Synergistic & Lenticular Design

Frostorm

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If your elementals are dealing with physical damage (slash, blunt, pierce), might as well as let go the elemental exclusiveness tbh. You don't have air/fire/water/earth/light/dark/whatever. You have damage elements, focus on those.
I set it up so it's a trio of trios:

Corporeal Elements
  • Earth
  • Wind
  • Water
Ethereal Elements
  • Fire
  • Ice
  • Lightning
Divine Elements
  • Arcane
  • Holy
  • Shadow
"Elements" in this context is simply for thematic purposes, and not referring to "elements" in the RPG Maker database. Each of the above is basically a skill tree that focuses on its respective school of magic. Sorry for the confusion with using the word "elements".

"Elements" in the sense of the RPG Maker database is used for the purposes of damage multiplication, which is not what I'm focusing on for the purposes of this thread.

If we're talking about "elements" in the RPG Maker database context then I have a total of 8:
  • Blunt
  • Slash
  • Pierce
  • Fire
  • Frost
  • Shock
  • Holy
  • Shadow
Arcane spells deal true damage (no element). I was already on the fence on going from 6 -> 8 elements by adding Holy & Shadow, so I definitely didn't want to add a 9th... It boggles my mind how some games have 12+ elements... (not even referring to Pokemon, let's not go there lol)

Wind+Fire = Simoon
I just learned a new word today, thx! lol

Edit: Sorry, it wasn't my intention for this thread to turn into a topic about elements. There are plenty of threads for that. My goal was to explore the possible interactions of various game mechanics, with "elements" merely being one of many such mechanics.
 
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TheoAllen

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If I'm going by thematic elements, I'll probably do it like this.

Earth = Defense buff + Blunt damage
Wind = Speed buff / Non-stat debuff (blind) + Slash damage
Water = Non-stat debuff (poison, wet, suffocate, or freeze if you want to mix this with ice element) + Blunt/Slash/Pierce damage

Heat/Fire = Attack buff + Heat damage
Cold/Ice = Stat-debuff (slow, def down) + Cold damage/Pierce damage
Lightning = Multi purpose (stat buff/debuff) + Shock damage

Arcane/Holy/Shadow = Non-stat debuff (silence, MP leak, etc) + Arcane damage

Not every thematic element needs to do something to the enemy. Some just mostly focus on buffing, some damaging. If you're looking for a thematic skill tree. I'm doing similar to what you have done. My heat element type is mostly for offensive while the earth element one is for defensive. It basically "what role is this 'class' does". It could get even more interesting if your character has access to the two of those classes.

Arcane spells deal true damage (no element). I was already on the fence on going from 6 -> 8 elements by adding Holy & Shadow, so I definitely didn't want to add a 9th... It boggles my mind how some games have 12+ elements... (not even referring to Pokemon, let's not go there lol)
Frankly speaking, I don't think you need to even add holy/shadow as in a sense, arcane already cover both. Unless you have a specific idea that you couldn't let it go or you have an OCD that it must be trios/
 

Frostorm

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Well, I could easily remove Holy & Shadow from the element database while retaining the actual trees, as I did with Arcane. That would have no bearing on the trio-ness of it. There would only be a specific subset of enemies that are currently weak/resistant to Holy & Shadow damage and I wasn't planning on offering the player any Holy & Shadow resistance modifiers on gear and such. So yea, I probably will keep at it 6 elements in the database. I never liked the idea of having that many in the 1st place, hence my reluctance when I implemented it. The Holy tree is mostly healing anyways so the element wouldn't really have mattered save for 1 skill (Smite).

Arcane was in a similar boat as Holy in the sense that its skills were mostly caster utility and mana management spells, with only like 2 direct dmg spells. Which was why I had no issues giving it no element in the database. Guess I'll just do so for Holy & Shadow as well.

I guess I just saw so many people employing it on the forums, I was just kinda like... eh, why not. It sure feels better being back down to 6!

I also do keep each element tree focused on a certain mechanic or stat. Very pretty much like your examples with a few differences here and there. Most people already intuit that Earth is defensive in nature, Fire being purely offensive, and so on and so forth...

It's just that I have a friend who helps with writing/story for my project and he's constantly throwing ideas at me but w/o the perspective of a designer/dev. He never takes into account if a certain idea is feasible to implement, how it would work mechanically, or its effects on game balance. He just goes by "this would be cool!"... He's a great writer/world builder though, which is to be expected since he's our D&D DM. Holy, Shadow, Arcane was basically his idea, plus more such as Chaos, Celestial, and crap which I refused to implement. I really don't know how to deal with teammates like this...
 
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Frostorm

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So @Wavelength brought up a good point in this post (the thread in which I've foolishly closed lol)
Wavelength said:
Frostorm said:
In my game, DEF does the following:
  • Increases Max HP by 1 per point
  • Reduces physical damage taken
  • Reduces chance to receive a Critical Strike
  • Increases Block chance with a shield
So, I'd be very careful about using this kind of design. Essentially, characters become exponentially more powerful as their DEF increases, because not only do you have (for example) 5% more HP, but you also take 5% less damage and critical hits 5% less often.
I think you've mentioned your STR stat improves not only damage dealt, but also Crit Chance and Crit Multiplier? So this kind of design is very tricky, because each point of it is worth far more than previous points. Multiplying 100 damage by 105% (an arbitrary amount I chose for the purpose of example) three times for a 1 point gain in STR increases that damage to 116: a 16-point gain. Once you've gained 9 points it's 373 damage, and the 10th point would bring it to 432: a whopping 59-point gain!

The compounding effects aren't quite as strong with defensive stats because raw damage will shrink at a slower rate with each compounding factor, but you still have to be careful about the "triple accumulation" of effects that serve a similar purpose (allowing you to endure more hits) for such effects as Increased MHP + Reduced damage taken + Increased Crit Resistance.
I figured this post would fall close enough under the topic of "synergistic design" and could apply to other projects, not just mine. My question is this: How do you go about balancing your stats mathematically when they do multiple things while each thing they do may or may not be a variable in all situations?

Using the stats in my project as an example:
  • Strength
    • Increases physical damage dealt (double Dexterity's effectiveness)
    • Increases Critical Strike multiplier by 1% per point
  • Intellect
    • Increases magical damage dealt
    • Increases spell Crit & Hit chance by 0.1% per point
    • Increases spell Critical Strike multiplier by 1% per point
  • Dexterity
    • Increases physical damage dealt (half Strength's effectiveness)
    • Increases Counter, Crit, & Hit chance by 0.1% per point
  • Constitution
    • Increases Max HP by 1 per point
    • Reduces physical damage taken
    • Reduces chance to receive a Critical Strike by 0.1% per point
    • Increases Block chance with a shield by 0.1% per point
  • Willpower
    • Increases Max MP by 1 per point
    • Reduces magical damage taken
    • Increases healing received by 0.1% per point
    • Increases spell Resist chance by 0.1% per point
  • Speed
    • Hastens turn order
    • Increases starting Focus
    • Increases movement range
    • Increases Dodge chance by 0.1% per point
A good dev's goal should be to make every stat useful and ideally equally valuable, in my opinion. With that in mind, how do you guys go about balancing the value of your games' base stats?

Let's take a look at Strength vs Dexterity for instance. Notice how I mentioned that they both increase physical damage, but STR does so at twice the rate of DEX. This is reflected in the damage formula of most of my physical skills (e.g. "normal" Attack: (a.atk + a.atk + a.agi) / 3).

So let's say our hero has 10 STR and 10 DEX, this means his normal Attack would deal 10 damage. We also have to take his Critical Strike chance and Critical Strike multiplier into account since those are affected by DEX and STR respectively. Again, I will use the values in my project for consistency. Base crit chance is 5% and base crit multiplier in my game is 1.5x instead of MV's default 3x multiplier.

Formula provided by @Wavelength: normal_dmg * (1 + (crit_chance * extra_crit_multiplier))
Plugging in the numbers: ((10 + 10 + 10) / 3) * (1 + ((0.05 + (10 * 0.001)) * (1.5 + (10 * 0.01))))
Which simplifies to: 10 * (1 + (0.06 * 1.6)) = 10.96
We can round this to 11 damage. So now we have our baseline for which we can compare against incremental stat increases.

Ok, now let's boost our hero's STR by 10 and compare it to increasing his DEX by 10.
20 STR & 10 DEX:
((20 + 20 + 10) / 3) * (1 + ((0.05 + (10 * 0.001)) * (1.5 + (20 * 0.01))))
= 16.67 * (1 + (0.06 * 1.7)) = 18.37

10 STR & 20 DEX:
((10 + 10 + 20) / 3) * (1 + ((0.05 + (20 * 0.001)) * (1.5 + (10 * 0.01))))
= 13.33 * (1 + (0.07 * 1.6)) = 14.83

So in terms of raw damage, STR wins (a result I was expecting). Of course, this didn't take into account DEX's other secondary effects, which affect Hit and Counter chance in addition to the Crit example above. Basically, the question to ask is: Are the boosts to Hit & Counter enough to make DEX as valuable as STR?

If years of playing WoW has taught me anything, it's that Hit % should not be underestimated. 1% Hit is almost always worth more than 1% Crit, and that's assuming a 2x multiplier! (at least before you're Hit capped) Counter is also basically a free attack when you're hit by an enemy.

From a design standpoint, my goal's with DEX was to not just make it useful as an offensive stat, but also secondarily as a semi-defensive stat as well, hence its effect on Counter chance.

I think @Wavelength's initial point was that the offensive stats (at least in the way I have it setup) might end up being more valuable than the defensive stats. This is why I tried to give DEF & MDF so many secondary effects, in order to increase their value to something closer to STR/DEX/INT. Whether it'll be enough or is overkill remains to be seen, something further testing will eventually reveal. He also cautions the use of compounding effects, such as my use of +Max HP, reduced physical damage, +block chance, and crit evasion all wrapped up in the Constitution (DEF) stat. I hope this was as educational for you as it was for me!

Edit: I wanted to add that my game utilizes armor scaling for defensive calculations (i.e. damage mitigation via DEF & MDF). The formula being a modified version of Yanfly's:
value *= (100 + target.level) / (100 + armor) (where "armor" is DEF or MDF)

Obviously, this means DEF & MDF will become less and less effective as you stack more of it. This was another factor that led me to add all those secondary effects to these stats, in the hopes that they would remain valuable despite the diminishing returns.

PS: Do you guys think my stats are balanced overall? If not, how so? How do you design your stats and what do they affect? Do they multiply synergistically with each other like my STR/DEX example?
 
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Wavelength

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So @Wavelength brought up a good point in this post (the thread in which I've foolishly closed lol)

My question is this: How do you go about balancing your stats mathematically when they do multiple things while each thing they do may or may not be a variable in all situations?

A good dev's goal should be to make every stat useful and ideally equally valuable, in my opinion. With that in mind, how do you guys go about balancing the value of your games' base stats?
It's a good question that deserves a much more expanded discussion (few developers get it totally right), but to answer in a more summary manner:
  • I usually avert this issue by having one stat equate to exactly one benefit (more HP, higher crits, more frequent actions, etc.), and by avoiding the use of stats whose value depend on each other (such as HP and DEF) whenever possible
    • For example, I might remove DEF from the game entirely, or I might leave both stats in the game but make it so that you can't choose to build up your Max HP - it just increases a little with level and DEF is the defensive stat you elect to build
  • If you do go with stats that each offer multiple benefits, you can choose benefits that don't multiply off of each other (that does avert this issue, but it also makes the stat system into a sloppy mess) or you can accept that your balance target becomes much thinner by using multiplying benefits.
    • Essentially, you have to make sure that each stat offers the same number of multiplying benefits (this will keep the exponential curve of each stat similar, which is absolutely necessary), and you have to do as good of a job as you can of making the overall power of benefits between different stats similar as well.
    • This is extremely hard to do precisely. When games use such a stat system and still feel good to play, it's usually because the other parts of the game are tuned well enough that imbalances between different stats or builds won't ruin the experience.
  • As always when balancing stats, it's good to theory-craft the expected difference in damage dealt over time or total hits a character is able to survive (during a combat), and compare that against other stats which help increase damage dealt or increase tankiness... and then to test it out and make sure that your assumptions about how the flow of battle will go (assuming these stat setups) ring true.
 

Frostorm

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Essentially, you have to make sure that each stat offers the same number of multiplying benefits (this will keep the exponential curve of each stat similar, which is absolutely necessary), and you have to do as good of a job as you can of making the overall power of benefits between different stats similar as well.
This is a good point as each additional benefit the stat offers increases the exponential power by 1. Linear becomes quadratic which becomes cubic and so on. My issue is, how do I assign value to things like Counter, Block, Resist, or Healing since they're highly situational? I'd probably have to pick an arbitrary figure, but I'm having a hard defining said figure. Maybe some kind of average related to the frequency of these events? But that would again be highly dependent on the encounter type, putting back to square 1.
 

Wavelength

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My issue is, how do I assign value to things like Counter, Block, Resist, or Healing since they're highly situational?
To use a relatively simple but realistic example, imagine your "most average" character has a "bread and butter" ability they'll be using most turns, which deals 100 damage with a certain realistic combination of stats, and has a 30% chance to Burn enemies for a fixed 20 damage per turn for 3 turns, and imagine that your "most average" formidable enemy has that same ability. The "value" of using this skill in this setup is 160 damage (a strict calculation would remove a few points for the chance the enemy will die before Burning for 3 turns, and might remove a bit more to account for situations where the enemy is already Burning, but let's assume that enemies tend to survive a few hits and the player has another almost-as-good option to use on those turns).

Now, we can play with numbers like Counter, Block, and Critical Hit percentage (Healing is somewhat different, but know that it tends to exponentially compound with damage-reducing stats but not with HP; Weak/Resist adjustments are far too dependent on other parts of game design to calculate here) to see how adjusting those numbers will change the effectiveness of that damage. Remember - we need to first calculate what a change to (for example) Counter % will do to the damage value calculation, then we also need to calculate the conversion rate of stat points (e.g. Agility) into effect points (e.g. change in Evade rate).

So let's say 50 points of AGI increase a battler's chance to Block by 5%, increase their chance to Counter by 5%, and also increase their chance to score a Crit by 5%.
  • The value of the 5% Block Chance can be calculated by 0.05 * 160, or 8 points of damage that are being prevented on average.
  • The value of the 5% Counterattack chance is completely determined by the battler's damage output. Assume their counterattack will deal 50 points of damage: calculate this by 0.05 * 50 = 2.5 points of damage. However, since Counterattack requires an enemy to use a counterable action on you, you'd have to multiply this 2.5 by the average number of counterable actions you expect the battler to take per turn - 0.4 feels like a reasonable number, so multiply 2.5 by 0.4 to get a pithy 1 point of extra damage for the 5% Counter rate!
  • The value of the 5% Critical Hit, assuming crits deal double damage, can be calculated by 0.05 * 100 (which is the extra damage you'd receive from critting, as the Burn damage isn't doubled), or 5 points of extra damage.
  • If you feel that 1 point of damage dealt is worth 1 point of damage taken by characters, you can sum up the value as 8 + 1 + 5 = 14 points of damage change on your average turn for increasing a character's stat by 50. (You could then calculate the same for the three effects of STR, for example, to compare how powerful 50 points of STR would be instead.)
    • Importantly, note that no multiplication was necessary here because extra Block, Counter, and Crit chances don't make each other better (unless Counterattacks can Crit, in which case those two do multiply). Where all three benefits multiply with each other, you would calculate the Percent Change that each stat offered, compared to the base action of 160 points, so 5%, ~0.6%, and ~3%, and then multiply them together as 160 * 1.05 * 1.006 * 1.03 = 174.1 which is just 14.1 points of damage: the multiplicative effect barely added anything here because the effects were each so small, but for 50 points of STR those effects might be much bigger!
  • If you feel that 1 point of damage dealt is worth a very different value than 1 point of damage taken, you don't need to convert one to the other; instead, compare the total extra damage dealt (6) to the amount of extra damage you'd deal for having higher STR, and the total damage avoided (8) to the amount you'd deal for having higher DEF. If the two parts combine to about the same value as increasing one of the other stats (e.g. the extra damage dealt was 60% of what STR would bring, and the damage avoided was 40% of what DEF would bring), then the stat is well-balanced.
 

Frostorm

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However, since Counterattack requires an enemy to use a counterable action on you, you'd have to multiply this 2.5 by the average number of counterable actions you expect the battler to take per turn - 0.4 feels like a reasonable number
Looks like picking arbitrary coefficients for certain things is simply unavoidable. Looks like I'm going to spend this evening creating an excel sheet as a tool for game balancing lol.

I wonder, how many of you devs here theorycraft and number crunch the maths for your game like in mine and @Wavelength's posts? It's simple arithmetic after all, not calculus or anything.:kaoswt:
 

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However, since Counterattack requires an enemy to use a counterable action on you, you'd have to multiply this 2.5 by the average number of counterable actions you expect the battler to take per turn - 0.4 feels like a reasonable number, so multiply 2.5 by 0.4 to get a pithy 1 point of extra damage for the 5% Counter rate!
Looks like picking arbitrary coefficients for certain things is simply unavoidable. Looks like I'm going to spend this evening creating an excel sheet as a tool for game balancing lol.
Yup, at some point you do have to just try some numbers, and in this case the 0.4 was completely arbitrary. But if you pay careful attention to things like "how often do my enemies use a counterable skill" during playtesting, your number will be a lot less arbitrary! :)
 

Frostorm

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I just wanted to run the numbers from my example if Hit were taken into account. Base Hit is 95%. Adding on to the existing formula: normal_dmg * hit_chance * (1 + (crit_chance * extra_crit_multiplier))

Using the same numbers/stats from before...(10 STR, 10 DEX)
...and the same attack formula: (a.atk + a.atk + a.agi) / 3

Plugging in the numbers...
((10 + 10 + 10) / 3) * (0.95 + (10 * 0.001)) * (1 + ((0.05 + (10 * 0.001)) * (1.5 + (10 * 0.01))))
...simplifies to: 10 * 0.96 * (1 + (0.06 * 1.6)) = 10.5216 <- less than before due to Hit

Now let's raise our hero's STR & DEX respectively again...
20 STR & 10 DEX:
((20 + 20 + 10) / 3) * (0.95 + (10 * 0.001)) * (1 + ((0.05 + (10 * 0.001)) * (1.5 + (20 * 0.01))))
= (50 / 3) * 0.96 * (1 + (0.06 * 1.7)) = 17.632 <- vs 18.37 w/o Hit calculation

10 STR & 20 DEX:
((10 + 10 + 20) / 3) * (0.95 + (20 * 0.001)) * (1 + ((0.05 + (20 * 0.001)) * (1.5 + (10 * 0.01))))
= (40 / 3) * 0.97 * (1 + (0.07 * 1.6)) = 14.382 <- vs 14.83 w/o Hit calculation

As you can see the gap is smaller now. The difference before was 3.54 vs 3.25 after taking Hit chance into account. This means DEX's effect on Hit chance is indeed increasing its value! I know the differences may seem minimal here, but that's simply due to using small numbers. The example figures used for these stats would be equivalent to that of a naked level 5-10 character lol. The differences would be far more noticeable at higher levels and/or with gear and stat allocation taken into account. Also, Hit chance would be much more valuable to a dual wielder due to my game's -15% Hit chance penalty when DWing.

If anything, the small differences simply mean I've underestimated how much Hit, Crit, & Counter should be granted by DEX. Though this doesn't seem to be the case when using end game numbers where STR & DEX would be in the 100-200 range.
 

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