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

[hong]

A role-playing game is one that makes use of the participants' mental and social faculties.

In the context of a tactical wargame.

 

[Wulf Ratbane]

It's great to see so many people get hung up on the first paragraph and fail to make it into the meat of the post.

As much as I'd like to knock a couple of them down I'm more interested in the math. Some of you have been very helpful.

I could live with effective caster level scaling with the square root. Start doubling the numbers in Nonlethal's chart, massage it a bit, then fill in the odd caster levels:

1st = 1d6
2nd = 2d6
3rd = 3d6
4th = 4d6
6th = 5d6
9th = 6d6
12th = 7d6
16th = 8d6
20th = 9d6
25th = 10d6
30th = 11d6

That's still a very steep increase in the early levels. I consider this a feature.

The main thing, when the numerical progressions slow down, is to still give the players some kind of cookie at each level. You can give them more spells, maneuvers, options overall, just slow down the numbers.

EDIT: Bleh. I'm not happy with that. Might as well just cut caster level in half.

 

[mmadsen]

While a legitimate question, I really have to ask if the XP gain rate is really even an issue.

Absolutely. As I said earlier:

I think we need to ask ourselves whether we should be comparing power to level, when the real issue is power as a function of time -- or, more accurately, encounters defeated.

Under the current system, the experience point requirements for each level increase faster than linearly, but the experience point rewards also increase faster than linearly.​

Under the current rules, a character with 130 "appropriate" encounters under his belt has gained 10 levels and is now an 11th-level character with power appropriate to an 11th-level character.

If we change the rules so that those 130 encounters mean the character gains 20 levels, but those levels only add half as much power, then all we've done is change the granularity of the game. Twenty-first level becomes the new 11th-level.

On the other hand, if we change the experience system so that characters level up more and more slowly, then those 130 encounters might only lead to, say, five or six levels, or to ten levels that only mean as much as five or six 3E levels.

Levels and the system for leveling up are intimately intertwined.

 

[mmadsen]

Part of the fun of the game is that the character improves regularly. Unfortunately, in D&D, these improvements come in big chunks (levels), which means if you delay getting another "chunk of improvement", you take out some of the fun.

Yes, I think the old design decision to have characters level up every 13 or so encounters is fine -- we just need to find a better way to handle the leveling up, so that players still get excited about making progress, but their characters don't become overpowered in "unfun" ways, while remaining underpowered in other ways.

 

[mmadsen]

According to Lanchester's Square Law, the power of force is proportional not to the number of units it has, but to the square of the number of units. Thus, two orcs should have four times the fighting power of a single orc.

The EL system asserts that doubling the number of units in a force adds two to its EL, which is, at its core, a measure of the level of the units involved. If doubling the number of units quadruples a force's fighting power, and that's equivalent to increasing the units' level by two, then each level should double a unit's power.

As I said earlier:

What confuses this is that D&D level includes multiple measures of offensive stength (to-hit and damage) and defensive strength (AC and hit points); it's not a single linear measure. For instance, in going from first to second level, an NPC fighter might multiply his to-hit chance by 1.1, his damage by 1.0, his avoid-a-hit chance by 1.0, and his hit points by 2.0, for a total quality factor of something like 2.2. As you can see, at lower levels, without better equipment, it's almost entirely about improved defense through extra hit points. As characters accumulate magic weapons, armor, etc., they can improve across all four of those dimension, and a 10-percent improvement in everything isn't a 10-percent improvement in fighting ability; a 10-percent improvement across four factors is a 46-percent improvement. Now compound that over multiple levels.​

It looks like Fighters and other "brutes" do increase at the meteoric pace the EL system assumes at lower levels, but they need magical bonuses to make up for the slower increase in hit points at higher levels.

 

[Nonlethal Force]

If we change the rules so that those 130 encounters mean the character gains 20 levels, but those levels only add half as much power, then all we've done is change the granularity of the game. Twenty-first level becomes the new 11th-level.

I agree completely. Being a 20th level character whose levels are half as significant in every way as a 10th level character - so they end up exactly the same character - is pointless. It means people level twice as fast but half as much at each level. No significant change is present.

On the other hand, if we change the experience system so that characters level up more and more slowly, then those 130 encounters might only lead to, say, five or six levels, or to ten levels that only mean as much as five or six 3E levels.

Levels and the system for leveling up are intimately intertwined.

I agree with your last comment, but not so much the paragraph above. What you propose is correct, and I can't argue with the logic. Assuming I am understanding your point (and I might not be - if so please try to reexplain!) what you are saying can be done in the current rules just by cutting the XP award per encounter. Cut the award per encounter and you slow down the progression easily enough.

What I'd actually like is a system that accepts that all level increases are not created equal. In other words, the relative power from 1st to 2nd might be much more significant than from 20th to 21st. Perhaps you might get 2nd level spells at 3rd level, 3rd level spells at 6th level, 4th level spells at 10th level, etc. [Not that this is what I am actually proposing, mind you. I'm just trying to demonstrate a system where the power curve is steep at the beginning and tapers off after midgame rather than the current 3.5 system where the power curve is moderate in the beginning and accelerates as the game goes on.

 

[babomb]

Heaven forbid a good conversation and common use of terms stand in the way of thread destruction and niche conventions.

Not to put to fine a point on it, but I'm not sure I'd call high school–level mathematics a niche.

Note that Lanchester's Square Law does not apply to technological force, only numerical force; so it takes an N-squared-fold increase in quality to make up for an N-fold increase in quantity.[/Indent]It's that last paragraph that's the most important to our current discussion. If we measure troop quality with a single variable -- let's say that ogres kill orcs twice as fast as orcs kill ogres -- then two ogres might seem like they'd defeat four orcs easily, but really they'd be overpowered, because multiplying the number of troops multiplies its offense and its defense. More orcs have more attacks, and there are more orcs to kill.

What confuses this is that D&D level includes multiple measures of offensive stength (to-hit and damage) and defensive strength (AC and hit points); it's not a single linear measure. For instance, in going from first to second level, an NPC fighter might multiply his to-hit chance by 1.1, his damage by 1.0, his avoid-a-hit chance by 1.0, and his hit points by 2.0, for a total quality factor of something like 2.2. As you can see, at lower levels, without better equipment, it's almost entirely about improved defense through extra hit points. As characters accumulate magic weapons, armor, etc., they can improve across all four of those dimension, and a 10-percent improvement in everything isn't a 10-percent improvement in fighting ability; a 10-percent improvement across four factors is a 46-percent improvement. Now compound that over multiple levels.

Hm. According to the CR/EL system, doubling the number of monsters (quadrupling the power) increases the EL by 2. That would mean characters roughly quadruple their power every 2 levels, or double in power every level, which is an exponential (2^x) curve. It doesn't seem like that an be right...

 

[Mustrum_Ridcully]

If we actually use a SQRT or logarithmic base for the "number" advancement, how can we ensure that each level also gives the players something new to play with?

We can't give them any abilities that increase damage output or staying power (except for the tiny fractions allowed by the new advancement scheme).

So, what's the alternative?
One possibility might be to give additional options that aren't per se more powerful.
Examples might be:
Getting the ability to trip, grapple or disarm foes (assuming that neither ability gives you really more power, so that the action to trip, grapple or disarm gives you just as much benefit as just hitting.)
Getting the ability to cast Fireball with a different energy type (assuming all energy types are created equal)
Instead of only wild shaping into a wolf, you can wild shape into a hyena.
Instead of healing 4d8 points of damage to a single target, you can spread out the healing among multiple targets.

These improvements seem a bit... shallow compared to what D&D gives us. So, might it actually be impossible to get a linear advancement, together with a constant "survivability" and a constant way to provide the players with mechanical incentives to get new levels?

 

[Calico_Jack73]

At its heart, D&D is a game of tactical combat, and the core mechanics are designed to serve this function.

See... this is where I have a problem. If I wanted to play a Tactical Combat game I'd play Warhammer. D&D is supposed to be a role-playing game but 3.0E started it's inexorable slide into tactical tabletop miniatures wargaming.
WOTC saw how much money Games Workshop was making on minis (back in the early 90's it cost $8 for a blisterpack of 2 unpainted space marine terminators) and wanted to get in on the action.

 

[Wulf Ratbane]

See... this is where I have a problem. If I wanted to play a Tactical Combat game I'd play Warhammer. D&D is supposed to be a role-playing game but 3.0E started it's inexorable slide into tactical tabletop miniatures wargaming.
WOTC saw how much money Games Workshop was making on minis (back in the early 90's it cost $8 for a blisterpack of 2 unpainted space marine terminators) and wanted to get in on the action.

This kind of ill-informed post is really off topic.