I'm looking for opinions/advice on which of these damage formulas to use.

[Aquachubolt]

I'm currently in the process of deciding on a standard damage formula. I've come up with two potential ones I want to use but I'm having issues weighing the pros and cons of each method.

Before getting to the damage calculations, I'd like to share the formulas I'm using to calculate the combat stats.

HP: (4 * Level * Base / 10) + (2 * Base) + Level = Stat Before Modifiers

MP: (4 * Level * Base / 100) + (Base / 4) + Level = Stat Before Modifiers

Other Stats: (2 * (Level-1) * Base / 100) + (Base / 10) = Stat Before Modifiers

Where Base is a integer that can be anything but realistically will only be around 10-150. These were designed with Formula One (detailed below) in mind, and are subject to change.

Now for the Damage Formulas:
Formula One: Is a multiplicative formula that multiplies the aggressor's attacking stat by the power of the skill, and then has that total divided against the defender's mitigation stat to get the pre-modifier damage.

(a.atk * Power) / b.def = Damage Before Modifiers

The benefit of this one is that it's nice and simple. It's clear how every stat operates and functions, and also helps less powerful skills scale into the later game and will keep things relevant for longer, along with every stat having a consistent power level and relevancy throughout the game. The main issue I see with this one is the fact that if values aren't balanced well it might result in a lot of chip damage.

Formula Two: Is a flat formula that adds the power of the aggressor to the power of the skill to get the pre-mitigation damage, and then multipies that by a fraction generated by the defender's mitigation stat to produce pre-modifier damage.

(a.atk + Power) * (1- (b.def / b.Def + 200)) = Damage Before Modifiers

The benefit of this one is that it's easy to compute your pre-mitigation damage in an instant. However, it isn't very clear how defensive stats would operate. The additive damage also means that lesser skills will fall further and further behind as HP totals scale higher and higher. The absorption based defense system would also make Def a near useless stat early game, and one of the, if not the, most important stat of all come late game, when armor values have started scaling to the point where you're getting obscene levels of damage reduction, which would in turn lead to an over reliance on Def mitigation methods and strategies revolving around it.

What do you think? Any suggestions? Perhaps a something can be taken from both of these formulas to make a better one? Looking for any and all feedback on this.

 

[bgillisp]

I actually use a version of #2 in my game, it was:

[(A.atk * (a.atk + power + a.level)) / (b.def + 20)] * 2 + a.level * 2

And I used a script to give enemies levels so that a.level made sense for them as well.

What I noticed is you have to keep your ATK values higher than your DEF values for any significant damage to occur, because if the two are equal, with 0 variance I usually did my attack * 2 + my level * 2 in damage. So I set it up so that armor and weapons of the same levels are such that the weapon is about 200% the armor's stat. This results in players doing decent damage to monsters still, except those that are supposed to have high DEF (or MDF).

 

[TheSkullWolf]

I love seeing people take the time to actually figure a good system out, not a fan of games that just have random numbers tossed in lol I know my feedback isn't any help, but a simple awesome work However, I found this link helpful when figuring mine out, kinda sent me the right direction I think. : https://www.gamefaqs.com/ps2/197344-final-fantasy-x/faqs/31381

 

[Vincent Chu]

(a.atk + Power) * (b.def / b.Def + 200) = Damage Before Modifiers

Pardon me if I'm misunderstanding the 2nd formula. Please correct me if I'm wrong, I'm fairly new myself and I'm purely looking at it from a mathematical perspective but wouldn't the 2nd formula actually mean that a higher def would actually result in greater damage bearing in mind that the damage is being multiplied by the def/(def +200)? For example, if the target's def was 10, you'd be multiplying it by 10/210 whereas if it was something much higher say 100 then you'd actually be multiplying the damage by 100/300. Wouldn't that be the opposite of what you would hope to achieve?

 

[Aquachubolt]

Pardon me if I'm misunderstanding the 2nd formula. Please correct me if I'm wrong, I'm fairly new myself and I'm purely looking at it from a mathematical perspective but wouldn't the 2nd formula actually mean that a higher def would actually result in greater damage bearing in mind that the damage is being multiplied by the def/(def +200)? For example, if the target's def was 10, you'd be multiplying it by 10/210 whereas if it was something much higher say 100 then you'd actually be multiplying the damage by 100/300. Wouldn't that be the opposite of what you would hope to achieve?

You are quite correct. It should have been (a.atk + Power) * (1- (b.def / b.Def + 200)) = Damage Before Modifiers.

 

[kaisielizen]

o-o why are such complex formulas (I want to write "formulae" for some reason) necessary? My "standard" damage formula is a.atk * 7 - b.def * 2 (same for standard magic attack but with mat and mdf). And I'm just purely curious.

 

[Vincent Chu]

I haven't got around to doing damage formulas yet but I was rumoured to have been quite mathematical back in high school (a long time ago). I also studied Maths and Further Maths at A Level. I wouldn't mind trying to explain maths related stuff (not programming though) if you message me.

 

[Aquachubolt]

o-o why are such complex formulas (I want to write "formulae" for some reason) necessary? My "standard" damage formula is a.atk * 7 - b.def * 2 (same for standard magic attack but with mat and mdf). And I'm just purely curious.

I don't think these formulas are too complex. Not the first one, at the very least. As for why I style them this way, it's mostly because I like to standardize it. I'm not so much a fan of any form of Atk-Def, and I don't like putting a coefficient in front of either; I like it when every stat has equal value in the equation. Am I explaining myself well here?

 

[kaisielizen]

I don't think these formulas are too complex. Not the first one, at the very least. As for why I style them this way, it's mostly because I like to standardize it. I'm not so much a fan of any form of Atk-Def, and I don't like putting a coefficient in front of either; I like it when every stat has equal value in the equation. Am I explaining myself well here?

No :\ In this context, I don't know exactly what you mean by "standardize" and "value," so I'm confused.

 

[Aoi Ninami]

"Value" in this context means one point of any stat is worth the same as one point of another; for instance, in your example of (a.atk * 7 - b.def * 2), gaining ATK increases damage output by 7, but gaining defence only lowers incoming damage by 2. The idea is to make the player's decision of "which stat should I upgrade?" more balanced.

However, this is largely a lemon. Regardless of the formula, increasing damage output and lowering incoming damage can't be directly compared to each other; which one is worth more (and therefore, what formula is best balanced) depends on how your game looks overall. If enemies have a lot of HP and fights take a long time, so that the player takes a lot of hits per fight, mitigating each hit by a small amount will really add up. But whether that's worth it also depends on what recovery options are available to the player, and so on.

Anyway, the general problem with additive formulae (yes, that is the correct Latin plural, although in English both are correct) is that if it's possible for the player to return to early areas in the middle or late game and fight early enemies, with additive formulae it's much easier to run into the situation where your DEF outweighs their ATK and they can't do any damage at all. There are a number of ways around this problem; I won't go into a lengthy discussion here. I'm using an additive formula in my game (the much simpler a.atk*2 - b.def) because I've decided this is best for my game after giving it a lot of thought.

 

[sciencewarrior]

(a.atk + Power) * (1- (b.def / b.Def + 200)) = Damage Before Modifiers

The benefit of this one is that it's easy to compute your pre-mitigation damage in an instant. However, it isn't very clear how defensive stats would operate. The additive damage also means that lesser skills will fall further and further behind as HP totals scale higher and higher. The absorption based defense system would also make Def a near useless stat early game, and one of the, if not the, most important stat of all come late game, when armor values have started scaling to the point where you're getting obscene levels of damage reduction, which would in turn lead to an over reliance on Def mitigation methods and strategies revolving around it.

I believe the additive damage will actually keep cheaper and weaker skills effects for longer. Let's create a hypothetical example with two skills:
Gust has a Power of 10 and costs 2 MP
Typhoon has a Power of 50 and costs 10 MP

Now let's assume the character has an attack of 10 when she learns Typhoon. That means that, by paying 5 times the MP, she increases her damage output from 20 to 60, a whopping 3-time increase. That will be balanced by the fact that she won't have a lot of MP to spend freely.

Several levels later, she has an attack of 90. Now Gust does 100 unmodified damage, while Typhoon does 140, a 40% increase for the same fivefold increase in MP. While she may have the pool to spare, you can create circumstances where the player will be able to one-shot an enemy with a Gust, or choose to conserve MP through a long stretch without rest stops, even if it means prolonging the fight for another round.

The defense curve you created is fairly interesting: https://www.wolframalpha.com/input/?i=plot+1+-+(x+/+(x+200))+from+x+=+0+to+999&wal=header

It takes a Defense of 200 to reduce the damage by 50%, and 800 to reach a 75% reduction. At lower levels, higher Defense is more important for survivability, while at higher levels, HP starts to dominate. Dividing instead of subtracting the defense factor blurs the difference between high-Def/low-HP and low-Def/high-HP monsters, but I feel it does simplify balancing a lot by removing the cases where the party simply can't damage a boss or takes absolutely no damage from mooks.

Other Stats: (2 * Level-1 * Base / 100) + (Base / 10) = Stat Before Modifiers

As an aside, this could be simplified as (Level - 1) * Base / 50 + 5 * Base / 50 = (Level + 4) * Base / 50

 

[bgillisp]

@sciencewarrior : That's a nice curve there. What I've noticed myself is those of us using this kind of formula also have lower stats in our games. For example, in my game, any stat over 200 is rare. In fact, it is so rare, it takes usually the ultimate weapon or 2nd best weapon to hit it for ATK (or MAT), and same with DEF.

However, here are what I've noticed are the advantages for that formula:

1: Almost impossible to do 0 damage. I have gotten it to do 0 damage, but that usually takes a DEF of 999 vs an ATK of 1 or something equally silly.

2: Buffs/debuffs feel more worthwhile. With a straight additive formula, like 4 * a.atk - 2 * b.def (the default), it's hard to justify spending a turn to raise your DEF, as that usually just results in 20 less HP damage taken or so. 20 Hp is pretty meaningless if you use the default HP curves, as those give you pretty high HP already.

3: You can get high damage easily, just give an enemy 1 DEf or 1 MDF. I've gotten 6K damage with a critical hit and about 100 ATK that way.

 

[kaisielizen]

"Value" in this context means one point of any stat is worth the same as one point of another; for instance, in your example of (a.atk * 7 - b.def * 2), gaining ATK increases damage output by 7, but gaining defence only lowers incoming damage by 2. The idea is to make the player's decision of "which stat should I upgrade?" more balanced.

However, this is largely a lemon. Regardless of the formula, increasing damage output and lowering incoming damage can't be directly compared to each other; which one is worth more (and therefore, what formula is best balanced) depends on how your game looks overall. If enemies have a lot of HP and fights take a long time, so that the player takes a lot of hits per fight, mitigating each hit by a small amount will really add up. But whether that's worth it also depends on what recovery options are available to the player, and so on.

Anyway, the general problem with additive formulae (yes, that is the correct Latin plural, although in English both are correct) is that if it's possible for the player to return to early areas in the middle or late game and fight early enemies, with additive formulae it's much easier to run into the situation where your DEF outweighs their ATK and they can't do any damage at all. There are a number of ways around this problem; I won't go into a lengthy discussion here. I'm using an additive formula in my game (the much simpler a.atk*2 - b.def) because I've decided this is best for my game after giving it a lot of thought.

Thanks so much for explaining! I understand now. My battles do synergize well with my formulae - and I've done a lot of testing and all that. But I do see the value of your formulae, too.

 

[Aquachubolt]

Dividing instead of subtracting the defense factor blurs the difference between high-Def/low-HP and low-Def/high-HP monsters, but I feel it does simplify balancing a lot by removing the cases where the party simply can't damage a boss or takes absolutely no damage from mooks.

Can you explain what you meant by this? I'm a bit confused.

 

[Aquachubolt]

I've also been experimenting with hybridizing the first two formulae, and I've come out with something I'm quite pleased with.

Formula 3: (a.atk * (a.atk / 2 + Power) / (b.Def / 2) * (1- (b.def / (b.Def + 200)) = Pre-Modifier Damage

This one adds half of the users attacking stat to the skill Power and then divides the damage by half of the Defenders Defense, before applying the absorption formula from Formula 2.

Thoughts on this one? Is it better or worse than either of the other two do you think?

 

[sciencewarrior]

Can you explain what you meant by this? I'm a bit confused.

Sure! Since the Defense factor reduces the attack by a certain percentage, it doesn't make much of a difference giving a monster 200 Def and 500 HP and another 0 Def and 1000 HP. In an additive formula like Aoi's, on the other hand, you may discover that the first monster is basically invincible, because the heroes can't deal enough damage to overcome its Defense.

I believe formula 2 is fine as it is; adding more factors won't necessarily make it better. Fine tuning is what will make your game shine.

 

[Aquachubolt]

I believe formula 2 is fine as it is; adding more factors won't necessarily make it better. Fine tuning is what will make your game shine.

The hybridized formula is the result of doing a few simulated battles. Basically what ended up happening is that both formula one and formula two ended up doing chip damage when stacked up against the comparatively high HP totals the current formula generates.

One such example calculation:
Let's say there's a 1v1 encounter, with two level 50 actors. We'll say for the sake of this that the player actor has a relatively high Attack stat base of 125, and that the enemy actor has average defensive stats of 80 base for both Def and HP. We'll also just assume the player character has a weapon with 50 Atk equipped. We'll also use your Gust and Typhoon examples from before, so 10 and 50 Power, respectively.

This equates to;

Player Actor- 186 Attack

Enemy- 1,810 HP, 86 Def

With formula two, the player would deal:
Gust- ( 186 + 10) * (1- (86 / 286)) = 137
Typhoon- ( 186 + 50) * (1- (86 / 286)) = 165

With formula three, the player would deal:
Gust- (186 * (103) / (43) * (1- (86 / 286)) = 312
Typhoon- (186 * (143) / (43) * (1- (86 / 286)) = 433

With formula 2, it would take upwards of almost 11 turns of using Typhoon to kill it. Formula 3 allows that same enemy to be killed in 4 turns with the same move, which significantly speeds up what would otherwise be a sluggish battle.

I suppose this could be remedied by changing the formula for calculating HP, but I rather like it how it is now, and so I think Formula 3 would be the best fit...

You know, I think typing all this out has solidified how I feel. Thank you all for your input, I believe I'll be going with the hybrid formula.

 

[Vincent Chu]

This is just my opinion but I would prefer it if the power of the skills themselves played a bigger role. As your example shows, the relative difference in damage output doesn't seem that great considering that Typhoon has so much more power than gust. While such a formula is great for retaining the usefulness of cheaper/weaker skills, the more powerful skills appear rather unnecessarily wasteful.
However, this can be compensated for by simply inputting higher power values for different skills to justify their usefulness without having to alter the formula itself.

 

[Kes]

@Aquachubolt Red text (and blue text) is reserved for mods. You can read our Forum Rules here - number #11.
[mod]Please edit your post #15 to remove the red text.[/mod]

Also
[dpost]Aquachubolt[/dpost]
If you want to add something, simply edit your earlier post.

Thanks.

 

[Aquachubolt]

a.atk * (a.atk / 2 + 5) / b.def / 2 * (1- (b.def / (b.def + 200))

Ok, quick question. I just started actually implementing the new formula, and the above is what I'm putting into the Formula box in the database. However, this is causing the attacks to do zero damage. Can someone please tell me why?