Literary and Trigonometric Game Design

[Stupendous Press]

I just discovered these boards, and I can't express my excitement at the prospect of an RPG Theory board.  Time to dive in!

Potential, Skill, and Advancement
I started brewing some theories over at RPGnet, and I'm hoping to both clarify them and find new voices of criticism.  The heart of my theories thus far focus on experience and advancement, though they begin to dabble in the building blocks of character creation.  My initial concept was to fix all characters on a finite scale of potential, which they would have from the beginning.  This would partially replace conventional experience or point gain, as this pool could never change size.  Upon character creation, the player is free to use as much or little of their character's potential as they please, resulting in more or less experienced characters, respectively.  Unspent potential could be used as an aid to checks during play, however.  There are a few more elements, but that is the foundation of my ideas, that characters of any experience level could be balanced in a Simulationism or even Gamism sense (assuming I understand the terms properly).

Next I needed to better define this linear progress of inexperienced to experienced, unskilled to skilled.  Thanks to a fine article the writer pointed me to, Experience Curves by Sergio Mascarenhas, I had an opportunity to better solidify an idea of a tri-stage experience line, inexperienced, experienced, and master.  A character begins progress on a skill with no practical knowledge, but an innate understanding that may be weak or strong, that I'll call a Talent (commonly represented with Attributes in many games).  The next step is with the skill itself, which I'll call (coincidentally) Skill.  This is a gathering of practical knowledge and applied expertise.  Beyond this is what I call Mastery, which steps past fundamental understandings into the realm of things previously inconceivable.  Mastery is defined by very specific feats of prowess with a given Skill rather than broadly applicable proficiency.

Beyond application to skills, the experience curve could easily be applied to the entire pool of potential that a character begins with, indicating how easy or difficult it is to apply this potential to advancing a character's skills (or other as-yet undefined abilities).  On top of the experience versus potential dichotomy is that of age, which turns the dichotomy into a trifecta.  Once again (and throughout my design concepts) three factors form the balance of a given rule.  I want to include the natural aging process alongside the advancement process of a character, at least in the core rules.

Literary Conflict
Many of my ideas are also formed by the ideas of the Heroic Journey and the classic literary device of conflict.  You'll have to forgive me for not elaborating on the Heroic Journey.  Conflict is typically defined in three forms, that versus self, versus nature, and versus man.  In a role-playing system context, we have skill use of a self-contained nature (many forms of movement, knowledge and recollection, morale and fear, etc.), skill use against static elements (set difficulties like weight lifting, finding hidden things, solving puzzles, etc.), and skill use opposed by another character (combat, social interaction, etc.).  I want a system that is designed to handle conflict based on its use in storytelling first, and this is the best classification of conflict I've found.  When boiled down to their essence, aren't all systems solely designed to resolve conflict?

Math
After some thought, it occurred to me where I knew the S-curve graph from Sergio's article from.  It's a sine curve, like in trig.  Once upon I time I was fluent in the language of mathematics.  An unfortunate teacher crushed my appetite, and I've since forgotten almost all of what I knew.  Math achieves the goal of any gaming system, to provide a language that is uncompromising in its precision and is not subject to normal linguistic interpretation through which various problems can be solved.  If we consider a conflict in a story to be a problem the analogy between game mechanic and mathematical equation is clear.  On the flip side of the coin, because the language of storytelling is so imprecise, a translation between narrative language and system language can become tenuous.  Despite this, I prefer systems with a healthy amount of "crunch" so that players can comprehend conflicts accurately and respond with confidence, providing for an environment of mutual understanding and clarity.

I believe that the experience curve shown in Sergio's article is true to life, and therefore useful for a system.  As it could be represented by a sine curve, progess along it could be identified and calculated with the various formulas for plotting points on a sine curve.  My mental loss of trig handicaps me here, unfortunately, because I can't remember where to begin on such a concept, but I'm sure it's possible.  I'm also quite sure that such formulas can be written with variables instead of numbers.  If those variables could come to represent factors in a narrative context, perhaps a viable gaming system could be derrived.  Perhaps that doesn't make complete sense, but it's the best I can come up with right now.

Argument
If these three elements, literary devices, mathematics, and gaming, could come together, I think an effective game system could be reached that would be capable of describing a wide variety of narrative styles.  Certain elements, such as aging, could potentially be plug-and-play to further widen the scope of possible application.  Also, if formulas can be reached to define the underpinnings of the system that are independent of hard numbers, the game could balance on any scale, thus allowing the scale of story to range from one-shot to epic.

These are all my hopes, and as of now I have no concrete system content.  These are all theories that have been waiting for proper application in the back of my mind.  Thanks for reading this far, if you have.  I'm very curious if any or all of these approaches have been tried before, in what ways, and to what degrees of success.  Either way, I'm also curious as to other people's criticisms of my theories to describe narrative elements.  I'd also like to explore reigning these theories down into a workable system, because otherwise it's just dust in the wind.

[M. J. Young]

Welcome to the Forge. Do you have a name? Silly question; of course you do. Most of us use names here--it makes us feel like we're talking to people.

My impression is that you're looking for that elusive system that will please everyone. I don't know that it's possible. I do think, though, that there are some fairly basic concepts that you're missing.

When boiled down to their essence, aren't all systems solely designed to resolve conflict?

Are they? There are indeed systems that are designed to resolve conflicts (Legends of Alyria springs to mind), but there are far more systems designed to resolve tasks--that is, a character's success or failure at a specific attempt, rather than the overall outcome of a conflict situation. To clarify the difference, in D&D and most other task-oriented games, you roll the dice to see whether you hit the opponent and how much damage you did. In Legends of Alyria, you roll the dice to see who wins the fight and how dramatically. The players then decide whether any blows were even attempted--a dramatic win could be achieved merely by staring down the opponent such that he withdraws his challenge.

But then, these games are attempting to do completely different things. D&D is attempting to produce a challenge to the players, a means by which they can show off how well they play the game by overcoming monsters and other obstacles to collect treasure and experience. LoA is attempting to give the players the tools to create stories about the conflict of good and evil. Different tools are used to do a different job.

Let me encourage you to tackle the articles section. The Provisional Glossary, although technically a draft with a few recognized mistakes in it, is the most recent and thus the best statement of the model generally found most useful around here; at least, it's the place to find out what we understand when you say gamist and narrativist and simulationist, along with a lot of other words and ideas. I'll also recommend my own Applied Theory as a fairly good summary of some ideas about design as connected to those concepts. It may at least show you why one game design isn't going to satisfy everyone.

I hope that helps.

--M. J. Young

[Rob Carriere]

Stupendous Press,
Welcome! Sorry to hear about your frustrating math experience, especially since you seem to have a natural sense for it. You slightly misrembered the specifics, the curve you want is an arctangent, but you're quite right, there's a whole industry out there doing S-curves by means of trig. (The cumulative normal distribution is another popular choice, as well as several functions chosen more for the possibility to compute them rapidly on cheap hardware than for the beauty of the S shape they produce.)

In essence, what the S-curve will do for you is take care of the phenomenom that it becomes progressively harder to get better as you improve a skill. This means that you can have a system set up like:

Step 1: Figure total effort spent so far, including any bonuses ('reading the Book Of Aaarghgh is equivalent to 3 weeks kung-fu practice').  The result of this step is effort expressed in some unit of time ('371 hours')

Step 2: Apply the S-curve function to the number from step 1, the result is your skill.

Obviously, the S-curve needs to be calibrated. First, you need to define the extent of your "finite scale" ('skills range from 0 to 100' or something like that) and second, you need to come up with a couple of anchor points ('16 hours of practice will give you a skill of 3, 50 hours will give you...' or whatever is appropriate for the sort of game you want to create). After that, it's a curve-fitting excercise, which I'm sure any number of people here, including myself, could help you with.

The big advantage of doing things this way is that you decouple the concern of non-linear progression (The S-thing) from the concern of how much progress you've already had. In other words, all your other rules could be about determining the amount of effort spent and completely ignore the question of how much effect that effort will have on your actual skill value. This means that you won't be be needing complicated progress formulas at all. You determine effort spent, then plug that into the S-curve formula, and out pops the skill level. (The disadvantage is that it's more work for the player this way, naturally.)

Was that anything like what you were thinking about, or am I way off base?

BTW, I second MJ's suggestion about the articles, they'll give you the mental tools to really focus on what you want with your game. Also, I too would appreciate a real name. I'm Rob.
SR
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[Stupendous Press]

Thank you for the replies.  First off, my name is Jeremiah.  Pleasure to make the acquiantances of real people. :)

I dipped into the Glossary briefly to figure out what the GNS model was about, but I haven't had time to dive in properly.  Once I find the time, I tend to devour philosophical and theoretical arguments.  For now, let me answer your two replies in order.

M. J., I think maybe I wasn't clear enough about how I defined conflict.  I mean conflict in a far more general sense, so it would be better defined as action resolution.  As I was saying in my post, conflict can be against another person, against nature or the environment, or against self.  This can include direct opposition, or even simple things like, say, constructing a tool.  Perhaps its too broad a usage, but I think we're talking about the same thing in different terms.

Rob, thank you for the insights!  Having graphed out the basic Y=X curves of all the trig functions, I felt sine made sense given that you truncate each end at the first interval.  It normally makes an infinite wave pattern, but within a single unit it creates the desired S-curve.  Still, my math is old and fuzzy, so I will take your word that an arctangent better describes what I'm after.

To better describe the graph I envisioned, let me try and lay it out.  The Y axis would represent proficiency with a skill, where the bottom half is Skill and the top half is Mastery (Talent would be factored seperately).  The X axis would represent resources, be they time, practice, education, or what have you.  The S-curve would start at 0 and end at 1 (to make it simple).  Starting at 0, it would take a tremendous amount of resources to move up to the first tier of proficiency, as the S is nearly horizontal at start.  This is the initial hump of learning something new.  After the hump, learning becomes increasingly easy the more one knows, because one is gaining confidence and proficiency, so each new thing comes easier.  This continues until a peak of Skill is reached, where the character reaches the top of their general proficiency, and all subsequent learning must proceed into Mastery.  Mastery, however, gets harder and harder to advance as each new technique would be further from general proficiency and more esoteric and unfamiliar.  Thus, the S-curve bends back to near-horizontal.  If it were projected infinitely, absolute Mastery of a skill (reaching the 1) would require infinite resources, and thus be impossible.

I think the idea of either end approaching infinite cost and the center approaching zero cost (and infinite gain) is a fascinating model.  If the exact number of possible progression is set by some other statistic, possibly derivative of Talent, the issues of infinite cost or gain can be circumvented.  The system can state from the outset that once a certain minimum cost (perhaps a single unit of Potential), the peak has been crested.  There's also the option of allowing infinite progression of a Skill, given a set minimum cost (one unit Potential) forever.  Mastery would become a divergent curve, if it were explored at all.  Of course, there's a point where Skill just becomes glut, as difficulties may never rise beyond a certain point.  This could either be implicit or explicit.  Such an idea is largely because I've always been intrigued by point-buy systems without ceilings, and finding a way to keep them from breaking at the top levels.  Since available Potential willl never exceed the starting amount, such single-minded advancement of one Skill would already be implicitly impractical.  Also, if the Potential itself follows a similar S-curve, spending the initial units and final units of Potential would require greater and greater investment (of what, I don't know).

Well, I hope that explains my thoughts behind the application of the S-curve.  In the article I linked, the third graph down is a good illustration of the concept.  I borrowed some ideas from it, and some just matched by coincidence.  If anyone knows some good websites or other places I could re-educate myself in trig curves I'd be much oblidged.  For now, there are all manner of issues to contend with.  I'd like to try and throw ideas at the wall as to how to make the system as fluid as possible, so it can fit into any needs of scale.  I'm also curious as to how to handle specific skills so the system can be defined enough for ease of use, but flexible enough to mold to each game's needs.  If the Skill aspect can be concrete, and the Mastery somehow be loose and dynamic, it might work.  Talents might have to be somewhere in the middle... not sure about that.

Thanks again for the responses, and the advice.  I'll dig into those articles as soon as I find some time.  Such an elusive quarry...

Jeremiah

[Selene Tan]

M. J., I think maybe I wasn't clear enough about how I defined conflict. I mean conflict in a far more general sense, so it would be better defined as action resolution. As I was saying in my post, conflict can be against another person, against nature or the environment, or against self. This can include direct opposition, or even simple things like, say, constructing a tool. Perhaps its too broad a usage, but I think we're talking about the same thing in different terms.

The term "conflict resolution" has a specific meaning here at the Forge. Roleplaying Theory, Hardcore: Conflict Resolution vs Task Resolution is a good explanation of the term.
If you haven't fully read the glossary yet, it's a good idea. There's also the Theory Wiki, which contains stuff from the glossary, but hyper-linked to other terms and with outside links to articles and forum threads as well.

Rob, thank you for the insights! Having graphed out the basic Y=X curves of all the trig functions, I felt sine made sense given that you truncate each end at the first interval. It normally makes an infinite wave pattern, but within a single unit it creates the desired S-curve. Still, my math is old and fuzzy, so I will take your word that an arctangent better describes what I'm after.

The third graph down from the article you linked to does look like a sine curve, but arctangent (and any other Sigmoid function) is shallower than sine at the edges and steeper in the middle, which I think is what you're after.

And welcome to the Forge. Prepare to get your socks knocked off by RPG revelations. :P

[Stupendous Press]

Thank you, Selene.  I see where the confusion would come from now.  Once again I've got ample motivation to dig into the articles, hopefully starting tonight.  I anxiously await the loss of my socks.  Wait, maybe I said that wrong...

PS: Didn't check your links until I posted, but may you live to be a thousand years for the Wikipedia link.

[Rob Carriere]

Jeremiah,
The third curve in the referenced article is indeed more like a half-wave sine than like an arctangent. I think that's a bad idea, though. The reason is that the half-wave sine has a limited domain (i.e., the horizontal axis goes from 0 to 1 and then stops.) Since the horizontal axis represents effort, this is like saying that after a certain amount you cannot invest more effort into a skill.

In contrast, the arctangent has an infinite domain, so you can keep on investing in the skill forever and ever, it will just get less and less effective. This seems more natural and more in line with your description.

As a warning, most of the sigmoids, including the artangent, have a slope of 1 at the center--a 45 degree angle. You seem to want near-zero cost, which would be a near-vertical angle, or near-infinite slope, at that point. This can be done, but the standard signoids don't do it.

SR
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[Stupendous Press]

I was satisfied with a horizontal axis of 1 from a strictly theoretical standpoint, in that the 1 would equal a whole.  More specifically, it would be an arbitrary whole designating the maximum possible resources one could devote.  Likewise, the vertical axis equals 1 to represent the maximum possible skill level.  My hope is that if I can find equations to suite my needs, my system can be built on fractions of 1 instead of whole numbers.  Those fractions can then be applied to a real whole in game-terms to define actual cost and gain.

Part of the catch with the centerpoint is that my thinking involves allowing the real center of the graph to have a slope of 1.  Since the game elements the math would apply to involve whole numbers on a fixed scale, I can ignore the issue of a zero resource cost at the center.  Whatever fraction is derived would have an in-game assumption that its derivative cannot be less than 1 game unit of resource.  Likewise once the crest is peaked.  Since the translation assumes a minimum, the fraction I get from the curve can effectively be infinitely small.

Now, it's entirely possible that while all this sounds good in theory, it won't pan out when I figure out how on earth to arrive at these equations.  I don't know if sine or sigmoid will be easier in a utilitarian sense to base equations on.  I still don't know where to head with those fractions.  My proverbial plate got a little full in the last few days, so I haven't been able to apply any focus to this project.  Once I can I think I need to start considering real game elements like defining at least Talents and Potential, which should form the heart of Skill advancement.  Before that, I want to read the articles here.  I'm hoping that what composes Skill advancement can be entirely contained within the character, rather than arbitrary systems set as a constant within the game.  It would be harder to balance, but I feel offering players that kind of freedom simply feels better.

[Rob Carriere]

Jeremiah,
I would suggest that you focus on the other aspects of your system for the time being. The reason is that I think you have a pretty clear picture in your mind of what you want from the S-curve and I'm confident that that picture is achievable.

By clarifying the rest of the system, you'll be implicitly creating the exact specifications for your S-curve, and then it's a matter of curve-fitting.

SR
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