Attributes

[Maxus]

One thing that I think is notable about Kratos is that he doesn't actually have the same strength as the Colossus of Rhodes. His strength works *differently.* He actually seems to have some sort of counter-surge that lets him, say, throw off the guy stepping on him, or stop Atlas from squeezing him to death, but he doesn't actually regularly throw people 50 feet in the air with a flick of his hand. Or punch down buildings.

Very true.

On the other hand, he does seem to turn it on when he's desperate or determined, and I think we can agree that he's much, much stronger than a normal man, even just walking around

Hm.

So what would that mechanic be in 3.5 terms? Every few rounds, you get to spend a 'surge' of superhuman strength? Add the surge's bonus to, say, your effective size modifier for grappling, or your Strength check for tripping, or whatever else?

[RiotGearEpsilon]

Your Strength is a function of whatever strength you're currently opposing, with some upper limit on the function.

[IGTN]

So there comes a point where one is forced to ask what exactly it is that an "attribute" is supposed to do that is separate from a "skill" and the answer is frankly vague. For TNE purposes I am supposing that attributes represent skill categories and are essentially your defaults. We can also use them for defenses, based on the idea that a defense is passive and essentially a skill default situation. I am ambivalent about using them for attacks. On the one hand, the strength of a hero adding to the power of his mighty axe slash is evocative and obvious, but of course that kind of forced specialization is inherently problematic.

Perhaps, to encourage stat division, stats could add to your abilities sideways. You might have a powerful axe slash, but you can only use it so often before you become too sore to use it, or you get a secondary effect for it based on strength (preferably one that doesn't interact with D20 rolls if possible); it might, for instance, allow you to push the enemy back an amount depending on your strength.

There could even be multiple options on moves, where a move might do one str-dependant thing and an int-dependant thing, or even one for each ability; you might get them all, or you might have to choose one, depending on your attributes and the situation.

[erik]

To clarify my stance on why I think attributes aren't total bunk, I figured I'd give a representation of how I intend to use attributes in a non-crappy manner.

I put my d6TN5 thing on the back burner for a year or so, but I'm liking a lot of Savage Worlds stuff lately and have started working on it again to adapt it to some of their mechanics, albeit with enough overhauls that it's hard to say which one is being adapted towards the other.

As this relates to attributes, I set up 4 attribute sets which are used as defensive values and as pools for related skills which could be purchased:

Might (defense difficulty for others to inflict physical damage)
• Melee Combat
• Athletics

Coordination (defense difficulty for physical attacks to hit you)
• Ranged Combat
• Maneuvering

Charisma (defense difficulty for others to inflict mental damage)
• Persuasion
• Coercion

Awareness (defense difficulty for mental attacks to affect you)
• Intellect
• Perception

Each skill set under the attribute gets 1 d6 by default, and then whatever rank is put into the governing attribute will grant that many d6's to be diviied between the related skill sets.

So if someone had a Might of 4, then they could have 5 Melee Combat and 1 Athletics. for example.

Anywho, in that scheme, the attributes don't actually do anything other than set defense scores, and help quantify which skill sets the character is proficient in. I probably need to do some more tweaking with the exact number of dice handed out. I'll probably start a new d6TN5 thread once I have stuff fleshed out further.

[Manxome]

Powers of 2 are better for "balanced" choices, while uneven factors favor "unbalanced" choices.

Not to beat a dead horse, but I still don't see the justification for this.

Your previous explanations for why this is the case required a bunch of important assumptions that prevent you from applying it as widely as you seem to want to (e.g. defense uses the same attributes as the attack, attacker chooses attack type, all costs linear), but even with those assumptions I still don't think this principle holds.

My counter-example from the last thread looked something like this:

3 attributes: red, blue, white
6 attack types:

• Red + 1/2 Blue
• Red + 1/2 White
• Blue + 1/2 Red
• Blue + 1/2 White
• White + 1/2 Red
• White + 1/2 Blue

This example is "irreducible," in the sense that each attribute gets you something that you can't get for an equal investment in anything else. All attributes are isomorphs, but this has been true of all of your examples as well. And it satisfies your condition that any two builds with the same total number of points attack each other for the same net bonus using their optimal attacks...

6/0/0 vs. 0/0/6 results in both attacking at +6
6/0/0 vs. 2/2/2 results in both attacking at +3
6/0/0 vs. 3/3/0 results in both attacking at +3 (RW and BW attacks)
3/3/0 vs. 2/2/2 results in both attacking at +1.5
3/3/0 vs. 0/3/3 results in both attacking at +3
6/0/0 vs. 4/2/0 results in both attacking at +2
etc.

You've also previously admitted that you can make an unbalanced system with any number of attributes--your classic example to show why 3 attributes is naturally unbalanced actually works every bit as well with 4 attributes, which should at least show that it cannot prove your thesis.

At present, I see no particular reason that you would need to have any specific number of attributes to gain or lose this property that you are calling "balance". Though I'm also not certain that upholding the assumptions you used to construct the examples is a good idea in the first place...

[Username17]

Given sufficient fractional notation you can achieve similar results with five, seven, or even thirteen. The problem being that it requires sufficient fractional notation in order to mimic the kinds of parity that powers of two generate with whole numbers. Similarly, you can generate RPS systems with even powers of two, again if you invoke fractionalization. Which considering how difficult may people seem to find fractions, I stand by my statement:

Powers of 2 are better for "balanced" choices, while uneven factors favor "unbalanced" choices.

-Username17

[RandomCasualty2]

If you eliminate attack stats altogether, and just have defensive stats, then you can have as many defensive stats as you want and the system will be balanced without fractional systems or anything.

Quite simply you basically don't get to distribute points to attack stats. You choose where your defenses want to go. So if you use the typical D&D fort, ref, will, and distribute them, you're going to be pretty much balanced regardless of how you place them, so long as you can't dynamically change them based on situation and your monsters are fairly well mixed, if you want to be uber fortitude, then you're going to have a reflex and will Achilles heel, and that's fine.

[Username17]

Using the not-unreasonable sounding assumption that enemies have a greater degree of choice of who and how to attack than you do as to who and how you are attacked, a defenses only scheme punishes specialization regardless of how many piles you are distributing through. If you give yourself a boost to Resistance A at a cost of Resistance B then you are at a relative weakness over someone who invested equally in Resistances A and B. Simply put, you will be at an advantage against enemies with only A, a disadvantage against enemies with only B, and of course a disadvantage against enemies who can choose to attack A or B. More generally of course you are also at a relative disadvantage against any enemy who has the ability to attack resistance B, and no meaningful advantage against any enemy who has any attack that targets any resistance other than A. An enemy with A and C for example will simply choose "not A" and your investment in A resistance will come to nothing.

If there's no advantage to specializing, and for defensive purposes there usually isn't much, people won't do it voluntarily. That's why Fantastic! requires people to choose a defense with two strengths and two weaknesses. If anyone could pick a defense with no strengths and no weaknesses it is reasonable to assume that they would.

-Username17

[Judging__Eagle]

If you eliminate attack stats altogether, and just have defensive stats, then you can have as many defensive stats as you want and the system will be balanced without fractional systems or anything.

Quite simply you basically don't get to distribute points to attack stats. You choose where your defenses want to go. So if you use the typical D&D fort, ref, will, and distribute them, you're going to be pretty much balanced regardless of how you place them, so long as you can't dynamically change them based on situation and your monsters are fairly well mixed, if you want to be uber fortitude, then you're going to have a reflex and will Achilles heel, and that's fine.

I like that idea.

I'm guessing that you pick attack/de-buff types and then your overall level determines how powerful they are?

[RandomCasualty2]

If there's no advantage to specializing, and for defensive purposes there usually isn't much, people won't do it voluntarily. That's why Fantastic! requires people to choose a defense with two strengths and two weaknesses. If anyone could pick a defense with no strengths and no weaknesses it is reasonable to assume that they would.

Well, I was thinking that attributes would also govern skills. So having a high reflex would also help you move silently, do acrobatics and so on. Having fortitude would give you strength/con stuff, and will would be the mental stuff.

And as far as for choosing offenses for monsters, I don't really think that's necessarily going to be true. A generalized monster like a balor or solar is certainly going to have a lot of choices, but likely many monsters only get to attack 2 of them at most. A giant scorpion attacks reflex, and fort if it hits with its poison. Any brute is going to be all reflex attacks. Fey are going to probably attack will most often, and so on. Obviously against a gish type monster, being spread out is probably going to be optimal but there might be times where having max reflex is pretty awesome.

[Manxome]

Given sufficient fractional notation you can achieve similar results with five, seven, or even thirteen. The problem being that it requires sufficient fractional notation in order to mimic the kinds of parity that powers of two generate with whole numbers.

No, you get whole numbers with any multiple of two, i.e. even numbers, not just with powers of two. And you don't need any more fractional notation than I already used to set up a system with 13 attributes; you can get by just fine using nothing but than halves. You just have to add exactly half of your total attributes to each attack/defense type, and achieve a certain degree of symmetry so that each attribute contributes an equal amount overall. I'll do out an example for you with six attributes if you really care, but I doubt you'd have trouble doing it yourself if you actually tried.

There are also lots of tricks for eliminating the fractions if you care. You could multiply through and add one attribute to twice another, rather than using one and one-half. You can disguise them with multiple die rolls and cascading effects. Real systems are probably a lot more complicated than the abstractions we're applying here--like your SAME system, for example, which applies two attributes to each attack but uses them in different ways. This is only an approximation in the first place.

Similarly, you can generate RPS systems with even powers of two, again if you invoke fractionalization.

I'm not actually sure what you consider to be a valid RPS system, since I don't think you've offered any examples, and you certainly haven't given a technical definition. If you merely mean "one that isn't balanced in the sense used above," then you've already admitted that it can be done with any number of attributes.

One thing you might mean is that if you enumerate every possible build for a given number of points and compare each of them to every other, then sum up the relative combat advantage (using optimal attacks) in each match-up, every build does equally well "on average." That would actually mean that every "balanced" system already fulfills this condition, so clearly it would be possible with an even number of attributes.

You could add the condition that no build is allowed to "tie" against any build other than itself, and then it might require fractions or other weird stuff to do it with an even number of attributes. It also might require fractions or weird stuff for prime numbers if we're keeping the other assumptions. I'd have to spend some significant time investigating; it's not obvious to me how you'd construct such a system. (Note: in this paragraph, "might" means that I don't currently know the answer, not that I can prove that there exists no general answer.)

But even if you need prime numbers to do this "elegantly," you haven't actually presented any meaningful evidence of that yet...

And as far as for choosing offenses for monsters, I don't really think that's necessarily going to be true. A generalized monster like a balor or solar is certainly going to have a lot of choices, but likely many monsters only get to attack 2 of them at most. A giant scorpion attacks reflex, and fort if it hits with its poison. Any brute is going to be all reflex attacks. Fey are going to probably attack will most often, and so on. Obviously against a gish type monster, being spread out is probably going to be optimal but there might be times where having max reflex is pretty awesome.

Even if you assume that all monsters can only target one defense, or that they choose their attacks at random rather than deliberately targeting your weaknesses, the specialist is still worse off, if we're talking about PCs in an RPG. Two reasons for this:

1) The PCs are at an advantage in almost all combats. Introducing more uncertainty into the combat (e.g. by having variable defenses) reduces the liklihood of the more probable outcome (i.e. that the PCs win); therefore, the PCs are more likely to win if their defenses are consistent, because it reduces the odds of the monsters getting lucky.

2) The PCs are supposed to win a lot of fights consecutively, not to go 50/50. Winning one fight really hard and then getting slaughtered means you're worse off than if you just scrape by in two fights. Again, the PCs are better off with consistency.

[RandomCasualty2]

1) The PCs are at an advantage in almost all combats. Introducing more uncertainty into the combat (e.g. by having variable defenses) reduces the liklihood of the more probable outcome (i.e. that the PCs win); therefore, the PCs are more likely to win if their defenses are consistent, because it reduces the odds of the monsters getting lucky.

Well that's true, but it also removes a lot of tactics as well.

2) The PCs are supposed to win a lot of fights consecutively, not to go 50/50. Winning one fight really hard and then getting slaughtered means you're worse off than if you just scrape by in two fights. Again, the PCs are better off with consistency.

Well, not necessarily. It's nice to have a defensive specialist in the different areas, so when you meet the giant you can throw a reflex defense specialist at him, and the fortitude defender can take the life draining wraith, and so on.

But I think it may need a bit more thought as far as ranged attacks go, since if they can target your weak guys with ranged attacks, it'd sort of defeat the whole purpose. So maybe the idea needs a bit more polish.

[Username17]

Let's say that every monster can attack either one defense or two defenses. This gives six possibilities:

Fort
Will
Ref
Fort/Will
Fort/Ref
Will/Ref

Now, if you specialize in Will at the expense of Fort, then enemies fight you like this:

Fort: Bad!
Will: Good!
Ref: No change.
Fort/Will: Bad! (enemy chooses Fort)
Fort/Ref: Bad! (enemy chooses Fort)
Will/Ref: No change. (enemy chooses Ref)

Got that? You get a relative advantage in one condition out of six and a relative disadvantage in three out of six. And if you have more defense types, it gets even more stark.

Specializing defenses is bad in almost all cases. If you don't have to do it you won't do it.

-Username17

[Manxome]

1) The PCs are at an advantage in almost all combats. Introducing more uncertainty into the combat (e.g. by having variable defenses) reduces the liklihood of the more probable outcome (i.e. that the PCs win); therefore, the PCs are more likely to win if their defenses are consistent, because it reduces the odds of the monsters getting lucky.

Well that's true, but it also removes a lot of tactics as well.

Which is why defensive specialization should be mandatory rather than optional. If it's optional, then players have an actual tactical incentive to choose the boring option.

[RandomCasualty2]

Yeah ok. Frank's examples make sense. I guess the defenses just don't work once you enter choice into the equation.

I don't really like forced specialization since I'd really like to be able to have a generalist character as a viable choice. Gishes and the like typically are a balance of fort/ref/will, being average at everything but not exceptional anywhere. I'd like to allow that in the model somewhere.

[Judging__Eagle]

Ok, I see what you mean Frank.

What do you propose and what upsides and downsides are there?

[JonSetanta]

I don't really like forced specialization since I'd really like to be able to have a generalist character as a viable choice. Gishes and the like typically are a balance of fort/ref/will, being average at everything but not exceptional anywhere. I'd like to allow that in the model somewhere.

This times 10. I'm a 'balanced' player too and would be disinclined to take risky action, let alone leave town, if 2 out of 3 attacks will bypass the unnecessarily hyperfocused precautions and go straight to the heart or slap me in the face.

[Judging__Eagle]

.... I like to make characters that have a suite of able options.

Some of them include:

-Movement that others don't expect (higher than average speed; jump checks that _really_ shine, ridiculous "travelling" speeds).
-Being able to really focus on one type of damage style or an other
--"ranged" (casting some BS spell that creates a "rain storm", then casting Call Lighting with a lesser maximize rod (that an adventure had and the DM allowed, thinking erroneously that we'd sell such an awesome item) for 30 damage per round (not much, but it's not bad at lvl 6-7)
--melee (cast DR spells on self, then melee related buffs)


-having attack types that aren't expected (like a character that wears heavy armour, three swords; but relies on ranged thrown weapon attacks to deal damage safely and to attract enemies to themselves no matter what is going on)


Really... it's that I'm a rogue. some days I'm just not a good person. I do no harm, and try to avoid others coming to harm when I am there and can do something personally, but I'm very petty and want to look big. In games I do that by grabbing unexpected abilities and options.

It's one thing to say that you're a cleric or Sun and [W/e Domain is needed to get Persistent spell easily] with a bronzewood greatsword that you cast Thorns onto to the DM and group.

It's an other when you murder things that the Minotaur Barbarian needs more than one attack to kill (was created by straight out using the MM stat mods with class levels just tacked on to the monster HD (i.e. having both monster HD and Barb HD)).

Of course, I know that this is bad for long-term play, even if it's fun on a per-session basis.

[Manxome]

I don't think anyone said you had to be hyperfocused on one defense. Just that you shouldn't be able to freely move points around between your defenses.

The overall deadliness of the game should be set at an appropriate level, regardless of what other mechanics are used. Saying that you won't be happy if you have any weakness is kind of like saying you won't be happy unless you're good at everything; it's bad for the game, and once the game is rebalanced around the choice, it's ultimately self-defeating. You don't get to be better than everyone else.

[Koumei]

It's one thing to say that you're a cleric or Sun

I want to play as a Sun. Brilliant ball of gas/plasma/nuclear fire for the win!

With a fire-immune dung beetle to roll it around the place like a Katamari of Fiery Death.

[IGTN]

Maybe if, the more points you put into a defense, the cheaper it got to raise; so that, if you're raising Fort at the expense of Will, -1 Will buys you +2 fort, or even +1 ref/+1 fort, if your stats are baseline; lower Will and higher Fort might go 1 for 3, 4, or 5 (although you might be off RNG by the time it gets to 4 or 5, depending on pace).

Suppose we use the first way, where the first point of will dropped increases fort by +2, the second by +3, and the third +4, to a maximum of 3 points of Will down, for +2 +3 +4, a total of +9. The "fighter" takes this. They have a Fortitude bonus of +9, and a net will penalty of -3; the net difference is 12; he almost auto-beats TN 11 fort, and beats TN 11 will on a 14 or better (35% of the time); thus he is just barely on RNG.

So, against monsters:
Fort: Effectively immune
Ref: Neutral
Will: Weak, but not terribly as long as it isn't save-or-lose
Fort/Will: Weak
Fort/Ref: Neutral
Ref/Will: Weak

Against half of the monsters, he wins 35% of the time. Against a third of the monsters, he wins half the time. Against a sixth of the monsters, he always wins (to be fair, wins 95% of the time). Adding these up, (105 + 100 + 95) / 6 = 50%; this is the same as someone who is neutral to all stats. I'll call this a success; tweaking the numbers higher will make things more favorable to the PCs, of course.

Let's consider this further: Every save starts out with a buy amount and sell value of 1; when you move a point from one save at or below baseline to another, you subtract one from the save you're moving and add the sum of the buy amount and sell quantities. On odd-numbered trades to a save, the Buy Amount for the next trade increases; on even-numbered trades from a save, the Sell Value for the next trade increases. A save can be bought no higher than +9. If a save is raised, trades to raise it first must be undone.

This has the same net effect if one save is neglected. However, after three trades, Will has a Sell Amount of 2 (Fort has a Buy Amount of 3, but it can't be raised by more than 1 further). Reflex, though, has a Buy Amount of 1. Suppose the character decides to burn down a 4th point of Will to pump Reflex; Reflex goes up by 3; he could raise it again by spending another point of Will.

He now has a 95% chance to beat Fort attacks, a 65% chance to beat Reflex attacks, and a 30% chance to beat Will attacks.

Against the half of all monsters that use Will attacks, he is more likely to lose; against the third that use Reflex attacks, he favored to win (but it's no more certain than his loss against Will last time); against the one Fort-user, he is still invincible.

Adding up the numbers, (95 + 90 + 130) / 6 = 52.5; by overspecializing, he has made himself have a higher expected win value. Of course, the curve is wider, and one lost battle is a death, for a PC.

An underspecialist; let's say +2 fort +0 ref -1 will, would have a 60% chance to beat the fort monster, a 45% chance to beat each Will monster, and a 50% chance to beat each Ref monster, which adds up to 48.75% overall; so these numbers I pulled out of my ass don't work at the low end. Tweak them up, however, and they will be able to balance. Defensive specialization can be made favorable over generalization, provided that it's crazy enough.

Of course, add in abilities and tactics that force the monster to fight a certain way, and specialization becomes even more appealing; if there's an attack that causes the monster, if hit, to not be able to attack Will (and doesn't work on pure-Will monsters), and the guy's weakness against Will attacks gets covered up by being proactive. Likewise for being able to arrange your battle lines.

Of course, I still prefer associating attacks with your defenses in a non-RNG manner as the primary way to encourage specialization. The only problem with it is that it isn't easy.

[Username17]

I don't really like forced specialization since I'd really like to be able to have a generalist character as a viable choice. Gishes and the like typically are a balance of fort/ref/will, being average at everything but not exceptional anywhere. I'd like to allow that in the model somewhere.

As Manxome said, a defensive generalist is by definition "better" than other people, and that's not a character "choice" that should be sanctioned under any circumstances. There have historically been several models for handling this:

The 4e model is that defenses are often tied to attributes as are offenses, and you can (and therefore will) choose offenses that target a number of defenses that all spring forth from the same attributes. So for example a Grind Paladin focuses on Charisma and Wisdom, which allows him to swing swords versus AC, shoot lasers at Reflex, and strike fear into souls versus Willpower. But that specialization gives him only 2 of 4 good defenses (Willpower and AC), which is of course bad 70% of the time against enemies that attack one or two defenses. But specializing in the attack stats is good offensively all the time. So people still do it - all the time.

The Pokemon model works similarly, if non-numerically. Your attacks get STAB if you have sufficient types, and your defensive penalties just happen and you have to deal with that fact.

The Fantastic! model just gives people 2 attack types to be strong and weak against, out of a series of 10. Against enemies with 1 or 2 attack types this is disadvantageous 19/55 and advantageous only 3/55. But it still means that against the majority of enemies it doesn't make any difference.

---

But the long and the short of it is that no game should allow characters to have "even" defenses as a valid choice because that maps to "no weaknesses" which is a fucked character archetype to begin with.

-Username17

[TavishArtair]

Hello everyone.

What if Attributes existed as a game statistic, but were determined by Abilities selected instead of the other way around? Rather, instead of Abilities just having fiat effects that determine your relative "rating," you did have a baseline Attribute that was used as a variable in calculations, but it was derived from how many/which Abilities you had that related to that Attribute.

Just a thought.

[Manxome]

You just have to add exactly half of your total attributes to each attack/defense type, and achieve a certain degree of symmetry so that each attribute contributes an equal amount overall.

OK, it's been bothering me that I couldn't quite put my finger on what I meant by "symmetry" here. Turns out I was having trouble nailing it down because the "exactly half of your total attributes" part was a red herring! So, sorry, messed up a bit there.

The actual condition is much weirder. Or, at least, this is a sufficient condition--I suspect it may be necessary, but I've only proven so far that it's sufficient. Here it is:

Every attack type must have a complement.

More precisely: For every attack type T, there exists an attack type U such that a character's bonus with T plus their bonus with U gives a sum that is constant across all legal character builds.

So, for example, say you're doing a linear point-buy system with the attributes "red" and "blue". If one of your attack types uses red as the bonus, and the other uses blue, then those attack types are complements, because every character has the same total red + blue.

With me so far? OK, try this one:

Linear point-buy
5 attributes: A, B, C, D, E
5 attack types:

• Type 1: A
• Type 2: B + C + D + E
• Type 3: A + B + 2*C - D
• Type 4: 2*D + E - C
• Type 5: A + B + C + D + E

This is "balanced," by the definition we've been using. No, honest, it really is. Types 1 and 2 are complements, types 3 and 4 are complements, and type 5 is a complement of itself.

This may be easier to understand with an arbitrary example:

• Alice has stats 6, 7, 5, 2, 0 (sum to 20)
• Bob has stats 1, 4, 2, 5, 8 (sum to 20)
• Using Type 1, Alice has a 5-point advantage: (6) - (1)
• Using type 2, Bob has a 5-point advantage: (4 + 2 + 5 + 8 = 19) - (7 + 5 + 2 + 0 = 14)
• Using Type 3, Alice has a 17-point advantage: (6 + 7 + 2*5 - 2 = 21) - (1 + 4 + 2*2 - 5 = 4)
• Using Type 4, Bob has a 17-point advantage: (2*5 + 8 - 2 = 16) - (2*2 + 0 - 5 = -1)
• Using Type 5, both are at +0

Alice attacks with type 3, Bob attack with type 4, each of them have the same net attack bonus. You can chop off types 1 & 2, or types 3 & 4, or type 5, and it still works--you just need to make sure that every allowed type has a complement.

Formal proof:

Let a character be defined by an array of numerical scores, called the character's attributes.

Let an attack type be a function from attributes to reals (or integers, if you prefer). A character's attack or defense with this type is the output of the function when applied to that character's attributes.

Let the net attack bonus of character A against character B using attack type T be T(A) - T(B). Let the maximum attack bonus of A against B be the maximum net attack bonus of A against B over all attack types.

IF:
For every attack type T, there exists an attack type U (called the complementary attack type) and a constant C such that for any legal character A, T(A) + U(A) = C.
THEN:
For any legal characters A and B, the maximum attack bonus of A against B equals the maximum attack bonus of B against A.

Proof:
Let T be the attack type which yields the maximum attack bonus of A against B. By premise, there exists a complementary attack type U and a constant C such that T(A) + U(A) = C and T(B) + U(B) = C.

Therefore:
T(A) + U(A) = C = T(B) + U(B)
T(A) + U(A) - T(B) = U(B)
T(A) - T(B) = U(B) - U(A)

Thus, the net attack bonus of A against B using T is equal to the net attack bonus of B against A using U. Since we know that T is the optimal attack type for A against B, the maximum attack bonus of B against A must equal or exceed the maximum attack bonus of A against B. But since the same argument could be made with A and B inverted, the reverse is also true, and thus their maximum attack bonii must be equal. QED

This means you can do fairly arbitrary, non-uniform attack types with any number of attributes and still achieve the same kind of balance if you keep this condition in mind. For example, you could have a 3-stat system with attack types A, B, A+C, and B+C and it's still totally balanced, irreducible, and coefficient-free.

Still not sure quite what Frank means by an RPS system, though.

[TavishArtair]

Hello everyone.

What if Attributes existed as a game statistic, but were determined by Abilities selected instead of the other way around? Rather, instead of Abilities just having fiat effects that determine your relative "rating," you did have a baseline Attribute that was used as a variable in calculations, but it was derived from how many/which Abilities you had that related to that Attribute.

Just a thought.

Or to elaborate, if you took the ability Lightning Bolt, your overall Red power goes up by 1. If you then take the ability Fireball, your overall Red power goes up by 1 again. You could conceive different exchange rates: abilities being worth more than 1, variable costs, or even diminishing returns. When it comes time to actually use Lightning Bolt and Fireball, they do as many damage as your Red power.

The benefits of this approach is that choosing to use a lot of Red makes you good with Red, no need to plan (per se) what Attribute you select, and your Red abilities all scale by how strong you are with Red in a fairly real manner. The disadvantage is that one might be tempted to pick up seemingly arbitrary selections of powers in order to jack that Red rating up. This can be alleviated by limiting the abilities to a fairly narrow sphere in order to limit the amount of "my fiddling makes my swordfighting better" going around.