Four Stat System.

[Catharz]

So, back on the topic of healing, trying to get a few things straight.

When you try to heal someone, they make a soak roll against your healing 'damage' value. Whatever 'damage' is dealt is healed.

To encourage type-appropriate healing, a character subtracts his reaistance from the soak roll instead of adding it. This means that a character vulnerable to an energy type will almost never be healed by it.

Certain creatures benefit from 'damage healing.' Basically, when you fireball the fire elemental he thanks you.
I'm trying to figure out how to get this to work without making it too complex. My gut feeling is to make it act as a healing attack if it's completely resisted. If you hit a fire elemental for four damage and he has a resistance of 4, he heals four wounds. If you hit him for 5 he takes one wound.
Wait, would he heal 8 wounds? Hmm, that might be a bit out of control...

To keep things from 'going to crazy town,' creatures should probably be restricted from having too many damage healing types. One or two at most.

Is subtracting the resistance from the heal soak roll too powerful? It lets characters totally min/max their healing and get some fairly extreme values.
On the other hand, there isn't much to encourage players to vary their resistances. This would do it.

Lastly, having healing be a soak roll hoses tanks while letting the 'agile' types rock out wild. That's basically how D&D does it, but should the healer have to 'hit' the patient as well for balance reasons?

[Edit] It would be possible to give every character one damage-heal type, and make that the only way to heal. Humans, for example, would always heal from Life damage (assuming the life damage didn't beat their resistances). [/Edit]

P.S.
I'm always worried these days that I'll post something like this and then find that someone (perhaps me) has already posted the same thing almost word for word...

[Catharz]

I'm also interested in the ins and outs of a pseudo-realistic future setting SAME. There's already been some discussion of this, but I'm interested in seeing it carried further.

For one, I can see a lot of use for mental attacks which work to create openings or to avoid physical attacks. Feints, 'lookitthat!' distractions, and so forth. This can help keep characters untouched in combat, allowing for a level of rocket launcher tag without things getting unfun.

In the course of Johnny Mnemonic, Molly never takes a single hit. Admittedly, she probably has a fairly high Agility, but so does the vat-sam. If we can explain away some of his fuckups on the killing floor to an effective Elan/Moxie attack or two, the events become more believable.

I think I've already said that I favor the 'big guns for big folks' approach rather than 'you fucking can't dodge bullets.' The vat-sam apparently manages to dodge a shotgun blast at close range, and although we could explain this away by Johnny being a bad shot, in the story it's due to his wired reflexes.
Then again, it makes stat replacement issues which come with vehicle use possibly easier to deal with. It's fucking obnoxious that Strength is basically the 'my body' stat, while I have no problem with divorcing the other three from the meat. Oh well, I guess that's just being human.

I'm also trying to think about how to adjudicate various kinds of stat boosting & ability addition from drugs and cyberware...

How worthwhile is it trying to keep the system balanced when you want people to be able to do totally unbalanced stuff by spending enough cash?

[Manxome]

1112921731[/unixtime]]There's a whole set of math about how things which have only two as a factor are balanced as choices and things which have any other factor are not.

Could someone explain this in more detail, or cite sources for this math?

"Balance" is used to refer to a lot of different things, but in the context of games it usually has something to do with fairness, and here it seems to mean something orthogonal to fairness, and I'm not sure what that is.



Also, apologies for the thread necromancy.

On a side note, considering the number of references to the SAME system on these forums, this thread was remarkably difficult to find...

[Username17]

Could someone explain this in more detail, or cite sources for this math?

Honestly, I forget where the math got off to, it was being done in another thread about the time I started in on this project. But here's the deal with "balance" as defined here:

• Something is balanced against another thing if they are used in equal amounts. That is, if a +1 to N is balanced againsta +1 to M, it must be of equal value.
  
  
• Therefore basic tag abilities like "immunity to Blue Attacks" can be easily balanced against congruent abilities such as immunity to Red, so long as Red and Blue attacks are of equal commonality.
  
  
• Numeric bonuses are inherently more difficult to balance, since they represent what is essentially a number of tag abilities which are available in stacking (+1 to Red and another +1 to Red) or non-stacking (+1 to Red and +1 to Blue) varieties.

So that's the basics. Obvious enough right? Well consider the inherent question of specialization vs. diversification as regards to Attack and Defense. That is, it is intuitively obvious that specializing in an attack is inherently superior as a life choice to diversifying attacks. Because you choose what attack you are going to use, putting more points into a Red Attack is a better deal than not increasing your Red Attack and adding bonuses to a Blue or Green Attack that you don't use. Similarly, because your opponents choose which defense you have to use, investing numeric points into a Red Defense after it is already your best defense is a sucker's game if you could invest in more Blue Defense.

That is, once it is already tactically advantageous for you to use a Red Attack, putting points into your non-Red Attacks is sub-optimal. Once it is already tactically advantageous for your opponents to use a non-Red Attack against you, it is sub-optimal to put any more numeric investment into your Red Defenses at the expense of your non-Red Defenses.

In SAME you actually use attributes for attack and defense, meaning that within a narrow range of numbers (+/-5 or so) it can actually be a balanced and defensible choice to arrange one's attributes in any possible combination. So long as no character is being pushed off the random number generator, characters can move around freely within the number range and the inherent limitations of attack and defense pressures cancel.

---

But the question was I think about the inherent difficulties of 3 attributes. And it goes like this:

• In a binary system (no matter how many times it is iterated, 2 stats, 4 stats, or 32 stats), any trade-off from heads goes to tails, thus if you're specializing you get a +1 in your specialty for a -1 out of your specialty.
  
  
• In a trinary system (again, no matter how many times it is iterated), any bonus to Scissors comes at a cost to Rock and Paper. Inherently that means that taking a -1 out of your specialty gets you a +2 inside your specialty. You can set it up so that this is analagous to attack (where getting +2 to what you are doing makes you the win), or you can set it up so that this is analagous to defense (where getting -1 to more things is actually bad). But as far as I've been able to tell, there is no option C where it's a balanced standard.

So basically, if you want different characters to have different numbers and have that be "fair" (in that the guy who does more damage takes an analagously larger amount of damage in return), then you want to go for powers of two. If you want the different numbers to be "unfair" (in that your setup makes you specifically inferior or superior arbitrarily), then you want something based on odd primes.

---

Now actually you do want unfairness in any game system, because that's a good control on skillful players. That is, if every character has to be vulnerable to something, then you have the option of throwing out fire monsters if the player of the paper tiger is dominating the game.

But for other things you want fairness. That's why I generally advocate for a SAME system for there to be an odd number of energy types and an even number of stats and skills.

-Username17

[Manxome]

OK, so what am I missing about a 4-stat system that means that you're trading +1/-1 rather than trading a +3 to one stat vs. -1 to each of three other stats?

Are we assuming that bonus-trading cannot be done any more finely than +one half/-one half? Or perhaps that the 4 stats are grouped into pairs where you need to care about both parts of the pair in order to mount a single effective attack? And if either of those is the case, why does it need to be powers of 2 and not just multiples of 2?


Also, I note that this analysis appears to assume that you need to allocate all your stat points before gaining knowledge of your opponents, and that the system inherently gives greater selective power to the attacker than the defender, correct?

[Username17]

OK, so what am I missing about a 4-stat system that means that you're trading +1/-1 rather than trading a +3 to one stat vs. -1 to each of three other stats?

Ah. You're always trading +1 for -1. The question is thus how many points of topological equivalency each attribute has.

If a single point is topological equivalent to two others (as would be the case in a tri-stat array), then you can perform the same +1 for -1 action twice and get the same equivalent penalty as making the trade only once. If you have only one point of equivalency, then you only make it once period.

Consider the simplest case:

1. You have two points to assign between Red and Blue. You can make Red or Blue Attacks, and each Red attack adds your Red and subtracts your target's Red. Person A puts everything into Blue, Person B divides equally between Red and Blue.
   
   
2. You have three points to assign between Red, Blue, and Yellow. You can make attacks which are Red, Blue, or Yellow; and each Red attack adds your Red and subtracts your target's Red. Person A puts everything into Yellow, Person B divides equally between Red, Blue, and Yellow.

In set-up 1. when A attacks B he does so optimally with Blue Attacks and is +1 relatively when doing so. When person B attacks, he optimally does so with Red and is +1 relatively when doing so.

In set-up 2. when A attacks B he is going to do so with Yellow and is +2 when doing so. B's attacks perform at the optimum level as Red or Blue, but are only at +1 either way.

---

So SAME is topologically identical to having a Red/Blue for Accuracy and a Red/Blue for Power. Accuracy and Power also happen to be an even trade-off, which surprised the crap out of me when I ran the numbers. Were there six attributes instead, it would probably be topologically equivalent to having a Red/Blue/Yellow scenario - which inherently favors specialization.

Or perhaps that the 4 stats are grouped into pairs where you need to care about both parts of the pair in order to mount a single effective attack? And if either of those is the case, why does it need to be powers of 2 and not just multiples of 2?

That's what we're looking at. Nominally I could see the possibility of having a three-die system in which you actually had three red stats and three blue stats. But I struggled to make that work for a long time without success (six attributes has a certain appeal).

Also, I note that this analysis appears to assume that you need to allocate all your stat points before gaining knowledge of your opponents, and that the system inherently gives greater selective power to the attacker than the defender, correct?

Those are pretty safe assumptions. Although since it happens to be that people with evenly spread stats are tankers and people with uneven stats are glass hammers against everything except a mirror match (against which they are even more offensively anemic than the tankers and proportionately tougher as well), it is actually possible for you to know what your opponent's stat configuration is before assigning your own.

A character whose stats are more like yours will have a longer combat and a character with stats less like yours will have a shorter combat. That's the ultimate impact that attributes play.

Two Swordsmen or two Mages have a long duel with swords clashing and lights flashing. A fight between a Swordsman and a Mage is still anyone's game, but is a much shorter affair.

-Username17

[Manxome]

And, proceding logically, if you had 4 points to distribute between red, blue, yellow, and green, then the player who specializes has an even greater advantage over the player who generalizes (+3 vs. +1, compared to +2 vs. +1 in the trinary case).



OK, so I am now understanding that:

1) This has nothing to do with the number of stats, per se, but with the number of different attack/defense specializations.

2) This has nothing to do with the factors in this number; 2 is balanced in specialization vs. generalization and ALL varieties greater than 2 favor specialization, no matter what they are or are not divisible by.

3) This is based on the assumption that specializing in one attack type implies specializing in the corresponding defense type to an equal degree. So, for example, if both power and accuracy of an attack were strength vs. agility, rather than the one being strength vs. strength and the other being agility vs. agility, then none of this applies (because, of course, you've made the underlying balance problem fundamentally more difficult, by varying more things at once).


Does that all sound correct?

[Catharz]

1183783540[/unixtime]]And, proceding logically, if you had 4 points to distribute between red, blue, yellow, and green, then the player who specializes has an even greater advantage over the player who generalizes (+3 vs. +1, compared to +2 vs. +1 in the trinary case).

That depends on how many different attributes are used to determine the success of an attack.

In the SAME system, you can make physical attacks (which first check blue and then check red) or mental attacks (which first check green and then check yellow).

So if Jeff has a Red of 4, and he's fighting Jane who has balanced stats of 1, when he attacks he adds his Red to his Blue, for a total of 4, and subtracts Jane's Red and Blue, for a total of 2.

When Jane attacks (if she's smart or lucky) she adds her Green and Yellow (total 2), and subtracts Jeff's Green and Yellow (total still 2).

In both cases, the attacker comes out 2 ahead. This is therefore balanced.



It might seem as though this is just a binary system, but allowing all possible combinations of one accuracy stat and one power stat is still always balanced. This means that there are 4 attack modes rather than just two. In fact, it would be balanced to allow power/power or accuracy/accuracy attacks as well (cube mode), but it doesn't make as much sense flavor-wise.

1183783540[/unixtime]]1) This has nothing to do with the number of stats, per se, but with the number of different attack/defense specializations.

It's a matter of both. In the case of four stats, 2-stat attack modes work, allow for attacker and defender rolls, and make intuitive sense.

1183783540[/unixtime]]2) This has nothing to do with the factors in this number; 2 is balanced in specialization vs. generalization and ALL varieties greater than 2 favor specialization, no matter what they are or are not divisible by.

As stated above, the right method of attack stat combination keeps certain (power of two) stat arrays balanced. Other arrays will never be innately balanced narrow vs. broad.

1183783540[/unixtime]]3) This is based on the assumption that specializing in one attack type implies specializing in the corresponding defense type to an equal degree. So, for example, if both power and accuracy of an attack were strength vs. agility, rather than the one being strength vs. strength and the other being agility vs. agility, then none of this applies (because, of course, you've made the underlying balance problem fundamentally more difficult, by varying more things at once).

Right.

[Manxome]

1183794496[/unixtime]]As stated above, the right method of attack stat combination keeps certain (power of two) stat arrays balanced. Other arrays will never be innately balanced narrow vs. broad.

I don't see what this has to do with powers of 2. You could have 6 stats and use 3 in every attack and have the same property of balanced specialization vs. diversification. Heck, you could have 3 stats and use one and a half in each attack type and it still works perfectly.

The key thing appears to be that you're using exactly one half of your pools for each attack or defense (and each pool is equally represented in all of the attack options).

[Catharz]

1183796150[/unixtime]]

1183794496[/unixtime]]As stated above, the right method of attack stat combination keeps certain (power of two) stat arrays balanced. Other arrays will never be innately balanced narrow vs. broad.

I don't see what this has to do with powers of 2. You could have 6 stats and use 3 in every attack and have the same property of balanced specialization vs. diversification. Heck, you could have 3 stats and use one and a half in each attack type and it still works perfectly.

The key thing appears to be that you're using exactly one half of your pools for each attack or defense (and each pool is equally represented in all of the attack options).

Right you are

[Manxome]

On a side note, this was probably apparent, but you can give a trinary system (or higher) this type of balance by doing sneaky things to the stat costs.

For example, say that, in addition to the 3 main stats, each character also has a universal "stat maximum" that applies to all three, which can be raised by 1 point for a cost of 1 stat point.

So you start at 0/0/0 with a max of 0, and your first point can't be used for anything but raising the max by 1. Then your second point gets you to 1/0/0 max1. Your third point can take you to 1/1/0 *or* it can raise your max to 2, so after 4 stat points you could be at 1/1/1 max 1 or 2/0/0 max 2.

After 8 points, the specialist has 4/0/0 max 4 and the generalist has 2/2/2 max 2. After 12, it's 6/0/0 vs. 3/3/3, and so on.

This is not a way to permanently increase or decrease the sum of your stats; the cost for reaching any stat array is still a state function, not a path function, so getting your stats to 4/3/2 costs 13 stat points whether you go there by route of 2/2/2 or by route of 4/0/0.

And getting a +1 in your specialty trades against a -1 out of your specialty...assuming that you don't raise your max when you don't have to, because you are not an idiot.



A completely unrelated way to do it would be to make the attacker and defender share power in selecting the defender's defense method. Rather than always defending with whatever someone attacks you with, say that the attacker can attack with anything and choose ONE defense type that the defender CANNOT use; the defender then chooses from the remaining 2 types.

Now a complete generalist is weaker than a specialist (because you can NEVER be forced to use your single weakest stat), but a half-generalist is not. A 3/0/0 specialist battles a 2/1/0 generalist at a symmetric +/- 2, a 4/0/0 specialist battles a 2/2/0 generalist at the same bonus; a 7/0/0 battles a 4/3/0 at a +/- 4, etc. 1-stat builds are glass canons and 2-stat builds are tanks, and which stats anyone picks don't mean a darn thing.

Of course, as pointed out, your third stat will ALWAYS be zero, so unless there's some additional rules, you've effectively got a 2-stat system (except battles between specialists of the same type are now fast instead of slow).

[Username17]

For example, say that, in addition to the 3 main stats, each character also has a universal "stat maximum" that applies to all three, which can be raised by 1 point for a cost of 1 stat point.

So you start at 0/0/0 with a max of 0, and your first point can't be used for anything but raising the max by 1. Then your second point gets you to 1/0/0 max1. Your third point can take you to 1/1/0 *or* it can raise your max to 2, so after 4 stat points you could be at 1/1/1 max 1 or 2/0/0 max 2.

After 8 points, the specialist has 4/0/0 max 4 and the generalist has 2/2/2 max 2. After 12, it's 6/0/0 vs. 3/3/3, and so on.

That only works if everyone agrees to either hyper-specialize or completely diversify. If someone goes part-ways, balance is out the window.

If one person goes 6/0/0, another person can be 2/5/0. You can run the numbers on that at your leisure.

So no, you can't play jiggery pokery with stat costs on a trinary system and have it come out evenly. It always eventually comes down to RPS.

-Username17

[Manxome]

1183847417[/unixtime]]If one person goes 6/0/0, another person can be 2/5/0. You can run the numbers on that at your leisure.

So no, you can't play jiggery pokery with stat costs on a trinary system and have it come out evenly. It always eventually comes down to RPS.

Yes, if you have three damage types and defend against only two of them, you're trading a situational advantage for a situational disadvantage. 2/5/0 has an advantage against 6/0/0 or 0/6/0 and an equal disadvantage against 0/0/6 or 3/3/3.

If that's not considered to be a good thing, then why are we even interested in the trinary system in the first place? If you don't want the players to have any options other than "offensive specialist" and "defensive specialist," then only offer two options. The only reason to add the extra complexity of a third variable is if it actually lets you make some choice that wasn't available before.

This prevents specialization from being universally advantageous as it is without the extra cost for raising your maximum. I'm even reasonably certain that it prevents either specialization or generalization from being advantageous on average, though I don't have a mathematical proof for that.

Whether or not you want an RPS system is an entirely separate issue.

[Catharz]

An equally important issue is intelligence. A specialist, barring extraordinary situations, has one choice when making an attack. A generalist has to make some kind of choice, the wrong choice -> screwed.

At the same time, there's more reason to have a multi-stat system than defensive and offensive specialization (or generalization vs. specialization). Strawberry/Chocolate attacks damn' well better taste different from Potato/Steak attacks, and the generalist gets to use both. Hopefully this somewhat mitigates the penalty of having to guess.


...


An issue orthogonal to game theoretical balance, but at least equally important, is playability. IMO having four stats strikes a nice balance, where additional costing of stats, inverse rock/paper/scissors defensive mechanics, or three or more rolls per attack are unnecessary. All that's needed is some sort of hard cap to stop things from getting of the RNG.

The accuracy/power duality and body/mind duality are easy to grasp, and giving the attacker one roll and defender one roll keeps things interactive on a basic level.

Few balanced systems make quite as much sense. One I can imagine is a three-stat system like you were describing, with Body, Mind, and Motion. This might seem simpler and even more intuitively appealing, but I'm doubtful that the mechanical complications would be worth it.

[Manxome]

1183857444[/unixtime]]At the same time, there's more reason to have a multi-stat system than defensive and offensive specialization (or generalization vs. specialization). Strawberry/Chocolate attacks damn' well better taste different from Potato/Steak attacks

If you want to have more flavors of attacks than comfortably fit into what is otherwise the best stat system, I submit you should offer more than one flavor per stat, rather than adding in additional stats that end up making the game balance differently than you want.

You can either do that by making players precommit a character to a particular flavor at creation (forced specialization) or let them change on the fly (in which case you really have one flavor that's a union of all the choices).

Also, this is assuming that by "flavors" you mean things that are subtly different mechanically. If you're talking about pure story fluff, let the player say that he's making a strawberry/chocolate attack (or whatever) if that's what he wants, as long as he's not maneuvering for an in-game advantage from it.

[Catharz]

What I mean by different flavors is the difference between intimidating someone and bashing their skull in.

In SAME, you've generally got the flavor of mental vs. physical, but you've also got resistances/damage types which add in most of the needed diversity. The underlying implementation can vary (multiple damage tracks, single damage track, number of resistances, flavors of resistances, etc).

There's a point where "pure fluff" and mechanics should interface seamlessly. If they don't, there's a dissonance beyond just suspension of disbelief.

[Manxome]

So, getting back to the original numerics question...why do we care about the number of elements being an odd prime? And if your attack power in an element isn't necessarily the same as your defense in that element, how does any of the analysis done up to this point have any bearing at all?

Based on this very valid observation made by Frank a few posts back:

Similarly, because your opponents choose which defense you have to use, investing numeric points into a Red Defense after it is already your best defense is a sucker's game if you could invest in more Blue Defense.

...it sounds like there's no reason not to have all your elemental resistances be absolutely uniform, given the choice. Whether the number of resistances is 7 or 8 (or 2 or a million).

[Catharz]

Frank can probably explain this better, but I think resistances are intended to be inherently unbalanced.

If you have no control over who is attacking you, you want an even spread of defenses. If you do have control over who will be attacking you, you want to min/max your resistances. The benefit of Min/Max also varies based on how many different attack types you can expect to face, and how good your enemy's intel is.

If you have a party of three characters, an air mage, earth mage, and fire mage, and they're attacking an earth elemental, fire elemental, and air elemental, if each mage has a 'call out the challenge' power, they want to have maxed resistances against the creature challenged and minimized resistances against the creatures not challenged.


In the end though, players generally want even resists and NPCs want uneven resists.


Diferent settings take different tacts in assigning resistances. For example, Disgaea gives a player three fixed numbers to assign between the three resistances. Another proposed system gave a point of resistance for every technique of a certain type known. Another might simply allow free assignment. Character race or class (if they exist) are great ways to assign starting resistances.

Armors allow for additional planning, variation, and evening.


Hey, and Frank, sorry for being all up in your thread ninja-ing answers. Please tell me if I'm being a douche.

[Catharz]

It's mathematically balanced to allow Agility/Moxie attacks, Elan/Strength attacks, or even Moxie/Strength attacks, but how much does that fuck up the complexity of having defensive and offensive specialists.

I like the mental damage tracks/physical damage track dichotomy, but I also like the idea of an arcanist channeling a blast of pure wild magic, which uses a Moxie-based attack roll and a Strength-based soak.

[the_taken]

1112913772[/unixtime]]The game mechanical needs of a system of elements are only that it be varied enough to keep from stifling the story and odd enough in number to be unbalanced.

-Username17

Would, say for instance, this elemental system work?



For those that don't want to bother counting, there's 17 "elements" in the chart.

[Username17]

That system has a number of advantages, not the least of which is that it's fairly intuitive. You'll note however that some type combinations reinforce each other's weaknesses, and others cover them. Steel is just super awesome all around - only balanced in the original game by the fact that Steel doesn't have any good attacks (thus making any X/Steel Pokemon a critter who is defensively tough but offensively anemic by definition).

But as a starting point it works OK.

-Username17

[Manxome]

1187090493[/unixtime]]For those that don't want to bother counting, there's 17 "elements" in the chart.

I think the conclusion of the last sub-discussion was that the exact number of them isn't particularly important to anything.

I am a bit mystified that they decided that "normal" and "fight" needed to be distinct types, though, unless "normal" actually means "other."

[Neeek]

1187115257[/unixtime]]
I am a bit mystified that they decided that "normal" and "fight" needed to be distinct types, though, unless "normal" actually means "other."

They are actually different. Fight is used by martial artist-types of pokemon, and normal is physical attacks by non-martial artist-types, IIRC.

[Jacob_Orlove]

Right, "fight" would be stuff like "mega punch" or "karate chop" while "normal" is stuff like "bite" or "claw".

I only ever played the original pokemon game boy game (which remains awesome to this day), so I'm kinda amused to see that they added a Psychic hoser. I mean, Psychic was pretty much the best, but only because those pokemon had the best stats and attacks.

[the_taken]

Well, there's my new project: SAME Pokemon. I'll post the set of new math equations I developed in another thread, and start another thread in Wizo's anime boards.

----------

Two things, Frank.

Suggestion: Stealth and Acrobatics as the two agility based skills?

And is this math the way SAME works?

Accuracy = 1d20 + Agility/Moxy

Evasion = 8 + Agility/Moxy

Speed = Moxy + Agility

Damage = Base Attack Damage (+/- 20) + Strength/Elan + (Accuracy - Evasion)/2

Soak = 1d20 + Strength/Elan + Elemental Resist

Accumulated Wounds = (Damage - Soak)*1.5 + Previous Wounds