fix ability level interpretation

[ebrahimebrahim]

• use a more logistic-like scale rather than logarithmic to map experience to discrete levels this affects formulas that calculate xp costs, and possibly other stuff too
• have the raw ability levels in the ability tree represent actual experience for a given character where experience is something like (time spent improving skill) * (quality of practice)
• natural talents or deficiencies should then be properties that affect rolls against ability levels. one might as well view them as affecting "effective ability level", so it would be convenient for players to record effective ability level in the ability tree next to raw ability level.
• include a paragraph that explains, just to clarify, how "difficulty of a skill" is handled. with our new interpretation of ability level, it doesn't make sense to say that a "harder skill" requires more experience to reach the same level. instead, it is the difficulty level of the tasks that should reflect what we call "skill difficulty".

[yusufmte]

The main issue seems to be caused by having two simultaneous interpretations that don't always agree: experience (time*training) and performance (results of rolls).

In particular, I think that the "experience" interpretation has been causing all of our troubles. That is, the idea of having 0 experience be -2 by default would be peup because then how could someone have less than 0 experience, and how would the log interpretation make sense? And what about the fact that people of the same level of experience could have wildly varying outcomes?

We could alleviate these problems in some of the proposed ways, such as using a logistic scale, or using properties to denote natural talents. But we may keep running into problems due to the dual interpretation.

So would it be peup to just stick with what the actions dictate? That is, performance. A good climber is one who is challenged by a good cliff; a good archer is challenged to strike a target from a good distance away. And an abysmal (read: untrained) neurosurgeon would be entirely unable to perform a neurosurgery of even just fair difficulty. This all says nothing about experience. Doesn't this, throwing away "experience" and sticking with "performance" solve all of our problems?

• peup - peup - peup -

On the other hand, maybe the "dual interpretation" thing is exactly what we need...it connects the idea of Experience, something very tangible and the actual thing measured through the course of the campaign, with the Performance that the great peupfudge measures through its Action system.

And it seems nice for ability levels to actually purely represent experience...Hmm. In that case: There are two current problems wrought by the experience interpretation. The nonsense of the logarithmic scale, and the failure to account for experience-independent differences in ability. So, does using logistic scale + properties to account for talent, respectively, solve these issues? Is there any problem left, other than the problem of developing the exact logistic scale?

peup.

[yusufmte]

Followup: I think having the experience interpretation remains actually deals with the "neurosurgery" thing more clearly. Most characters would be -4, by definition, due to having had no experience with neurosurgery. And now that ability levels correspond purely with experience, the difficulty levels would have similar intepretations; since neurosurgery is something that requires a lot of experience to do well, it seems fair to give even a typical neurosurgery a difficulty factor of, say, 0, 1, or 2. And in that case most characters would be literally unable to do it, even if rolling ++++.

EDIT: This also is to say that the Experience intepretation "grounds" the Performance interpretation. That is, now we know what a good cliff truly is; it's one that a good climber is challenged by, and we know what a good climber is too: one who (assuming no talent or untalent) has a certain amount of climbing experience! Having Performance intepretation exist alone now feels peupy; we would be bouncing the cliff off the climber, and the climber off the cliff, with no frame of reference. So, I think for now I very much support having both interpretations remain, and fixing them in the proposed manners: logistic curve + talent properties. peup.

[ebrahimebrahim]

I'm going to try and make some remarks that clarify the situation.

Some points

Here are some facts I think we probably agree on

1. XP should be something like (time spent improving skill) * (quality of training). So, holding quality constant to make it easier to think about things, XP=time.
2. Why did we even want to make ability levels logarithmic in the first place? I think it's because of learning curves. Usually we think of learning curves like this: And we want ability levels to roughly correspond to performance. Another reason we might like logarithmic levels is to be able describe a very wide range of experience-amounts using just a handful of exiting-sounding adjectives.
3. Note that what we decide here has a direct quantitative impact-- the xp cost table uses a formula that is derived from our current broken interpretation of ability levels.

Questions

Here are the questions I think we need to answer to resolve things.

1. How should skill level depend on XP? What we choose should be easy to verbally describe, kind of like "a good climber is 1.85 times as skilled as a fair climber", except it should not be broken like we found that setup to be.
2. Where exactly are natural talents and natural deficiencies taken into account? Starting ability level? (But that breaks the level <--> xp <--> time correspondence). As a modifier to ability level? An xp discount to training?
3. Where should the inherent difficulty of a skill be taken into account? Neurosurgery is harder to master than climbing-- we need to be clear on where that comes into play along the track from xp to performance on an unopposed action.

[yusufmte]

Re Q1, the curve should have an asymptote. This makes sense and makes orders make sense.

Re Q2, I like the idea of suggesting (in the manual) two separate mechanics that can both be operational: natural "talents" which are properties that can modify ability level, and natural "affinities", which are properties that can modify xp cost for a specific skill.

[ebrahimebrahim]

Followup: I think having the experience interpretation remains actually deals with the "neurosurgery" thing more clearly. Most characters would be -4, by definition, due to having had no experience with neurosurgery. And now that ability levels correspond purely with experience, the difficulty levels would have similar intepretations; since neurosurgery is something that requires a lot of experience to do well, it seems fair to give even a typical neurosurgery a difficulty factor of, say, 0, 1, or 2. And in that case most characters would be literally unable to do it, even if rolling ++++.

EDIT: This also is to say that the Experience intepretation "grounds" the Performance interpretation. That is, now we know what a good cliff truly is; it's one that a good climber is challenged by, and we know what a good climber is too: one who (assuming no talent or untalent) has a certain amount of climbing experience! Having Performance intepretation exist alone now feels peupy; we would be bouncing the cliff off the climber, and the climber off the cliff, with no frame of reference. So, I think for now I very much support having both interpretations remain, and fixing them in the proposed manners: logistic curve + talent properties. peup.

For exactly the reason you're saying, I agree that we should keep the link between level and experience. That it helps to ground what a "good cliff" even means is, I think, exactly the reason we linked ability level and experience in the first place. In the end we have a nice chain of relations:

time <--> xp <--> lvl <--> performance

And we just need to figure out the xp <--> lvl part so that it makes sense.

The correspondences I put down are just rough. Really there are other things involved. For example if we go with your answer to Q2:

Re Q2, I like the idea of suggesting (in the manual) two separate mechanics that can both be operational: natural "talents" which are properties that can modify ability level, and natural "affinities", which are properties that can modify xp cost for a specific skill.

then the relations between things are kind of like this:

[ebrahimebrahim]

So far here is the aspect of things that I think I agree with:

where Q1, Q2, and Q3 are still needing to be resolved.

(by the way if you want to make a diagram like that to explain something then you can use this template with inkscape: xp_model.zip)

[ebrahimebrahim]

I think having the experience interpretation remains actually deals with the "neurosurgery" thing more clearly. Most characters would be -4, by definition, due to having had no experience with neurosurgery. And now that ability levels correspond purely with experience, the difficulty levels would have similar intepretations; since neurosurgery is something that requires a lot of experience to do well, it seems fair to give even a typical neurosurgery a difficulty factor of, say, 0, 1, or 2.

Actually now I'm not really seeing how this addresses the "neurosurgery thing" (i.e. Q3).

Let's say we decide that level = -4 corresponds to no experience in a thing. Then no experience in neurosurgery and no experience in climbing both result in a level of -4. But climbing is much easier to learn than neurosurgery, so where is that fact considered? I'm still not seeing where we should place the Q3 arrow in the diagrams above.

[yusufmte]

In the case of climbing vs neurosurgery, there are some differences that will already be in place with the system we've built.

First, as you mentioned, the majority of characters will have -4 (0 experience) in neurosurgery. Most characters would probably start with SOME experience in climbing--climbing trees when they were little or just general movement and climbing onto things could start people a little higher than that. So we can imagine they might start at -3 or -2 at least for climbing.

Second, it would be difficult to ATTAIN experience in neurosurgery, since there aren't many opportunities to do that. Even if they try to read a book or something, it probably wouldn't be considered very high quality training of the skill (resulting in meagre xp gain) so without real training opportunities, it would probably be very difficult to raise far above -4.

Third, one can consider neurosurgical tasks as generally requiring considerably more experience to do well than other tasks; I think this is the sense in which we are thinking of it as more "difficult" than climbing. (That is, "harder to learn" seems equivalent to "takes more experience to perform well in.") So, based on our experience interpretation of levels, the difficulty levels for typical neurosurgical tasks should be set higher than usual; say, +1 or +2 for even a typical operation. This is because a typical operation requires that much experience (let's assume, however much it is--we haven't defined it yet) to perform successfully.

So, combining these three factors...

• (1) most characters will be walking around with -4 neurosurgery

• (2) it will be difficult for them to find the training opportunities necessary to climb out of that hole

• (3) a typical operation might require surpassing +1 or +2

...most characters, if they attempt a neurosurgery, will have no chance of success.

If they aren't neurosurgeons, but managed to somehow scrounge up a bit of experience, and they are trying to perform an easy operation, they might have a 1% (++++) or 5% (+++o) chance of success, which seems fair.

So, I guess what I am saying is that the varying difficulty should be built into the difficulty factor associated with specific actions, not skills. And determining the difficulty factor for each action will require reasoning about how much experience it would take to successfully perform that action.

A possibility would be to also include a "difficulty multiplier" that decreases/increases xp cost for each skill, but I fear this would be redundant (if we can agree that the difficulty should already be built into the actions rather than the skills).

peup.

[ebrahimebrahim]

Okay I like this approach! Summarizing a bit:

• Skills are sometimes harder in the sense that more experience is needed to perform well at them. The actions being resolved for such skills have higher difficulty.
• Skills are sometimes hard to improve in the sense that "quality" training for them is not so readily accessible or is just not something that is done without more deliberate education. For such skills, XP rewards can sometimes be lower.

Here's also a diagram summarizing the idea:

Regarding the first bullet point above: When a particular neurosurgery task is assigned a difficulty of +2, that's because it's a neurosurgery and neurosurgery is difficult. It's not because this particular neurosurgery is more difficult than other neurosurgeries. I think this is an easy thing for a GM to misunderstand and mess up. We should make it clear that when the GM sets the difficulty for a task, it's an absolute difficulty which is related to how much experience is needed to get a certain performance, rather than a relative difficulty in which, for example, a particular neurosurgery gets compared to other neurosurgeries.

A possibility would be to also include a "difficulty multiplier" that decreases/increases xp cost for each skill, but I fear this would be redundant (if we can agree that the difficulty should already be built into the actions rather than the skills).

I agree that we shouldn't have a difficulty multiplier.

[yusufmte]

Peup, I agree that it would be easy for a GM to misunderstand and mess up (e.g. by assigning a "typical" neurosurgery a "typical" difficulty). So yes that we need to be clear about the "absolute difficulty" thing. More specifically...

Skills are sometimes harder in the sense that more experience is needed to perform well at them. The actions being resolved for such skills have higher difficulty. Skills are sometimes hard to improve in the sense that "quality" training for them is not so readily accessible or is just not something that is done without more deliberate education. For such skills, XP rewards can sometimes be lower.

...regarding your first point, we should add into the Actions section that this is how Difficulty factor should be decided by the gm. Regarding your second point, we should add into the xp reward section the concept that the reward amount should be based on quality of the training (and for some skills quality training could be hard to come across, which is expected).

But, peup! I think this is actually a really good change/clarification for the health of peupfudge overall, for other reasons. I think determining the difficulty factor was previously kind of arbitrary / just based on the gm's whimsical interpretation of the adjectives (and it kind of felt arbitrary when I tried to do it as gm in seed comet also). However, now we have an exact interpretation of difficulty factor--it's based on how much typical experience is required to succeed at the action! And not only that, but it's the exact same interpretation that will be used for abilities! So the "levels" that we describe in Numbers & Adjectives will consistently mean the same thing, and interpreting them should feel less arbitrary throughout peupfudge! Basically, what I am saying is that--if we properly clarify to the gm that experience is always how the levels should be interpreted, for both abilities and determining Difficulty factor--those links in the diagram are strengthened: xp cost will be tied to ability will be tied to performance in a clear way.

(If you have qualms with the above, you can leave this upcoming paragraph until we resolve the previous issue. peup.) If you agree, the last remaining peup here (I think) would be the natural talents/deficiencies and affinities/unfinities. What do you think of the idea of having them both be Properties that characters could have, where talents are ability modifiers and affinities are xp cost multipliers (each for particular skills)?

peup.

[ebrahimebrahim]

No qualms! I made certain things bold in your post so we remember to do those before closing the issue.

the last remaining peup here (I think) would be the natural talents/deficiencies and affinities/unfinities. What do you think of the idea of having them both be Properties that characters could have, where talents are ability modifiers and affinities are xp cost multipliers (each for particular skills)?

Yes, I like making it a property. Properties give maximum versatility while also not annoying people who aren't using them.

Another advantage of this approach is that there's already a mechanism by which properties can influence performance directly, because they can count as aiding factors that influence M. Relevant excerpts from the action section:

... ...

Here's a summary of the ideas so far:

In the case where a particular property (like a natural talent) always affects a certain ability level whenever one rolls against that ability, then I think it makes sense to just remember that the "effective ability level" is higher than the raw ability level. We can write into the manual the idea of keeping track of effective ability levels next to ability levels when it makes sense to do so.

[yusufmte]

Peup, agreed with all! So, the only remaining issue on this topic--aside from actually writing all this into the manual--would be to figure out exactly what the xp cost function should now be?

How should we start on that?

Things we would want the function to have:

• An asymptote

• Increasing xp cost between levels

• The ability to represent 0 experience (unlike logarithmic scale) at level -4

Does a down-shifted logistic curve meet these criteria?

peup.

[ebrahimebrahim]

Do you mean logarithmic curve or do you actually mean logisitc curve?

Unrelated question: Does our current suggested system require that everyone start at -4 for all abilities, until they use their starting XP to train things?

[ebrahimebrahim]

Also, do we really want an asymptote? I think orders can make sense without one; they just help you to go "off the chart" without have to get unnecessarily numerical. Having an asymptote means there's a max level, e.g. "legendary" might be the actual highest possible level. I'm okay with that actually, but just checking what you think...

[yusufmte]

Do you mean logarithmic curve or do you actually mean logisitc curve?

I think logistic...wasn't that what we were thinking might replace the current logarithmic curve?

Unrelated question: Does our current suggested system require that everyone start at -4 for all abilities, until they use their starting XP to train things?

Hmm, I think only if they are babies. The pre-starting-xp ability levels should be at the bare minimum that the characters could reasonably have, then the players can use starting xp to build their characters beyond that. (I think that's something we should consider writing into the manual also.) Perhaps "Neurosurgery" or "Physics" could be at -4, but there are some abilities that would be very difficult for non-baby characters to have -4 in, like "Running" or (in some worlds/settings) "Literacy."

Also, thinking about seed comet, the pre-starting-xp distribution is still something that I would make different between different tribes, based on what people are expected to have learned just by growing up in their tribe.

But I do think this is different than what we currently have, which is to default to -2. The pre-starting xp ability levels should be at the absolute minimum that's reasonable for the character (probably lower than -2 for most things); that is, what the character would have if they just barely scraped by in every phase of their life. (And then the starting xp, should the gm be generous enough to provide it, can allow the character to be more.)

peup.

[yusufmte]

Also, do we really want an asymptote? I think orders can make sense without one; they just help you to go "off the chart" without have to get unnecessarily numerical. Having an asymptote means there's a max level, e.g. "legendary" might be the actual highest possible level. I'm okay with that actually, but just checking what you think...

True, but I still think asymptotes make sense in general! Otherwise, a character can become indefinitely better (even if it becomes really hard in practice), which doesn't quite seem right. Also, having legendary be the actual highest possible level would be nice in terms of having the xp table we provide be able to account for all cases...And I think it would be cool for players to be able to think of legendary as the highest peussible.

[ebrahimebrahim]

The pre-starting-xp ability levels should be at the bare minimum that the characters could reasonably have, then the players can use starting xp to build their characters beyond that.

This makes sense. Pre-starting-xp ability levels should reflect the elements of the environment in which the character grew up that are common to all characters of the campaign. Then players can use their starting xp to fine tune things to the unique story of their own character. Pretty peup!

[yusufmte]

Exactly, pretty peup indeed! Then we will peup that into the manual.

Do you agree about all the criteria I suggested for the xp cost function (asymptote, negative double derivative, ability to represent 0)? If so, do you have any suggestions of such functions?

peup.

[ebrahimebrahim]

I agree with those criteria but I think we should impose more criteria to make our choice seem less arbitrary. Let's voice chat when we can to hammer out the details.

(For example with just those criteria, the function f(x)=9*tanh(x)-4 would work, assuming you want an asymptote at +5 so that +4 becomes the max level. But so would f(x)=9*tanh(a*x)-4 for any constant a.)

Coming up with a good specific function might involve looking at the xp table, and even looking at statistics of trained trees based on different choices.

And there's another constraint that I don't know if we can possibly ever meet: having the function be easy to verbally describe, kind of like "a good climber is 1.85 times as skilled as a fair climber" was easy to describe. Maybe we will end up just putting a graph of the function in the peupfudge manual...

[yusufmte]

Peup, agreed about imposing more criteria! Enough criteria that we are left with one choice would be ideal. And that this is something we should voice chat to heummer out.

It would be nice to have it be verbally describable, but probably would be hard to do, and I think a graph would be a pretty peup way to show it nicely!

Peup.

[ebrahimebrahim]

Possibly useful to know this for our discussion: The following code from gen_numbers.py is what generates the entries in the xp cost table:

# b = skill level base
# s = xp scale factor
# d = discount factor
b = 1.85
s = 50.0 / pow(b,-2)
d = 1.35/b

# Note that s is set so that the (3,3) position in the table has an xp cost of 50.
# Note that d is set to b'/b, where b' is a sort of modified base:
#  b' is the base you would see if you read diagonally down the table instead of straight down.
#  It represents how much harder it is, on average, to increase all children of a skill from a to a+1 vs from a-1 to a.

# a = attribute bonus
# c = current skill level
xp_cost = lambda a,c : int(round(s*pow(b,c)*pow(d,a+2)))

Basically it says that

---

Now that I think about this stuff again, I'm realizing that the previous approach to xp cost contained an approximation rather than the exact idea "a good climber is 1.85 times as skilled as a fair climber". I don't know if this approximation was intentional or if I just messed up earlier and got lucky. Let me explain:

~~Suppose we have a function which converts a level into an xp (this is the inverse of whatever will be our answer to Q1 from above). Suppose also that we go with what is currently written at the beginning of the manual: that for some constant A. Then, ignoring attribute bonus, the xp cost to go from level c to level (c+1) should be g(c+1)-g(c)=b^(c+1)-b^c, which is not what we get in the formula above if we ignore attribute bonus... But it's approximately correct:~~

Edit: Oops. Since b^(c+1)-b^c=(b-1)b^c, I peuped. We did implement "a good climber is 1.85 times as skilled as a fair climber" into the xp cost table previously.

---

Anyway, we can just use the exact xp cost g(c+1)-g(c) since things are complicated enough that it doesn't really matter if the xp cost formula is too complicated. Earlier we were motivated to keep the xp cost formula simple so that players could compute directly from the formula if they go off the chart, but I think now we're throwing that out the window. Also, if we have asymptotes in the right places then there may be no need to ever go off the chart.

---

Edit: Oh yeah, we also need to rethink how attribute bonus should play into the new setup. Our thoughts about that last time hinged on our being able to think of level as being related to xp via a logarithmic base-- this way of thinking is no longer necessarily available.

[ebrahimebrahim]

[ebrahimebrahim]

What do you think of this? Just putting down a starting point to get the discussion moving. The table is in heimsoy as xptablepeups_heim.ods

Every point of attribute bonus simply applies an 85% discount to the xp cost. I have no way of justifying this right now other than that I like the numbers in the table.

[ebrahimebrahim]

The issues described here have been solved by the following parts of the manual:

XP is to be interpreted as the product of practice time and practice quality, which we will refer to as simply practice. Each unit of XP corresponds to a certain amount of practice. The exact amount of practice contained in each unit of XP is decided implicitly the first time that the GM awards XP, and it crystallizes as the GM continues to award XP in a consistent pattern.

Abilities start at level 0 during character creation. The GM provides starting XP to each character based on the practice the character may have gathered throughout their life before the start of the campaign. If a character has a natural talent in a given ability, then they could get some ability levels for free prior to XP allocation; this would represent a sort of head start in the ability.

Ability level is a function of XP, and XP represents practice. But ability level is ultimately meant to represent a character’s proficiency. Of course practice generally improves profi- ciency, but characters with the same amount of practice can end up with different levels of proficiency. For example, a hobbit and an ogre may get the same amount of strength prac- tice, but the hobbit will still be weaker than the ogre. To incorporate this into Peupfudge, a property “ogre strength” may be added to the ogre’s character sheet. This property would add a certain number to the strength level, but it would do so in a way that should not affect the XP cost for leveling up. To keep track of this, the ogre’s strength level can be written in the character sheet as a sum: [unmodified level] + [modifier]. When the ogre needs to use their strength, they use the sum. When the ogre wants to spend XP and level up their strength, they use the unmodified level to determine the cost.

Equivalently, the hobbit could instead take on a “hobbit strength” property that reduces the strength level in a similar way. Whichever being ends up not taking on any modifier becomes the standard being for the purposes of level interpretation. How strong is a character with level 5 strength? It is as strong as a standard being that spent 5 levels worth of practice on its strength.