Annoying Game Questions You Want Answered

[jt]

In a D&D-ish thing, if HP and damage increase linearly, but the number of low-level monsters you're expected to be able to face increases exponentially, is there a clean way to make high level stuff survive getting swarmed by low level stuff?

Having high level stuff deal appropriate damage to low level stuff is easy - AOE attacks just deal the damage of regular attacks from a few levels ago - but that still leaves an exponentially increasing amount of damage coming from swarms of low level stuff. The solutions I've found are super ugly, is there an elegant one that I'm missing?

[Omegonthesane]

High level stuff tends to have larger AC than low level stuff, access to things like DR and miss chances etc.

The system also imposes something of a cap on how many exponentially many minions can be doing damage at a single time, in that there aren't infinitely many spaces from which to attack any given target with a partcular given weapon.

(Granted I had a habit of enforcing the Spot and Hide rules to determine encounter distance in an open field on the assumption that "not actually even trying to hide" was a -20 to Hide. This hilarious misuse of those rules tended to limit encounters to within 100 feet at time of detection, but I'd still defend the results as representing 'close enough that you can confidently draw a bead on them instead of vaguely shooting at that patch of brown that looks slightly different to the brown of the mountain side')

[Foxwarrior]

With a base 70% chance to hit someone of your level, scaling AC and attack bonus nets you up to 14x defensive power vs lower level enemies. There's also DR, and just generally gaining new defensive powers which lower level enemies have limited counters for.

Edit: dang it omegonthesane

[jt]

I'm hoping for something a little more concrete. I can grant new defensive powers at a regular rate, but I'm missing some sort of insight that lets me say "this power will prevent about half of attacks from enemies at CR-2, three quarters of attacks from enemies at CR-4, seven eighths of attacks from enemies at CR-6, etc."

AC bonuses don't really work - going from 80% to 40% is +8AC, but going from 80% to 20% is +12AC, which is not 8+8.

DR has a similar problem, where the magic amount of DR that makes 2x enemies work is not the same as the magic amount that makes 4x work. You could brute force it by having a bunch of material tiers and different DR values for each, like DR15/mithril + DR10/adamantium + DR5/orichalcum but this is way too awkward.

Not every enemy being able to attack at once is a fair point, but relying on it makes threat scaling way different for archers and melee attackers.

[Foxwarrior]

I don't think the defensive ability-assessing insight exists with much precision for non-boring defensive abilities.

[Omegonthesane]

You're not going to come up with an elegant linear formula like that which scales perfectly to allow enemies of any stripe to, in large enough numbers, threaten PCs of any level.

It is also easy to justify having a cut-off beyond which armies just don't contribute anything in D&D, because the combat engine slows to a crawl in mass combats anyway. Where you draw that line is a matter of taste, but it usually exists. So you then only have to come up with a formulation that doesn't break down in acceptable combat sizes.

So the most boring formulation of this would be "Your soul armour blocks 50% of damage from +2 weapons, 75% of damage from +1 weapons, and means you can never ever take damage from +0 weapons"

[OgreBattle]

In a D&D-ish thing, if HP and damage increase linearly, but the number of low-level monsters you're expected to be able to face increases exponentially, is there a clean way to make high level stuff survive getting swarmed by low level stuff?

Having high level stuff deal appropriate damage to low level stuff is easy - AOE attacks just deal the damage of regular attacks from a few levels ago - but that still leaves an exponentially increasing amount of damage coming from swarms of low level stuff. The solutions I've found are super ugly, is there an elegant one that I'm missing?

Soft counters include

Defensive stance- characters can raise their AC at expense of hit bonus, this makes lower level threats miss more often while warriors at high level still hit

Trampling littler dudes- dragons and elephants can walk through goblin mobs, dealing damage and knocking them over so their offensive ability is lowered

Maneuvering, obscuring - higher level characters have more ways to avoid being surrounded or being hit by 100 archers

Morale- the mob knows they can each individually die from a glance by PC’s

I don’t think it’s bad that an elephant will die when struck by 12 spearmen, so I don’t think you should have CR grant defensive buffs. DnD bows are also more accurate than guns in ‘real life’ so you can consider making ranger attacks and spells harder to aim

[Username17]

In a D&D-ish thing, if HP and damage increase linearly, but the number of low-level monsters you're expected to be able to face increases exponentially, is there a clean way to make high level stuff survive getting swarmed by low level stuff?

Having high level stuff deal appropriate damage to low level stuff is easy - AOE attacks just deal the damage of regular attacks from a few levels ago - but that still leaves an exponentially increasing amount of damage coming from swarms of low level stuff. The solutions I've found are super ugly, is there an elegant one that I'm missing?

Damage Reduction and Armor Class both give larger proportional protection when you are more higher level than your opposition. That is to say that getting +2 AC reduces incoming damage by 25% when your opponents hit you on a 13+ and reduces damage by 50% when your opponents hit you on a 17+. And DR 5 reduces incoming damage by 25% when your opponents do 20 damage and by 50% when your opponents do 10 damage.

This means that standard 3rd edition D&D defenses already inherently provide a larger proportional defense when your opponents are 8 bullshit enemies than they do when your opponents are 2 more meaningful enemies. Having the math work out is a little bit tricky, because of course you are working with five declarable variables (Hit Bonus, AC, DR, Damage, Hit Points) and have four hundred potentially comparable levels (levels 1-20 versus levels 1-20). But while Mike Mearls famously threw his hands up and declared it unsolvable it's actually just tedious. If you wanted to, you could make a python script that gave you all possible growth rates of AC and HP for whatever constraints you felt were reasonable and then you could just pick a paradigm.

But "it's not even math, it's arithmetic."

-Username17

[jt]

Omega, some sort of cutoff is necessary, but it'd be nice to be able to at least get to 4x cleanly, since that's a standard party vs a dragon, and it'd make sense for that to work in reverse too. Natural cutoffs will happen at a few places anyway, like the usual flying archer line.

OgreBattle's list of soft counters is useful, though that's all stuff I'd like to either use to implement whatever the math says should happen, or substitute out for the math. A trample feels more like an AOE attack to me, which I do have the math worked out for.

Frank, combining AC and damage changes is quadratic, not exponential. You can set up the numbers to work out at any given level, but the relationship between the other levels won't be the same. Like whatever you set up at level 8 to make 2x level 6 and 4x level 4 work, won't be compatible with level 6 facing 2x level 4. You can get close with piecewise fits (resetting the math with a hard cutoff every few levels), but it'll be ugly.

Foxwarrior's "I don't think this is possible" comment actually made me realize that you could pull it off if you stack battlefield control abilities that block roughly 50% of attacks and only work on things lower-level than when they were granted. I'll need to think about it a bit to figure out if there's a satisfying way to do this.

[Foxwarrior]

Yeah, I made that comment because I had considered bringing up Concealment and then remembered that I actually dislike that mechanic. You can try to figure out an approximation of what % of attacks a Wall of Stone spell will block by forcing people to spend their actions on moving instead, but I dare you to make your approximation precise.

[OgreBattle]

Yeah trampling is just REF save damage 'cause D&D usually doesn't have effects of dudes falling backwards into each other or being shoved into their fellow. It's such an evocative and 'basic' kind of movement interaction it should be in the game.



Make enough corpses and it's difficult terrain or cover

[Username17]

Frank, combining AC and damage changes is quadratic, not exponential.

Those words don't mean what you think they mean. Armor Class increases are in fact exponential. If your opponent hits you on an 11+, then a +1 AC reduces incoming damage by 10%, and the next +1 AC reduces incoming damage by 11%, and the next +1 AC reduces incoming damage by 12.5%, and the next +1 AC reduces incoming damage by 14.3%,and the next +1 AC reduces incoming damage by 16.7%, and the next +1 AC reduces incoming damage by 20%, and the next +1 AC reduces incoming damage by 25%, and the next +1 AC reduces incoming damage by 33.3%, and the next +1 AC reduces incoming damage by 50%, and the next +1 AC reduces incoming damage by 100% (unless your game system intervenes to make that damage reduction less than 100% with minimum hit rates or whatever).

That might not be the curve that tickles your fancy, but it is an exponential curve. While it's "true" that every point of Armor Class removes a linear and identical amount of average damage per attack, it's importantly more true that the meaningful statistic is "how many expected attacks does it take to drop you?" And that is not linear. Every point of AC increases the number of required attacks by more than the one before it. If it takes 5 hits to drop you, then with an AC 11 points over the attack bonus that's 10 enemy attacks to drop you; and with an AC 13 points higher, that's 12.5 attacks to drop you; and with an AC 15 points up that's 16.7 attacks to drop you, with an AC 17 points up that's 25 attacks to drop you; and with an AC 19 points up that's fifty attacks to drop you. Each point of AC increases the number of enemies you can wade through by more than the one before it.

Damage Reduction works similarly. Because again we aren't concerned about the absolute amount of damage removed from each attack, but by the total number of attacks your character can survive. Imagine that our "5 hits to drop" was calculated because of 8 point attacks against 40 total hit points. If we give out 3 points of Damage Reduction, that means you take 8 hits to drop instead of 5, which increases your "attacks to drop" number by 60%. If we give out a second 3 points of Damage Reduction, then the damage goes down to two, and it takes twenty hits to drop, increasing the "attacks to drop" number by 150%. A third addition of 3 points of DR would make you functionally immune to 8 point attacks and you'd only ever go down if the random element caused some attacks to do enough to penetrate the DR.

Yes, handing out raw hit points simply increases the number of attacks you can sustain by a linear amount, and repeated additions of the same hit point total provide a diminishing return. But Armor Class and Damage Reduction aren't like that. Determining how many attacks you want Orcs to take before a Knight of Level X goes down is a matter of preference, and implementing that preference is just an algebra problem.

-Username17

[jt]

Frank, you seem to think that exponential means "superlinear," which is wrong.

expected damage = base damage * accuracy
Accuracy increases linearly with attack bonus - your percent hit rate is (10 + attack bonus - AC) * 0.05.
Base damage increases linearly with dice or damage bonus or whatever. You could make it exponential, but it being linear is the premise of the question I asked.
The product of two linear increases x, is x^2. This is quadratic. This is not exponential. Exponential is when the variable increasing is in the exponent, as in 2^x.

expected rounds = hp / expected damage
Dividing by x^2 is an inverse square relationship. This is again not exponential.

If your opponent hits you on an 11+, then a +1 AC reduces incoming damage by 10%, and the next +1 AC reduces incoming damage by 11%, and the next +1 AC reduces incoming damage by 12.5%, and the next +1 AC reduces incoming damage by 14.3%,and the next +1 AC reduces incoming damage by 16.7%, and the next +1 AC reduces incoming damage by 20%, and the next +1 AC reduces incoming damage by 25%, and the next +1 AC reduces incoming damage by 33.3%, and the next +1 AC reduces incoming damage by 50%

One property of exponential relationships is that the ratio between subsequent values in the sequence is constant. 10%, 12.5%, 16.7%, 25%, and 50% are, in fact, different numbers.

The numbers you listed are described by 1 / (10 - x). Note the lack of an exponent.

[Username17]

Base damage increases linearly with dice or damage bonus or whatever. You could make it exponential, but it being linear is the premise of the question I asked.
The product of two linear increases x, is x^2. This is quadratic. This is not exponential. Exponential is when the variable increasing is in the exponent, as in 2^x.

This is gibberish. Like, I think I can see why you thought that was a thing you should say, but you shouldn't have said it because it's stupid and wrong.

Armor class increases your survivability by 1/X where X approaches zero. It's not a fucking quadratic curve. A quadratic curve has the absolute increase of the absolute increase be constant number because it's second order and that is how second order functions grow. Increases in AC do not work like that. You are instead dividing by a negative exponent, which is a form of exponential growth whose rate of acceleration itself accelerates. When your AC goes up, the increase in the number of attacks it takes to drop you is proportional to the number of attacks it took to drop you - which is the definition of exponential growth.

In any case, Damage versus DR and To-hit versus AC can easily be set to make the difference between 17th level and 14th level exactly the same as the difference between 5th level and 2nd level with simple linear bonuses on both sides. You don't even need hit points to change at all, and indeed the math gets much easier if they do not. Fixed hit points solves a lot of problems, but getting the game to work with rising hit points is just slightly more soul-draining math. But you can still do it, because you only need to solve for 20 levels, not for all possible values of X.

-Username17

[jt]

I would correct you if I thought your goal was to be correct, but it seems that your goal is to assert how smart you are and call me an idiot. This doesn't require correctness, as is so clearly evidenced by your posts, so learning that 1/x^2 is not exponential would be a waste of your time, and trying to teach you high school algebra would be a waste of mine.

[Username17]

I would correct you if I thought your goal was to be correct, but it seems that your goal is to assert how smart you are and call me an idiot. This doesn't require correctness, as is so clearly evidenced by your posts, so learning that 1/x^2 is not exponential would be a waste of your time, and trying to teach you high school algebra would be a waste of mine.

It's not 1/X^2 you stupid asshole. There's no X^2. Hit point gains increase survivability in a linear fashion. AC gains increase survivability in an exponential fashion. There's no square fucking numbers.

-Username17

[jt]

Yeah, I made that comment because I had considered bringing up Concealment and then remembered that I actually dislike that mechanic. You can try to figure out an approximation of what % of attacks a Wall of Stone spell will block by forcing people to spend their actions on moving instead, but I dare you to make your approximation precise.

Concealment is merely irritating; implementing what I suggested using mechanics like concealment would be outright infuriating. Nobody wants to try to attack a dragon, flip a coin to see if they're too scared to advance, flip a coin to see if they can get past the gale of air it's making with its wings, and then finally get to attack it if they got heads twice. The fact that the math works out tidily isn't much consolation.

But I'm okay with taking a 50% guideline and try to figure out how big of a Wall of Stone is going to approximate that at which level. That's not going to be precise at all, but the important thing is not getting every mechanic to be identically useful in all situations. The point is having a precise guideline so you can tell when something is overperforming or underperforming. And that guideline needs to at least approximate a function with the right shape, or your encounter building rules are going to yield garbage.

[jadagul]

You're both wrong. The relationship here is actually superexponential.

We all agree that damage taken per round decreases linearly with an increase in AC. I think we all agree that that's not really the thing we care about---we want to track how the number of turns survived scales with AC. That winds up being proportional to 20/N, where N is the number of sides of the d20 that result in a hit. Increasing AC by one decreases N by one. So survivability is inversely proportional to (hit bonuses minus AC).

This is a superexponential function: it asymptotically grows faster than an exponential. Specifically, it goes up to actual infinity, and if your AC is high enough in a system that doesn't make natural twenties into auto-hits or something, your survivability is infinite because you can't be hit. This is much stronger than an exponential distribution, which gets very large but never actually goes to infinity.

For it to be exponential growth, the rate of increase in survivability would need to be proportional to AC---with a constant constant of proportionality. In this case each point of AC increases your survivability by a larger percentage, so our growth isn't exponential; it's bigger than exponential.


(DR does the same thing. Damage taken scales linearly with DR, so survivability scales with 1/(1-DR) and survivability is inversely proportional to (damage minus DR). If DR and AC are both proportional to level, this makes damage taken a quadratic function of level, and so survivability scales like 1/ (1- level^2). This is where the quadratic thing comes in, but really it's inverse-quadratic and even more superexponential).

[Username17]

jadagul, I am willing to accept that. Although I've also heard J-curves defined as a subset of exponential growth because "superexponential" has the word "exponential" in it.

Regardless, in the extremely simple model where you get +1 AC, +1 to-hit, +1 damage, +1 DR, and+0 HP every level then level 10 versus level 10 is precisely the same as level 1 versus level 1 and level 10 versus level 12 is precisely the same as level 1 versus level 3. Thus, giving simple linear bonuses in a way that maintains level associations in the manner you'd want from some X^Y growth pattern is in fact pretty easy.

The question is merely one of deciding what the relationship you want from Level 3 to Level to look like and then solving the associated algebra problem.

-Username17

[jt]

jadagul, that's just a discontinuity at the end of the RNG. Since the goal is to impose a self-similar relationship across levels, it's not really relevant. That is, the problem isn't making CR 8 stuff twice as good as CR 6 stuff and four times as good as CR 4 stuff, it's doing that AND making CR 6 stuff twice as good as CR 4 stuff, CR 4 stuff twice as good as CR 2 stuff, CR 10 stuff twice as good as CR 8 stuff, etc. The chain of relationships means that CR 20 and CR 1 need to be on the same curve, even though it's not actually important that those are actually compatible with each other in play.

Attacks hit (21 + attack bonus - AC) * 5% of the time. If we set attack bonus to 0 and AC to 10+x, we get (11-x)*5%. If we take the ratio of that across two levels, we get
((11-x)*5%) / ((11-(x+1))*5%)
(11-x) / (10-x)
1 + 1 / (10-x)
This is in the form "+1 AC is 1.1 times as much as +0 AC," so to get it back to relative increases, subtract one and multiply by 100:
100 / (10 - x)
Which produces the numbers from Frank's earlier post.

We could also write this as:
100 * (10-x)^(-1)
Note that the "-1" is in the exponent, and the "x" is not. That's because this is a reciprocal function, not an exponential one. Exponential functions have the variable in the exponent.

Note that all of this is a result of dividing over adjacent levels for some reason. The original accuracy equation remains linear. You can tell it's linear because I gave an exact equation ((21 + attack bonus - AC) * 5%) for it, which is linear.

[jadagul]

jadagul, that's just a discontinuity at the end of the RNG. Since the goal is to impose a self-similar relationship across levels, it's not really relevant. That is, the problem isn't making CR 8 stuff twice as good as CR 6 stuff and four times as good as CR 4 stuff, it's doing that AND making CR 6 stuff twice as good as CR 4 stuff, CR 4 stuff twice as good as CR 2 stuff, CR 10 stuff twice as good as CR 8 stuff, etc. The chain of relationships means that CR 20 and CR 1 need to be on the same curve, even though it's not actually important that those are actually compatible with each other in play.

Attacks hit (21 + attack bonus - AC) * 5% of the time. If we set attack bonus to 0 and AC to 10+x, we get (11-x)*5%. If we take the ratio of that across two levels, we get
((11-x)*5%) / ((11-(x+1))*5%)
(11-x) / (10-x)
1 + 1 / (10-x)
This is in the form "+1 AC is 1.1 times as much as +0 AC," so to get it back to relative increases, subtract one and multiply by 100:
100 / (10 - x)
Which produces the numbers from Frank's earlier post.

We could also write this as:
100 * (10-x)^(-1)
Note that the "-1" is in the exponent, and the "x" is not. That's because this is a reciprocal function, not an exponential one. Exponential functions have the variable in the exponent.

Note that all of this is a result of dividing over adjacent levels for some reason. The original accuracy equation remains linear. You can tell it's linear because I gave an exact equation ((21 + attack bonus - AC) * 5%) for it, which is linear.

You sound like you think you're disagreeing with me, but I'm not sure why. Accuracy is linear, and that makes damage linear; and that makes survival time inverse linear which is superexponential. (And, as you say, not exponential.)

An inverse linear function will always have an asymptotic discontinuity---that's not falling off the RNG, that's just how inverse linear functions work. The end of the RNG means that you don't recover to a finite result after the asymptote, but that has very little to do with anything.

Now, as Frank points out, this equation does make level 10 have the same relationship to level 8 as level 4 has to level 2. What it doesn't do is make level 8 be "twice as good" relative to level 4 as it is relative to level 6 in any meaningful sense. And that's kind of necessary if we have an asymptotic cliff at the end like that, because level 9 (or whatever) is genuinely un-hittable by level 1, and I don't know what "half as good as totally invincible" actually means.

[jt]

Superexponential means that it increases faster than any exponential function. I'm not really sure what you mean applying it to something that's decreasing. 1/x doesn't decrease faster than much of anything, since it has an asymptote at 0, and even 1-x outruns that. It doesn't dominate the asymptotic behavior when you add it to an exponential equation (1/x+2^x looks like 2^x when you zoom out). It doesn't cancel out any exponential equation when you multiply them together ((2^x)/x still looks like 2^x when you zoom out).

Inverse functions are not self-similar. The ratio between 1/2 and 1/3 is 1.5, the ratio between 1/3 and 1/4 is 1.33. I think you're talking about how this can be shifted, 1/(x -y) produces those values for y=0, x=2,3,4 and also for y=10, x=12,13,14. But this is true of every function so it's not really a notable property. This sort of self-similar ratio is necessary if you want your encounter guidelines to always return the same number of monsters when you ask it for a given level delta. Like if you're using 3E's "-2 CR means double the monsters" rule.

You could avoid this problem entirely by changing your encounter building rules to a more friendly curve, like quadratic or something. That means a level 10 party can't face as many level 8 monsters as a level 4 party can face level 2 monsters, though. I was worried players would find this dissatisfying though so I wanted to see if it's possible to preserve the exponential relationship that people are used to. (And it is: I'm half done with a system that deals with it.)

[Schleiermacher]

I've been poking around the old game design threads about the SAME damage system, but there are some questions I couldn't find conclusive answers to:

1. Is it or is it not a problem in SAME to decouple the accuracy stats from the damage stats? Each stat needs to oppose itself, but does an attack that rolls Agility vs Agility to hit and Elan vs Elan for damage break the symmetry, or not? As far as I can tell it's fine to do that, but I saw arguments both ways.

2. How would SAME interact with non-damaging attacks? It would be easy to model something like a net as an SA attack that binds the target rather than dealing damage if it hits, and you could preserve the property of a better attack roll making the resistance roll afterward more difficult, but that probably still breaks the property of attack and damage being equally valuable. Are all kinds of conditions and debuffs supposed to be inflicted by stacking up esoteric "damage", so a net would just be a "magic" Earth attack that binds you if it inflicts enough "wounds" and incapacitates you if it fills up all your health boxes?

[jadagul]

Superexponential means that it increases faster than any exponential function. I'm not really sure what you mean applying it to something that's decreasing. 1/x doesn't decrease faster than much of anything, since it has an asymptote at 0, and even 1-x outruns that. It doesn't dominate the asymptotic behavior when you add it to an exponential equation (1/x+2^x looks like 2^x when you zoom out). It doesn't cancel out any exponential equation when you multiply them together ((2^x)/x still looks like 2^x when you zoom out).

Inverse functions are not self-similar. The ratio between 1/2 and 1/3 is 1.5, the ratio between 1/3 and 1/4 is 1.33. I think you're talking about how this can be shifted, 1/(x -y) produces those values for y=0, x=2,3,4 and also for y=10, x=12,13,14. But this is true of every function so it's not really a notable property. This sort of self-similar ratio is necessary if you want your encounter guidelines to always return the same number of monsters when you ask it for a given level delta. Like if you're using 3E's "-2 CR means double the monsters" rule.

You could avoid this problem entirely by changing your encounter building rules to a more friendly curve, like quadratic or something. That means a level 10 party can't face as many level 8 monsters as a level 4 party can face level 2 monsters, though. I was worried players would find this dissatisfying though so I wanted to see if it's possible to preserve the exponential relationship that people are used to. (And it is: I'm half done with a system that deals with it.)

I'm pretty sure all of this is wrong.

The function we're looking at isn't actually 1/x; it's 1/(1-x). (Or 1/(20-x) with appropriate scaling). As x increases towards 20, the function increases super-exponentially, and eventually spikes to infinity at x = 20.

And since this is an actual asymptote, it totally dominates exponential growth. 1/(20-x) divided by 2^x still goes to infinity at 20; it just takes a stupidly long time to get above one. 2^x divided by 1/(20-x) is just (20-x) 2^x, and goes to zero at 0.

The inverse proportional growth blows up in finite time, which exponential growth doesn't, and so it's a much faster growth.

---

I agree with you that inverse functions are not self-similar. Any function that's self-similar in the way you're asking for must be an exponential, since that's the unique solution to the differential equation dy/dx = k*y. But that self-similarity isn't actually necessary for the thing you're asking it to do.

To-hit bonuses are in a race against AC. It doesn't matter what my to-hit bonus is in a vacuum; what matters is the difference between my to-hit and your AC. So the thing we're actually tracking is x-y. So if to-hit and ac both increase linearly with the same slope, then level 3 characters will have the same relationship to level 1 characters that level 13 characters have to level 11 characters. And as you observe, this is true no matter what function we subsequently plug (x-y) into.

(And yes, if damage and DR scale by level, then that's another relationship, but it's independent and if we plug D-DR into some formula then the same level difference will have the same relationship.)

Now none of this holds if to-hit and AC don't scale linearly, or if they scale with different slopes. And I think that's what you're thinking about. But for your goals, letting that happen would be really stupid. You want level X to have the same relationship to level X+2 regardless of what X is. By far the simplest way to do that is to let to-hit and AC increase linearly with level with the same slope. And then we plug that difference into some function that determines how much better level X+2 is than level X.

---

At this point, we can decide if we want that second function to be an exponential. There's a decent argument for doing that, and there's a reason the 3.x designers picked it. The self-similarity says that however much advantage X+2 has over X, then X+4 has the same advantage over X+2. So in 3.x we have the goal that one level 10 character is equal to two level 8, or four level 6, or eight level 4, or sixteen level 2, or 22.6 level 1 characters.

And that's bullshit, because no one thinks that 23 level 1 characters should beat a competent level 10 character. Not even the designers, who just threw up their hands and said that at a nine level difference you get no XP because it should be a trivial challenge. But it's a lovely goal.

But now suppose that all level difference comes from to-hit versus AC scaling, in the way Frank described, with the 1/(20-x) scaling you get from that. Say an equal-level opponent has a 50% chance to hit you, and each level changes that number by 10 percentage points. If you drop in four hits, then:

with an equal level opponent you drop in 8 attacks;
with a one-level advantage, you drop in 10;
with a two-level advantage, you drop in 14,
with a three-level advantage, you drop in 20;
with a four-level advantage, you drop in 40;
With a five-level advantage, you never drop.

This is a super-exponential scaling, and it goes from 8 (50%) to infinity in five steps. But all that is true regardless of your opponent's level; all that matters is the relative level difference.

If we run the numbers, you tie with an equal-level opponent. With a one-level advantage, you drop in ten attacks and you take out one every seven attacks, so you have a 1.5-to-1 advantage. With a two-level bump, you take 14 attacks and you kill someone every 6, so you're slightly better than twice as good. With a four-level advantage, you drop in 40 attacks and you drop someone every 4.5 attacks, so you kill nine people before you die. The first two-level bump is a 7/3 advantage and the second two-level bump brings you to a 9/1 advantage, which is way better than 49/9. That's because our scaling is 1/(20-x) and not exponential.

But none of this depends on the level your opponent is, only on your relative difference.

[OgreBattle]

I've been poking around the old game design threads about the SAME damage system, but there are some questions I couldn't find conclusive answers to:

1. Is it or is it not a problem in SAME to decouple the accuracy stats from the damage stats? Each stat needs to oppose itself, but does an attack that rolls Agility vs Agility to hit and Elan vs Elan for damage break the symmetry, or not? As far as I can tell it's fine to do that, but I saw arguments both ways.

I believe the reason is to encourage no dump stats, or just pumping one stat alone.

2. How would SAME interact with non-damaging attacks? It would be easy to model something like a net as an SA attack that binds the target rather than dealing damage if it hits, and you could preserve the property of a better attack roll making the resistance roll afterward more difficult, but that probably still breaks the property of attack and damage being equally valuable. Are all kinds of conditions and debuffs supposed to be inflicted by stacking up esoteric "damage", so a net would just be a "magic" Earth attack that binds you if it inflicts enough "wounds" and incapacitates you if it fills up all your health boxes?

old thread on SAME:
http://tgdmb.com/viewtopic.php?t=39645

So petrifying someone is dealing Earth Damage until you drop 'em. There's another thread on Assymetric Threat's non-damage maneuvers and why you'd use them:

"
-Your basic attack is unlikely to drop an enemy and you want to debuff them.
-For whatever reason you do not want to kill or injure your opponent, but you want to reduce the threat they pose.
-You want to capture the opponent.
-There are multiple enemies, and you'd rather debuff the group than attempt to drop a single mook.
-There is a specific action you want to cause or prevent (such as the pulling of an alarm) more than you care about the welfare of one of your opponents.
-Your basic attack is unlikely to work, and you'd like to accomplish something.
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