sides, so I guess that proves it."

Okay, Wulf. Fine.

Let's get out out compass and ruler.

Whip up a party of characters. Ideally somewhere in the sweet spot, where they've got enough spells/abilities/whatever that they can meaningfully "go nova", but before the asymmetric show up and throw everything out of whack.

Then pit them up against a monster of equivalent CR. Don't conserve any resources--Go all out, nova, no such thing as overkill, etc.

Now take those same characters but instead of having them start fresh, have them start with half resources--spells, HP, and so forth. Then play them conservatively, as if you expect to fight another encounter after this one.

Now, I don't have a high enough Wisdom score to cast Divination, but I'm guessing that one of those will be a fun, thrilling combat, and one will be a boring cakewalk.

The most basic definition of CR is that "A single CR X monster is an appropriate challenge for a party of level X". Now maybe you and I have a different definition of "appropriate challenge", but I lean towards "fun and thrilling" rather than "boringly easy".

 

[Mustrum_Ridcully]

The most basic definition of CR is that "A single CR X monster is an appropriate challenge for a party of level X". Now maybe you and I have a different definition of "appropriate challenge", but I lean towards "fun and thrilling" rather than "boringly easy".

I don't think that Wulf (or anyone else) is a great disagreement with you that what feels "appropriate" or "fun" is not necessarily the same as what 3E uses to define an appropriate encounter.

I think we might be going a little to off-topic here. I think it's accepted that there were some flawed or at least suboptimal assumptions that lead to the 3E math. But to understand how 3E math works, we more or less have to take them as a given.

---

Oh, and before any mod intervenes, I think we perhaps should look closer at our posts before submitting them, and eliminate unnecessary snark or condescending. (Necessary one off course has to stay. )

 

[Johnny Angel]

Right, there's no need to get any dander up. But of course you're thinking, "But wait, I have the following reasons to pursue this grudge, including, but not limited to, a clear case to be made about who is to blame..." ect. Forget about it. And I'm addressing here whoever is thinking about not letting it go for any reason whatever: let it go. Just let it go, and let's talk about game design.

The question has arisen about whether the CR/EL system assumes a fresh party. Nifft has the distinct impression that the designers specifically meant the system to be useable for about four encounters per day, and thus presumably playtested this notion. The question is not whether or not they said it, but what it would imply if that were the case. It seems to me that this would mean that in the 4th encounter you're scrambling for resources, whereas in the first encounter you would be flush with resources, making the EL a very different creature at either end of your business day. That suggests an intrinsic problem with the EL system. It represents something more like an average of the high point and the low point.

Some of the official modules that have come out begin encounters with already reduced in total effectiveness because the monster is fresh out of a battle or has already used some special ability. I can pore through them looking for a concrete example if you insist, but what I recall is that the EL of the encounter is reduced in these cases. That suggests to me that in the minds of the designers, the EL assumes full capacity at least on the part of the enemies. If it didn't also assume so on the part of the PCs, then it's not clear that these Party CR and enemy CR are comparable.

 

[AllisterH]

1) The ability for a PC to use 100% of his resources in a fight is unchanged from 4e to 3e.

2) The CR of a creature is not based on how many resources you have used, or have left. CR is a fixed value representing combat effectiveness/threat, and it assumes a fresh party. (If it didn't, it would be ing useless.)

3) It is impossible (well, not impossible, but impractical) for a monster's effectiveness to double every 4 levels. However, in 4e, the XP award for a monster doubles every four levels. The power curve does not advance as fast as the XP curve.

4) Ergo, it is more efficient for the 4e party to fight above their level. They will earn XP faster than the threat increases. And it doesn't matter if they have to "go nova" to do this, because-- just exactly as was true in 3e-- there is no penalty for retiring for the day.

.)

How does this work? I'm honestly feel like I'm missing something here...

My understanding of the encounter budget was that every PC (& NPC I'd assume) contributes to this budget and the DM basically matches the monster to the budget...

So how does a party gain faster xp?

 

[Wulf Ratbane]

My understanding of the encounter budget was that every PC (& NPC I'd assume) contributes to this budget and the DM basically matches the monster to the budget...

So how does a party gain faster xp?

Obviously the DM is in control of what the PCs face. I assume that the DM sets the budget, and that he's able to go above or below that budget if he chooses.

The caution here is for the DM who thinks he's creating proportionally tougher encounters with a bigger budget, when in fact the award will be increasing at a pace faster than the commensurate risk.

It's not that the PCs are gaining XP faster than the DM wants to-- he's the one setting the XP budget, after all.

But they might be gaining XP at a rate that increases faster than the amount of risk they're actually facing.

As a DM, I don't care if the PCs get twice as much XP if the encounter is actually twice as hard.

I do mind them getting twice as much XP if the encounter is actually only 1.4 times as hard (for example). That's not ideal.

 

[Nifft]

I am pointing you to an outside source where you can read some actual work on the math behind the d20 system, instead of relying on your recollection of what the 3e designers said their intent behind the system was.

Deflecting you to Upper_Krust's work was my way of trying to be polite.

I'll let someone else tell you how well you're doing with "polite".

Because really, I can't be bothered bootstrapping you up to speed on the conversation. The fact that CR/EL is broken-- and that the designer's intent is shot to hell-- has been settled around these parts for at least 5 years. [...] I won't be "proving" that CR assumes a fresh party. For the record, I also won't be proving that the sky is blue, that water is wet, or that bunnies are cute.

So. It seems to me that you're saying: CR is such a uniform, well-defined, precise metric that it cannot be discussed at all if initial conditions aren't precisely met; and also, it doesn't work.

Man, what?

(Also: the condescension isn't actually making your case stronger... whichever side you turn out to be on.)

I am eager to engage on this subject. If you have something interesting and insightful to say, I am all ears. I think my track record on this thread from the beginning is pretty good on that account, and I am not going to get dragged farther off topic.

Your track record in this thread consists of bombastic attempts to shut people up. You did ask one question about the stuff that actually brought me into this thread, but you seemed to lose interest when it turned out to be non-trivial. Feel free to go back and "engage" some of the stuff already in this thread.

This is the second time I've mentioned that stuff, by the way. Last post is on page 2, if you are interested in "engaging".

EDIT: And if I want to appeal to authority, I'll appeal to my own authority. The thread was asking about MY PUBLISHED WORK. I'm up to my elbows in the guts of 3e.

The fact that CR/EL is broken-- and that the designer's intent is shot to hell-- has been settled around these parts for at least 5 years.

Fortunately, we already know your opinion on the species known as "published designers", so I'll assume this is a shameful admission on your part, and not an attempt to shut up anyone who doesn't bow before bombast.

Cheers, -- N

 

[arscott]

Obviously the DM is in control of what the PCs face. I assume that the DM sets the budget, and that he's able to go above or below that budget if he chooses.

The caution here is for the DM who thinks he's creating proportionally tougher encounters with a bigger budget, when in fact the award will be increasing at a pace faster than the commensurate risk.

It's not that the PCs are gaining XP faster than the DM wants to-- he's the one setting the XP budget, after all.

But they might be gaining XP at a rate that increases faster than the amount of risk they're actually facing.

As a DM, I don't care if the PCs get twice as much XP if the encounter is actually twice as hard.

I do mind them getting twice as much XP if the encounter is actually only 1.4 times as hard (for example). That's not ideal.

Wulf, my original point (which got sidetracked into an irrelevant-for-the-purpose discussion about what it actually means to "go nova" was this:

in 4e, if you throw monsters worth twice baseline XP, the party will die. Or at bare minimum, not win and not actually gain the non-commensurate XP award.