Maarzan, are you referring to my skill system or in regards to Lunamancer's health system?

Quote from: Saurondor;898762Maarzan, are you referring to my skill system or in regards to Lunamancer's health system?

Sorry for being unclear.

The 2 elements/questions were for the health system with extra labels.

The comparison to sports was directed to the discussion of your skill system.

Quote from: Maarzan;898739Take a look at real time individual sports, say 100m dash.
Everyone has his current potential, but the athlete will not achieve the same time in every race. It will be a certain distribution leading to results next to his potential while generally staying at this potential (more Training, better equipment, technique improvements, illness, injuries etc can all modify the potential of course) . So there will be people that will not swap places unless some accident happens and there will be people who will usually be better or worse but on a special day things could swap and there are other athletes with similar potential, where every race could swap playes back and forth.

Well yes, and actually my day job is related to sport event timing so I see that quite often. Athletes who just have a bad day and don't just cut it. Some might drop out after some leg of the competition such as swimming. I guess my experience in all this has influenced both the skill systems in my games and the fatigue mechanics based on cardiovascular performance. How can this be represented if skill is a fixed number? Even if you're an Olympic medalist you can still have a bad day. How do you break a record if skills are fixed numbers?

The long tails are the "black swans" of the game, the unexpected events. You're striving to get in first, to get a gold medal, and then maybe, hopefully, set a world record. How can I model this if my 3d6 is bounded between 3 and 18? The graphs I've shown present very small odd of outstanding success: Olympic records.

So say we're in a triathlon. You can have a age group competition and an elite competition. Among the age groups you have skilled to expert triathletes. The masters and legendary triathletes are in the elite group. You can sort things out among the age group, some getting lower rolls (and larger times) and some getting good rolls (and smaller times) that lead to a win. Then you have the elite who will sort it out among the master and legendary levels. Of course one triathlete can have a bad day (roll really really low) and drop out after finishing the swimming stage.  The rest have rolls in the ballpark and that resolves their final standing in the race. There can be though an outstanding roll, a roll that adds a minute to every bike lap and sets that triathlete ahead and ahead every lap. This is equivalent to rolling a +16 difference, way over the 0 required to succeed, way over the 10 required for outstanding success. It's an outstanding win, even possibly a world record.

One of my particular interests in game mechanics are the infinitesimal odds of something outstanding happening. That's why the curves have such long tails and they can't be easily reproduced by 3d6 or similar die rolls. It's the ability of the dice to produce something outstanding and totally unexpected. That's why all the skill curves overlap to a great extent among themselves even if with just small odds of such an event occurring. Because you really can't break an Olympic record by modeling only values equal or less than the current Olympic record.

Quote from: Xanther;898699And that's your implementation.  I will repeat, all you have done is convert every task into: IF skill x AND task y THEN MAY succeed.   Where do you get these percentages?  They are very precise.  Do you see that all you are doing is using the word "skilled" as a place holder for a number because once you have the skill level (described with a word) and a task difficulty (described with a word) you then go to some table or graph (or other numerical reference) to get such percentages.  That is, how did you make those curves? How do you adjudicate where someone is on the curve; roll a die?  All you have done is cloak the number in words.

Just some advice on your probabilities.  If I am a player with an expert skill and I fail an unskilled task 13% of the time, then I'm going to be upset. That is incredibly high in play.  Of course it all depends on what qualifies as an unskilled task.  If you set it high enough then there is no problem for the expert, but then the unskilled person may be doing some pretty tough things more easily than one would expect.  This naturally occurs when you do it this way and have such low resolution and dynamic range in your skill levels (your mention only 4 levels, see below for more explanantion).  I've seen this occur in play as this is not new.  What ends up happening is GMs ignore making experts roll for unskilled tasks because the failure rate is unrealistic and/or doesn't matter (if doing your degree of failure thing).

Let me revisit this. Now with a bit of time.

QuoteDo you see that all you are doing is using the word "skilled" as a place holder for a number because once you have the skill level (described with a word) and a task difficulty (described with a word) you then go to some table or graph (or other numerical reference) to get such percentages.

If my character is expert at something this is the probability curve for the roll. It's not a table, it's a roll. In one case I might roll a 7 (quite common), in another time when I use the same skill I might get a 10 or a 4, or a -2, or a 16, etc. The skill level "expert" is not a number, it's a set of numbers that go from -8 to 22 according to this graph:

[ATTACH=CONFIG]64[/ATTACH]

Now I'll add "experienced". The curve is in orange and the "expert" curve is in black for reference. Notice how the "experienced" curve is slightly to the left of the expert curve.

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The more common outcomes are 3 and 4, not 7 like the expert curve. The curve also reaches to 21, almost as high as "expert" (22), but also goes lower, to -14 instead of -8.

The orange curve is the "experienced" skill level. When I use my "experienced" skill I'll get a number along that curve. When I face an "experienced"  challenge the challenges's value will be along that curve. Usually 3 or 4, but could be higher or lower as well.

Now when I actually use my "expert" skill against an "experienced" challenge I subtract the challenge's roll (experienced) from my skill's roll (expert) and get the following curve:

[ATTACH=CONFIG]66[/ATTACH]

Favorable outcomes occur from rolls that are 0 or higher. As you can see in this case it's more probable to get favorable outcomes than not. I'll usually get outcomes in the range of 4 and 5. I've decided (as designer) that +10 is very good and -10 is very bad. An outcome of 4 or 5 places me well above the "just good enough" of 0 and halfway to the "really awesome" of +10. If I get a 5 I don't just narrate success, I narrate something better than if I get 0, which is good too (success), but lesser success than a 5.

For a quick simulation of sport performances I would use a base potential value and add a bell shaped dice amount on top of it.
This dice would be full-open ended to the low side (to represent accidents etc). On the high side it would depend on teh kind of competition. Some elements liek a single shot at archery could see a perfect result for a newby (the shot has to land somewhere after all) For eve´rything else it would be 1 time open roll.
You could probably even fine tune this with adding a best-of-mechanism for highly skiled athletes and least-of for newbies. (and I don´t believe in beginners luck, it is probably rather a question of unusual self-esteem and preconditioning surprising the opponent or the observer)

Quote from: Maarzan;898924For a quick simulation of sport performances I would use a base potential value and add a bell shaped dice amount on top of it.
This dice would be full-open ended to the low side (to represent accidents etc). On the high side it would depend on teh kind of competition. Some elements liek a single shot at archery could see a perfect result for a newby (the shot has to land somewhere after all) For eve´rything else it would be 1 time open roll.
You could probably even fine tune this with adding a best-of-mechanism for highly skiled athletes and least-of for newbies. (and I don´t believe in beginners luck, it is probably rather a question of unusual self-esteem and preconditioning surprising the opponent or the observer)

What would be your target value?

Ok a little bit more on the comparison between numeric and word skills.

Let suppose I have a 4d6 base roll and a skill at farming labeled "3" as in number 3.

Farming = 3

[ATTACH=CONFIG]70[/ATTACH]

On this graph we see the base roll in black, the modified roll with the 3 added (orange) and the success/failure when we compare it to a target value of 19 (cyan).

The character's skill at any given time is also a "set of numbers". In this case ranging from 7 to 27 (orange curve). In any one usage of the farming skill the player will obtain one of such values and compare it to the target value (19 in this example).

In the skill as word system the curves are as follows:

[ATTACH=CONFIG]71[/ATTACH]

The base roll is unskilled (black) and all the others are shifted to the right to represent "higher skill". It seems like I'm adding a value to shift them right and someone could claim that "skilled" is 1 and "expert" is simply "skilled" + 2, but it's not. There's no number you can add to the "unskilled" curve that will transform it into the "expert" curve. The following graph shows the "skilled" curve shifted right (shown in orange) so it's aligned with the "expert" curve.

[ATTACH=CONFIG]72[/ATTACH]

Each curve isn't just shifted to the right, you'll notice it's also taller and tighter around its central value. As characters get better they're not only better in general (shift right) they're also consistently better (tightness around central value). Experienced characters tend to roll lower a lot less than their unskilled counterparts.

The following graph shows a side by side comparison of the 4d6 roll and it's modified counterpart in black and cyan respectively, and the "skilled" and "experienced" curve in orange and green respectively.

[ATTACH=CONFIG]73[/ATTACH]

The blue curve is an exact replica of the black one just shifted +3 to the right. The green curve is shifted right, yes, but it's not the same. For starters it's bimodal with 3 and 4 being the most occurring values, unlike the orange curve whose mode is a single value (0).

Given that each skill level is a combination of dice there's no integer you can add to one that will transform it into the other. So "expert" is not "skilled" + 3 or "skilled" + n.

Bell curve, schmell curve.

Tell me, planes have planned arrival and departure times. Of course, the world is an imperfect place, so the actual times often vary from the scheduled time.

So, this would be best modeled as a bell curve, right?

Wrong.

What's the most a plane could possibly be delayed? Well, as Saurondor hints at when mentioning long tails and black swans, the longest a plane has ever been delayed historically is not an upper limit. On the other hand, how early could a plane possibly be? Well, even with teleportation technology, the earliest the plane could arrive is at its prior departure time. More realistically, there's a minimum time it would take based on the craft's capabilities and safety, even under ideal conditions. And departure time certainly can't be too early or all the people who bought the tickets would miss the flight. So there's a hard bound on the early side.

This is not a bell curve at all. It's only open at one end.

Allow me to suggest, this is a far better model for real world phenomenon than the over-rated bell curve is.


Furthermore, Maarzan raises the example of archery and correctly notes that the arrow has to land somewhere, so even the beginner has a chance at hitting the bullseye.

If I follow through with this example, the absence of skilled aiming would make anything within the general direction about equi-probable to hit. The relative difficulty, then, of hitting the bulls eye is the area of the bullseye as a proportion to the field defined by the general direction. A very small chance, but a chance just the same. Other areas on the target can be likewise computed. This proportionality is best modeled in a linear fashion, e.g. 1% bullseye, 6% first ring, 13% second ring, 20% third ring, 60% miss.

From there, all you need is a traditional, binary, linear hit roll paired with a damage roll which determines degree of success. Successful skill use over-rides the proportionality test when the skilled use is superior. So here I assume a d20 damage roll, with 20 indicating bullseye, 16-19 indicating first ring, 11-15 indicating second ring, and 1-10 indicating third ring. The binary hit roll is expressed as a percentage, with each 10 points of said skill translating to a +1 bonus on the damage roll. A range bonus may also be applicable, depending on type of bow used.

So when it's all crunched out, someone with, say, 60% skill (and a 20% range bonus) has the following probabilities: 12% miss, 20% hits 3rd ring, 22.6% hits 2nd ring, 17.2% hits 1st ring, 28.2% hits bullseye. Here, you see sort of a bell curve effect. Of course it's bunched up on the bullseye end because the skill is moving the curve in that direction, beyond which the hit can't get any better (if there were a hit better than bullseye, the curve would continue to show).

And what I'd like to point out is this: the curve effect shows itself despite using linear mechanics. Obviously, the curve manifests because multiple variables are coming into play. You would also still get something curved if each of the linear variables were replaced with curve ones. The point is, this is not necessary. If we are being specific about the factors involved (remember the point of this thread, specific is what makes good narrative, generic is the enemy). This is in addition to the point that if you are going to just combine every factor into a generic probability stew, there is nothing realistic about the standard bell curve.

The point is, whatever the intricacies of your system, you are not using the word "expert" to find out what happens; you are using a variable which you have encoded with the word "expert". You are not employing a system of simulation which bypasses numbers as you had alleged.

Other than that, I don't see the specifics of the system as being relevant.

I add the dice result to my base skill potential, which is itself a percentage of some norm value, for example the current world record.
i.e. say current WR is 57,92 for 100m breaststroke long course, make the norm 57 sec. I would have approx.  68,5% as base potential and adding (3W10)*0.2% would result in values between 1:22,5 (69,1%)  and 1:16,5 (74,5%) which is quite nicely fitting to the last 10 years (OK, looking at the reducing amount of training I got and the corresponding tendencies over these years, you would probably get better fit with assuming a decreasing potential and a different variable range. As the lower number of competitions probably doesn´t show the less probable rolls the variable range could even be OK or too small but necessiating changes in the base potential.

It would look similar for the archery. 100% would be the area of the arrow head pount blank and then skill would map to a certain base percentage remapable to a larger area and thus distance to the original center aimed for. The trick with the dice would be, that the unskilled value plus novice dice would need to map randomly to the distance from target proportional to the area. Higher skill and expert dice would then narrowing the assumeable target area unless a low-end roll indicates a botch.

This looks very similar to Lunamancers solutiomn, except that the dostrobution at a certain skill is probable not flat with just moving shots inside until they stack at the center..

Quote from: Manzanaro;898936The point is, whatever the intricacies of your system, you are not using the word "expert" to find out what happens; you are using a variable which you have encoded with the word "expert". You are not employing a system of simulation which bypasses numbers as you had alleged.

Other than that, I don't see the specifics of the system as being relevant.

I never alleged I bypassed numbers I alleged that your allegation that it would be necessary to represent skills as numbers for the sake of simulation was a necessity. In a way you specifically mentioned as skill = numeric skill level to yield a list similar to:

Farming 4
Fishing 2
Hunting 5
etc.

I proposed a prose respresentation of the character in which the background and skill sets is narrated. For example "He grew up and worked in the family farm until he enlisted and..."

So I get an idea of what type of "farming" experience the character has.

This fired a lengthily discussion around two main topics: ambiguity and actual numeric equivalence.

First, ambiguity, this is false. Representing Farming as 4 is no clearer than "he grew up and worked in the family farm". What is farming 4? Is that good in what? Farming is a broad topic. Does the character have professional education? Is the character specialized in a particular crop such as rice, corn, wheat, sorghum, etc.? Does the character have special knowledge of agrochemicals, soil composition, irrigation techniques? Does the character have veterinary knowledge? Is such knowledge good to cure an infection, prescribe medication, operate? Does the 4 cover farm tools, all farm tools?

The value of Farming 4 is clear in the mechanical sense, in particular when the mechanics are linear. I can read 4 and say, well that's a 20% bonus and that's good if I want to ...?? <- whatever here.

But nobody is 4 across a field as broad as farming. What about electronics? Electronics 4 means what? The character is good in everything regarding electronics? From TV, to dish washers, to satellites, to AC motors, etc.

So Farming 4 means the character enjoys the same "bonus" when trying to fix a combine that to irrigate rice than to provide a pesticide or herbicide to recommend fertilizers for a type of soil to heal a dog to operate a horse? It can't be that broad.

Secondly, numeric representation. The skill level of "expert" is not "unskilled" +4 . Although I'm converting them to numbers in the end to process them through the simulation they don't hold the same relationship as 1, 2, 3, 4. If I rolled 4d6 as I exemplified previously, and I added 2 to the roll then each value in 4d6+2 has a corresponding value in 4d6, just two points lower. This does not happen with skilled vs expert. Each value on the expert curve does not have a corresponding value in the skilled curve with a fixed difference of value N. That is Er = Sr + N (expert roll equals skilled roll plus constant N) for all values in Sr. To say skilled is 1 and expert is 4 is to give the false impression that the rolls on expert are simply those of skilled + 3. This is not true! The skill system progression is non-linear.

Quote from: Saurondor;898737Xanther, first of all I apologize if I sounded rude by saying wrong wrong wrong. I should have been more moderate about it.

Fair enough Saurondor.

QuoteNow skills are not numbers, they're a set of numbers that have a higher or lower probability of occurring. Some values in the set "expert" are actually lower than some "high" values in the set "experienced". When I talk about an "expert" skill I'm not talking about a 5 that is better than a 3 ALWAYS. I'm talking about a set of values which generally tend to come out higher than experienced, but it's not always so. So an expert will usually get rolls around 5, but might come up with a 3 at times. An experienced will usually roll around 3, but might get lucky and get a 5 every so often.

You actually can't get these curves and outcomes by just rolling 3d6 or similar rolls as these lack the long tails characteristic of the rolls I'm using:

I understand that 3D6 is only an approximation to the normal distribution.  As you add more D6 you get a better approximation.  Can you describe what you are using?  It looks like what you get is a normal distribution.  Let me know if my terminology is unclear.  I've spent most of my adult life with such mathematics that I forget what is common and what is esoteric.

I understand what you are talking about on sets of values.  A 5 always beating a 3 is one way to do it, but not your way.  You can use numbers and get exactly what you are doing, and you are using some numbers anyway to get those curves.

Let's ignore for the sake of an easy example that 3D6 does not give exact shape of the distribution you are using. I will then just use 3D6 as the generating function for your distribution.  What you are doing is shifting the center, first moment, of your distribution based on skill level.  Using 3D6 with a modifier to the roll or target number does the exact same thing.  Alternatively, you could shift the first moment and vary the second and higher even moments of you distribution by adding more D6.  The second moment is the width, and the fourth moment describes the tailing you mentioned.  In short, if you used a number based approach and 3D6, adding a +1, +3 or +5, provides a set of shifted curves just like you show.  Again recall I am using 3D6 as an example knowing the shape is not a perfect fit.  You can use dice or other methods even to generate the curves but the +n modifier approach will still work.  
 

QuoteNow, following your recommendation

Seeing that the black curve (unskilled) goes from -20 to +20, what value would you suggest I place on unskilled? Should it be -20, -18, -2, 0, +4, +8, +10 or +20, or any of the others that lay under the curve? What's the best fitting number to the word description? And in what way would that make it clearer for you?

I'd need to know how you generate those curves to give a better answer but the values on the x-axis are purely arbitrary.  That is, you can change them by normalizing to a given height.    
The value you want to assign to skills is determined by the difference between the peaks for unskilled-skilled-expert etc.  If the shapes of the curves are the same, then you can use the generating function for that curve for any and all skill levels and just shift that shape with the modifier.

IIRC there was about a 3.5 value shift between peaks of two consecutive skills, so the numerical difference between skill steps should be 3 or 4, if that was the case, to reproduce your curves.

As a practical matter, 4D6 is close enough to the normal distribution that the differences are undetectable.  Likewise if the peak shifting between skill steps is not constant with what you are currently using, you could make it so without changing the qualitative aspects of task resolution.

Saurondor, the number 4 was an example, just like "Farming" was an example. By no means was I saying that incremental bonuses was the only possible way to simulate skills.

I have a very hard time believing that you really thought that was my position. It certainly isn't logically based on anything that I actually said. Whereas you really DID say that you wanted a simulation that avoided using numbers.

As far as your thoughts on ambiguity? Firstly, I'm assuming that either the players have rough familiarity with the rules, or they are not designing their own characters. Either way can be fairly effective in avoiding the bafflement of not knowing how the skill system works.

Secondly, you profess scorn at the idea of an all encompassing Electronics skill. Why? I mean, no it isn't realistic. So what? Who is the one chasing the perfect "Alpha Simulation" again? (Or whatever you called it.) I have been cognizant of the limitations of tabletop simulation since post one, and have kept them consistently in mind throughout this thread.

And finally, how on earth does "he grew up and worked on the family farm" give you any sort of precise idea of the character's farming experience?? It doesn't answer ANY of the hypothetical questions that you go on to ask.

Quote from: Saurondor;898932Ok a little bit more on the comparison between numeric and word skills.

OK catching up on the thread I think I see the semantic disconnect here.  

Every thing you are doing with the word skills is more typical of number based.   It is not so much a distinction between number versus word, but between fixed dice number and variable.

I'll use dice number as a short-hand for your random number generation, as that is the most common way people generate random numbers in tabletop games.

QuoteThe base roll is unskilled (black) and all the others are shifted to the right to represent "higher skill". It seems like I'm adding a value to shift them right and someone could claim that "skilled" is 1 and "expert" is simply "skilled" + 2, but it's not. There's no number you can add to the "unskilled" curve that will transform it into the "expert" curve. The following graph shows the "skilled" curve shifted right (shown in orange) so it's aligned with the "expert" curve.

Of course, you are not just shifting the curve but changing its second and fourth moments, it's width and tail.  But notice how the height increases.  I'm guessing that whatever you are using normalizes by area.  What you show here is actually a neat inverse of more dice with more skill.

As you go from left to right, these curves can be approximated by nD6, (n-1)D6, (n-2)D6, etc.  That is you use fewer and fewer dice the curve gets tighter.  Along with a positive modifier offset to shift the curve to the right.  If you add a modifier plus change the number of dice you get your curves.  You'd have to look at the details to see if using a reasonable number of dice and reasonable numbers cold make this work.  For example you can avoid using 6D6 and modifiers of +12.  Nothing fundamentally wrong with that, just a feel thing.

I really would like to know how you get these curves.  I don't think they arise from dice, but maybe I am wrong.  As this is a game design thread area, practicality and playability might trump precision in statistics.  So you are going to need to work within the limits provided by rolling dice for your random number.


One thing may be to give up on the different curve shapes for different skill levels versus a constant task difficulty.  For example, the tighter distribution for greater skill is good to keep things from going really bad, but why should that come at a cost of things not going really well?  I suspect the answer is you probability calculator can't do asymmetric distributions.  The cheap way of mimicking things, but not really getting the shape, is to say all 1s rolled, for example, count as 2s.   Is the desire just to cut off the really bad chance for high skill?  Then the asymmetric distribution trick is a good one.

QuoteEach curve isn't just shifted to the right, you'll notice it's also taller and tighter around its central value. As characters get better they're not only better in general (shift right) they're also consistently better (tightness around central value). Experienced characters tend to roll lower a lot less than their unskilled counterparts.

As mentioned above, they are also consistently less spectacular.  The chance of them being much better than average is also reduced.

QuoteThe blue curve is an exact replica of the black one just shifted +3 to the right. The green curve is shifted right, yes, but it's not the same. For starters it's bimodal with 3 and 4 being the most occurring values, unlike the orange curve whose mode is a single value (0).

Just a mathematical terminology point.  The green curve is not bimodal.  By your definition all your curves are bimodal because they all have two x values that share the same y value.

If you want to learn more about distributions, the mean (first moment) is the peak position in your case, the variance (second moment) gives you your width, and the kurtosis or fourth moment describes the tails.  If you want asymmetric distributions, look up ones with a non-zero skew, or third moment.

Quote from: Xanther;898957I'd need to know how you generate those curves to give a better answer but the values on the x-axis are purely arbitrary.  That is, you can change them by normalizing to a given height.    

The curves are generated using a fixed 4d6 roll and subtracting Nd6 from it. The value N is 5 for unskilled and one less for each higher level, down to 0 for legendary.