OT: Making a Game System (part 2)

[Omnirizon]

OK. thanks for all input so far. here's the next section...

for a recap. recall 'threat' is an abstract amount of threat the weapon poses that forces a defender to expend 'vitality' to parry, avoid, or whatever. I think I will now begin calling threat 'attack', because it sticks somewhat with naming conventions, and is easier to abbreviate.

at the core, the attack and defense system works like this:

attack/defense = vitality loss

I am choosing this model because then there is always some vitality loss for the act of defending one's self; basically defending one's self is stressing. with skills, experience, and stats that stress becomes easier to handle, more natural, fewer mistakes are made, ect, and vitality loss and the ratio of vitality loss will be lowered.


been discussed so far is how to determine the attack and defense values. I'm leaning towards some kind of average of values drawn from stats, skills, arms, ect; I'm desiring some kind of average that will penalize over-specialization (such as harmonic or geometric). Lokean and others suggest that harmonic means are too severely skewed towards smaller values, and also are not conceptually "correct" in my system. Lokean suggested geometric means are more suited, so I think they will be used.

at the moment, I am looking at the following going into an attack value:

perception
psyche
skills
arms

perception and psyche are base stats
skills are skills (ZOMG!)
arms is the bonus to attack provided by equipment.

these values may be weighted, but we will worry with this later
strength and dexterity are moderated through arms. basically, arms have a minimum str and dex value. they can be used with less than this value, but then suffer to their 'arms' value contribution to the attack average. also, if the user has higher str or dex then required, an additional bonus is provided. I will take the difference of required stat minus actual stat, and then get the natural exponent of this. The 'arms' value of the weapon is multiplied by this result, and that product is what goes into the 'arms' portion of the attack average. (I am using all this math for a reason! I want diminishing returns and curvilinear models, I think those are most accurate for what we are dealing with here.)

so basically...

exp(reqstat - stat) * armsvalue

this will have the effect of severely penalizing a deficient stat, while providing a diminishing bonus for excessive one. also, this can be used to make some weapons more deadly with dexterity, and others with strength, making character design more personal. The very strong but clumsy character will have a really good reason to use an iron club rather than a rapier for example.


thoughts?

EDIT: wait, exp(x) wouldn't be working right, ln(x) would be right, but doesn't have the pleasant quality of being a 1 when stats = reqstats. but maybe people can see the idea I'm going for. will have to work on the formula a bit. maybe:

ln(e + (stat - reqstat))
?

[Endoperez]

Physical attributes should have at least as much effect on combat efficiency as perceptiveness and psyche. If equipment doesn't level up with you, you'll have to get new equipment. If it's expensive, physical attributes are weaker than others until you can buy the best stuff you can use.

Also, what is the arms value for unarmed martial arts?

[JimMorrison]

An odd observation: It seems that by using (stats-reqstats) in a system where you have multiple stats involved, creates a highly abusable problem. Essentially as 'reqstats' climbs, it becomes more and more profitable to only have the minimum in whichever is the primary stat (that you need more of, to wield the weapon), and to push extra points into secondary stats, because you can always get a higher resultant difference, and thus a better contribution to the equation.

[Omnirizon]

Originally Posted by JimMorrison

An odd observation: It seems that by using (stats-reqstats) in a system where you have multiple stats involved, creates a highly abusable problem. Essentially as 'reqstats' climbs, it becomes more and more profitable to only have the minimum in whichever is the primary stat (that you need more of, to wield the weapon), and to push extra points into secondary stats, because you can always get a higher resultant difference, and thus a better contribution to the equation.

not if you calculate both seperately and then average the result. EDIT: and weight the result

if I wanted to get more exact, I could then weight the calculations in the average, so weapons that have a low dex and high str requirement (like a big maul or something), might also not really benefit from dex much at all, so it could be weighted less. this would of course require assigning all weapons these weights, but in reality I don't think it is that hard since almost every weapon (except very unusual ones) can be classed into a handful of categories in which weightings are shared.

[Endoperez]

That doesn't work well. Imagine a Warhammer with str 8/dex 4 requirements. Psyche 10, Perception 8, str 7, dex 4 guy will be slightly penalized for not being strong enough, but his high psyche and perception increase the value. Someone with strength 10, dex 8, psyche 7 and perception 4, on the other hand, has essentially "wasted" all the exraneous points in str and dex and is even further penalized for not having high secondary scores.

Your system makes the secondaries too important. The primary stats are penalized by the equipment system you've described. Equipment shouldn't triumph over good stats and skills.

Perhaps different fighting styles should use different stats in their calculation. Perhaps something like this:

skill:            fencing       archery       wrestling
(primary stat)     dex           perception    constitution
(secondary stat)   perception    strength      psyche
(tertiary stat)    psyche        psyche        dex
arms               rapier?       longbow?      spandex?

Psyche would be part of all or almost all fighting styles, but the other two important stats would vary wildly.

[Lokean]

Omni, let me recount for you the tale of the most terrifying re-enactment veteran I've ever met.

Bear in mind that I am English, so when we do reenactments there are two main versions: Everyone gets pissed and falls over one another, then gets more pissed afterwards; Everyone wears real armor and wields real weapons that have been blunted or wrapped in leather, broken bones are not unheard of, everyone has fun and then goes home to nurse torn muscles and bruises the size and colour of a Black Magic aubergine (that's the roundish purple egglpant, to you americans).

She did the second sort, she was five foot three and looked like nothing so much as a china dolly. For any relevant physical stat you felt like selecting, she was probably below average. However, nobody ever liked to see her standing even roughly opposite them in the battle line, because she used a two handed sword that was taller than her. And she would run, screaming blue murder, at the opposing battle line and use the weight of the sword and momentum of her charge to throw herself, followed by the spinning arc of death that was the returning upswing of the sword, clean through the ranks...

The point I'm getting at here is that what mediates whether you can actually wield a weapon is less to do with your physical capacity in everyday life (she was weak, clumsy and always exhaused after the fights) than with your skills with the weapon in question.

Further, I'm afraid the natural logarithm is another one of those functions that only exists for positive, real numbers. So if you want to use it you'll make it impossible to use a weapon if you have three points less in the required stats, since this would drop the argument of the function below zero. And you can't even go that low, since you have to keep the argument of the function above one, such that the output is not negative, such that the geometric mean can be used.


In reply to End and JimMorrison, it's actually highly dependant on the value assigned to the weapon as a multiplicative factor, (the arms value, according to Omni). If we assume that the intent is that being just barely capable with the weapon should mean that the 'average fighter' remains average we find that the arms value of the weapon should initially be set (for playtesting) as the arithmetic mean of the requirements for the weapon. This actually means that it suddenly becomes extremely beneficial to the person that invests in a weapon's primary stats, since the natural logarithm increases more rapidly than simple addition at low values.


Endo's two examples actually come out as follows:

Weapon: Warhammer (requires str 8, dex 4, arms value 6)
Psyche 10
Perception 8
Arms (str 7, dex 4) = 3.25 (if his strength was only 6 he couldn't even use the weapon, since ln(e-2) is less than zero)
Geometric Mean = 6.38

Weapon: Warhammer (requires str 8, dex 4, arms value 6)
Psyche 7
Perception 4
Arms (str 10, dex 8) = 12.99
Geometric Mean = 7.14

[Omnirizon]

Originally Posted by Lokean

Omni, let me recount for you the tale of the most terrifying re-enactment veteran I've ever met.

Bear in mind that I am English, so when we do reenactments there are two main versions: Everyone gets pissed and falls over one another, then gets more pissed afterwards; Everyone wears real armor and wields real weapons that have been blunted or wrapped in leather, broken bones are not unheard of, everyone has fun and then goes home to nurse torn muscles and bruises the size and colour of a Black Magic aubergine (that's the roundish purple egglpant, to you americans).

She did the second sort, she was five foot three and looked like nothing so much as a china dolly. For any relevant physical stat you felt like selecting, she was probably below average. However, nobody ever liked to see her standing even roughly opposite them in the battle line, because she used a two handed sword that was taller than her. And she would run, screaming blue murder, at the opposing battle line and use the weight of the sword and momentum of her charge to throw herself, followed by the spinning arc of death that was the returning upswing of the sword, clean through the ranks...

The point I'm getting at here is that what mediates whether you can actually wield a weapon is less to do with your physical capacity in everyday life (she was weak, clumsy and always exhaused after the fights) than with your skills with the weapon in question.

Further, I'm afraid the natural logarithm is another one of those functions that only exists for positive, real numbers. So if you want to use it you'll make it impossible to use a weapon if you have three points less in the required stats, since this would drop the argument of the function below zero. And you can't even go that low, since you have to keep the argument of the function above one, such that the output is not negative, such that the geometric mean can be used.


In reply to End and JimMorrison, it's actually highly dependant on the value assigned to the weapon as a multiplicative factor, (the arms value, according to Omni). If we assume that the intent is that being just barely capable with the weapon should mean that the 'average fighter' remains average we find that the arms value of the weapon should initially be set (for playtesting) as the arithmetic mean of the requirements for the weapon. This actually means that it suddenly becomes extremely beneficial to the person that invests in a weapon's primary stats, since the natural logarithm increases more rapidly than simple addition at low values.


Endo's two examples actually come out as follows:

Weapon: Warhammer (requires str 8, dex 4, arms value 6)
Psyche 10
Perception 8
Arms (str 7, dex 4) = 3.25 (if his strength was only 6 he couldn't even use the weapon, since ln(e-2) is less than zero)
Geometric Mean = 6.38

Weapon: Warhammer (requires str 8, dex 4, arms value 6)
Psyche 7
Perception 4
Arms (str 10, dex 8) = 12.99
Geometric Mean = 7.14

It sounds to me like she had a high Psyche score too

Ok, so given these suggestions, how about this...

str\
    \
dex----------weapon-------|
    /                     |
skl<                      |
    \                     |
per----------tactics------|---attack
    /                     |
psy/                      |
                          |
random roll---------------|

this is basically a method called 'Path Analysis' used in mathematical modeling. 'weapon' and 'tactics' are called 'Moderators' because they moderate the effect of raw stats and skills into attack.

* str/dex/skl will be a Gompertz Function with an intercetpt of 1, upper bound of 1.5 or 2, and lower bound of 0. Gompertz Curve
* skl/per/psy will be a natural exponent
* random roll is a.... random roll

the three can be averaged geometrically, and then perhaps multiplied by the 'arms' value.



this makes the weapon have minimum requirements for use, less than required is penalized (down to 0 effect), while more than required provides a bonus (maybe up to 1.5 or 2 times effect)

tactics on the other hand has no requirement, but is a penalty for too low tactics, while an unbound but exponentially more expensive bonus. I was thinking that ideally this bonus should be in practice rarely higher than the maximum weapon bonus (of 1.5 or 2).

I'll need to work out just _how_ the str/dex/skl sigmoid curve is computed, to prevent gaming the system (it may require some weighting method, where weighting of the stat/skl is tied to its requirement level somehow)

Lastly, note that 'skl' enters the computation twice (in weapon handling and tactics). I thought this was intuitive, since training to use a weapon involves not only handling it, but the movement and footwork that goes into placing the energy moving through the weapon onto your opponents body. In fact, it is a little hard to separate out str/dex/skl/tactics/muscle memory and whatever, so in a sense the 'weapon' moderator is also a part of the 'tactics' moderator. 'skl' then serves as the conceptual link between them, and str/dex versus psy/per highlights the muscle memory versus the instinct/perception that guides muscle memory. The basic point is that now skill is more important than other stats. It isn't doubly important, rather it simply influences two separate calculations, so has more weight.

despite the slightly complex path analysis going into this formula, it is still easy to implement. the formula and procedure is universal, all that needs to be assigned is weapon minimum requirements and some 'arms' or 'attack' value. This is what I'm going for, a universal and intuitive formula that doesn't require ad hoc treatment for different weapons.


How does this look? Does it satisfy the issues you guys were bringing up?

[JimMorrison]

Originally Posted by Lokean

...she was five foot three and looked like nothing so much as a china dolly. For any relevant physical stat you felt like selecting, she was probably below average. However, nobody ever liked to see her standing even roughly opposite them in the battle line, because she used a two handed sword that was taller than her. And she would run, screaming blue murder, at the opposing battle line and use the weight of the sword and momentum of her charge to throw herself, followed by the spinning arc of death that was the returning upswing of the sword, clean through the ranks...

I am SO turned on right now.....


And Omni, that looks pretty good so far. Obviously, you can't properly test and refine the math until you finalize other aspects of your system, then you'll need to come back and calculate results to insure that you're getting numbers that actually make balanced sense.

I'll admit, I don't remember much of the technical aspect of higher maths. Unfortunately for me, I was always highly intuitive with numbers, and soon after school, I reverted fully to my old ways. I can make numbers do what I want them to do, and I can tell you why they aren't doing something in particular - but I do get lost in all of these means, and natural exponents, and Gompertz curves..... I just hack it out until it works.

[Endoperez]

Lokean, thanks for running the numbers in my example. I have no idea how you calculated them, but I'm glad that at least some people understand all the math Omnirizon is talking around.

How does this look? Does it satisfy the issues you guys were bringing up?

It seems much more intuitive, yes. Still, after Lokean's example I think even your first suggestion could be made to work.

I liked the term "arms" better than "weapon", because that could have included the armor you're wearing.
Also, if I understood this "moderator" business correctly, the "weapon" side will increase if your strength/dex/skill increase, details depending on the exact weapon. That could work very well.

[JimMorrison]

That's actually a beautiful mechanic to differentiate between a "finesse" fighter, and a "brute" fighter. Typically this is done with hard-coded gear limitations, but if you just make heavier armors give a stronger penalty to Dex primary weapons (still a small skill penalty to Str based weapons, too), then you give the player the choice of how much of their offensive capability to trade off for higher protection.