How do you begin to balance your numbers and formulas?

Seirein

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Worth noting is that, in many games, the effect of increasing Defense is often unclear. In games with more complex damage formulas, you often can't tell how much an increase in Defense will actually reduce damage by.

In some other games, the problem is that Defense doesn't have a major effect point-by-point. The typical Dragon Quest damage formula is something along the lines of "(Attack - Defense/2)/2" -- which means you need four points of Defense to negate one point of damage. You can get armor upgrades that will have zero impact because they don't give you enough of a Defense boost to get over that four-point hurdle.

And as an extra point: Attack is often consolidated in one piece of equipment, the weapon. You usually get several pieces of armor in RPGs for your Defense. Therefore, players can often use a lower-Defense helmet or shield with offensive benefits and still remain roughly on par with how durable they'd be with pure-Defense gear.
 

Aesica

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Worth noting is that, in many games, the effect of increasing Defense is often unclear. In games with more complex damage formulas, you often can't tell how much an increase in Defense will actually reduce damage by.
Does the player really need to know the exact details though? I mean, if everything is properly balanced in your game, all they should really need to know is that "this piece has more DEF than that piece, so it's an upgrade in terms of reducing physical damage."
 

Tai_MT

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Agreed to your point about combats that end quickly favor ATK over DEF, but complete disagreement to your point that DEF lets you tank big hits while HP lets you tank many hits. I believe it's actually the other way around in an additive formula (and neutral in a multiplicative formula).

Because DEF is a stat that provides value on every hit you take, whereas HP is a value that is raised once and provides no extra value until you get a (free) full heal, e.g. at a save point or an Inn, the value of DEF against a single hit needs to be lower than the value that HP brings (as a whole).

For example, in an RPG where the formula is a.atk - b.def and all numbers are relatively small, you'll usually see DEF values raised by like 2 on a level-up, whereas HP will be raised by 10 or more. Sometimes the difference is even more extreme and it's like 100 HP or 2 DEF (this is usually where stats' magnitude is multiplied via formulas, such as the Epic Battle Fantasy series where you have stats like 7 ATK, 5 DEF, and 2,000 HP).

Putting this into the perspective of dungeon run vs. boss battle, it means that HP is actually the stat that you want to build in order to survive huge hits from a boss, since (using your own formula) 10 HP will help you take 10 more damage from a huge single hit without dying, whereas 2 DEF will help you take just 2 more damage from a huge single hit. Over the course of a dungeon where you're sustaining, say, 30 hits on your way through, though the 2 DEF will decrease your total damage taken by 60, which is a lot better than adding a measly 10 HP to your total.

Long story short: HP for surviving huge hits, DEF for tanking many hits over time (in additive formulas). I believe this holds true under any circumstances (except wildly imbalanced stat systems) and any factors, though I'd be open to counterexamples.

For multiplicative formulas, since the DEF stat is essentially multiplying your "Effective HP", I believe that ideally you want to sort of raise both in equal proportions in order to most effectively survive either big hits or repeated hits.

The reason I think that way is because of the way most of these RPG's are designed. You'll get into roughly 25-35 encounters in a single dungeon and one shot most of the enemies in those encounters. You'll have a few where you take some damage (especially if you're under leveled), but the damage is already so minimal that those hits really don't matter to most players (players will only heal up from the dungeon damage at certain thresholds where they think they'll need the extra HP). So, the amount of HP typically just matters for the dungeon crawl itself. How many hits can the player sustain before needing to cast "Heal" on someone. I don't deny that DEF plays into this, but in general, that's the way HP seems to work. It's a "fuel meter" to get you through the dungeon. Essentially a resource that needs to be managed. The fewer hits you take, the less "refilling" of that meter you need to do. You can accomplish this in many ways. Overwhelming attack... formulas that allow you to zero out damage via a defensive stat... skills that nullify/reduce damage... raising evasion... lowering enemy hit rate... there are a lot of methods by which to extend your HP, but in general, it's use is tied to "tanking many hits". But, DEF on the other hand... if the stat itself never comes into play (due to ending battles quickly, as we've discussed), then its purpose is to tank those massive hits that Bosses do. Most RPG design follows these two rules. HP tanks all the really tiny hits from the regular enemies in a dungeon. It's rarely necessary to refill this during a dungeon until close to the end... or you rarely refill it more than once. However, if the boss has an AOE or a Damage Spike attack... The DEF stat comes into play to keep everyone alive during that combat. The higher your DEF in that instance, the less those Damage Spikes will hurt you. In essence, the DEF stat isn't "tanking many hits" for you. It's tanking a few hits that are necessary to tank to survive.

For example, you have four party members, you trudge through the 35 encounter dungeon... you've sustained roughly 300 HP damage (in this instance, we'll give everyone 800 HP) across all four members equally (just for the sake of the example) so everyone is only missing 75 HP. Your defense came into play on each of those hits, but you've sustained only maybe half a dozen to a dozen hits during the whole dungeon run. Limiting how much damage you took wasn't near as important as those enemies not hitting a "threshold" to cast Heal magic... or drop a consumable. Their HP let them tank the many hits. But, then they heal up just before the boss (most players do this, just to have the best chance of winning, even if they're a few HP short... not sure why, but it's interesting :D ). They step into the boss room... and that boss has a single attack that does a lot of damage. The party doesn't have to tank "many hits" now. They have to tank a few hits that will do a lot of damage. If that boss uses his big attack every few turns; every third turn, lets say (I'm using this just because bosses usually have 3 or 4 attacks, and we're just saying they use everything evenly and randomly for the sake of argument), then the party has to contend with this large hit every few turns and it will result in needing a heal after each hit... unless the player has high defense. That high Defense will tank the powerful hits to prevent the player from hitting the "threshold" of needing to heal and run their resources dry quickly.

I'm sorry if that doesn't make a lot of sense. Basically, I'm using the concept of "when does the player need to act/react" for how these stats work. In practice, they won't need to act/react much at all in the dungeon because their HP won't reach the "threshold" for requiring action. Thus, the HP is being used to tank the many hits they'll sustain along the way. But, in a boss fight where spikes of damage can occur, they will be "acting/reacting" more frequently and healing away that damage far more frequently. That is, unless they've got higher defense to tank the large hits that require the frequent heals.

Does that make any more sense?

Formulas that de-emphasize defense in such situations make those heals even more frequent in boss fights than they might otherwise be (like the default ones for the RPG Makers). It's generally why I prefer the trade off to those that use simple addition and subtraction. My Defense isn't de-emphasized and a player can use it to heal up less often during a boss fight, but the trade off is that sometimes they will do zero damage to an enemy or the enemy will do zero damage to them.

I genuinely love how we're focusing in on the intricacies of comparing stat allocation to football team management :D :D :D (I wonder what the Cleveland Browns' stat allocation looks like? :p)

There's probably something to be said about the effects of grinding alongside an all-out attack strategy, and comparing it to me (a lanky 6'0", 160-pounds-soaking-wet nerd with skilled hands and great gamesmanship, but average athleticism) taking on the NFL's dumbest running back, and how he'd still crush me (both in terms of winning a football game, and literally) no matter how much I outsmarted him on the field. At some point we probably have to be okay with letting players brute-force their way through obstacles if we're allowing them to grind.

I don't mind letting players grind if they want to. Or even Brute Force things. If a player chooses to spend a little bit of extra time to gain some extra stats for a perceived edge, I have no problem with that. I just de-emphasize that edge in boss encounters where stats count for less than they do in normal encounters (because the bosses use gimmicks instead of just tanking a ton of hits and dealing a lot of damage). I also removed all stat gain from levels too... so you're getting indirect power from Levels now instead of Direct Power. I ended up putting the stats behind equipment (where the largest boosts will come from, thus making balancing a little easier on me as a dev) and doing Quests (as incentive to do as many Quests as possible rather than a ton of combat to then breeze through a Quest).

Personally, I just prefer if all stats are useful for something in a game. As a player, I find it a little annoying that I can equip a piece of armor that has 50 defense on it... but it only results in like 20 damage being reduced from normal hits. Because now, at that point, I'm thinking, "the game is lying to me about how effective this is". I just personally dislike the idea of a stat point that is useless.

But the larger point I was making was that, unless you're grinding to extreme levels and getting some stats automatically on level-up, an all-out attack strategy where you're dumping all of your points/equips/whatever into ATK or MAG is unlikely to work against bosses, where it really counts. Even if you could kill a boss in 3 turns (unlikely), if that boss can one-shot your party with his AoE, it's not going to matter. Sure, it's nice to wipe every normal encounter with a single skill; sure, it's nice to be able to grind more quickly by doing so; sure, that's 95% or 98% of battles... but that glass cannon approach won't cut it against bosses in any turn-based game, so the player is going to have to invest in some DEF if they want to progress in the game. (With that said, games should certainly do a better job lining up the things that you have to do, with the things that feel good!)

Yep, I agree. But, many of those games have a default amount of DEF they give you at each level and it's usually enough to get you through boss encounters by using an all-encompassing "brute force approach" against everything. My larger point is that for those 2% of instances when defense matters... you're investing a lot of resources into that. You buy the equipment, you maybe distribute stats into Defense, just for those 2% of encounters. In fact, you're spending the vast majority of your money for the defense there. That 2% can also be negated by simply overleveling. In Final Fantasy V, I personally had this issue. The minute the game gave me jobs and a ship, I went looking for the easiest way to get JP so I could max out as many jobs as possible, so I could swap them in and out as necessary or use their buffs that were useful. The side effect of this? I maxed out the first set of crystals fairly early into the game... and I was level 38 when I did so. I proceeded to steamroll the next 10 bosses in the game in one to three hits. Even with the low level equipment. Your example hinges on the boss hitting your party with a powerful AOE. But, if not all bosses will do that, then the player can still "brute force" the boss, not worry about defense, and just use "Revives". This is a tactic I use in Pokémon against the Elite Four when they're powerful. Gain more levels? Grind? Switch Pokémon? Nope, I saved all the money I got in the game, spent it on nothing except Pokeballs I might need... and when I got to the Elite Four, I dumped it all into Revives as they're cheap, can be used every single turn if necessary, and keep me in the fight long enough to get hits in or to run the enemy dry of their most powerful skills.

One of those examples is one in which I wasn't trying to break the game, but did so as a side effect of doing something else I wanted to do... The other example is one in which I broke the game by not grinding and by simply dumping all my resources into just coming back from the dead.

In the case where the player's ability to allocate stats is less (such as a system where stats are given automatically for level-ups, and the player only uses equips and/or small bonus point allocations to adjust stats), yeah, then the all-out attack strategy can be fine, and it probably feels more appealing to the player. But even then, from a raw mathematical standpoint, the stats seem to be more balanced against each other than you believe they are (as discussed a lot above, as well as in @Aoi Ninami 's post).

I think it largely depends on the combat system being used. What I've found through most of my gameplay of RPG's is that once you step outside of the "predicted realm" of where the dev thinks you should be for any given area... the stat importance of everything other than "Attack" drops off the map. You don't need Defense because you kill everything in one hit (or close enough to it, that it doesn't matter). You don't need MP, 'cause you're doing very little healing or even spending it on using Magical Nukes. You only need a single point of speed more than any enemy in order to get first turn against them (unless turn order is that of active time battles). You don't need Magic Defense either, 'cause you're one-shotting things.

It largely begs the question of, "What if a player knew they could nullify all damage from the baseline enemies with Defense instead of relying on raising their attack to end the battle quickly? Would they do it that way?" I mean, we used to have cheats for "God Mode", which simply made you immortal and immune to damage... which were very popular. Often more popular than cheats that let you kill everything in one hit... So, it begs the question. Which is a better design perspective? Are they equally valid? Should it be an option to nullify 100% of damage through Defense in the same way you can nullify 100% of damage through attacking and killing an enemy with a single hit?
 

Sednaiur

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In my opinion, this topic asks a very important and interesting question.

I love to think about the many different ways, one can balance a game, battle-wise, so I do so, pretty often.
The first RPG I played was a super simple one, called "Seiken Densetsu" on the Game Boy (you start alwas small, right? ^^) where you had something along the lines of ATK - DEF and you got 999 HP on max level. Back then this system intrigued me and I then later encountered it again in the Playstation Game "Gekka No Yasoukyoku" where you lowered taken damage 1 by 1 through defense and dealt more damage the same way.
And then, one day I played "Final Fantasy 7" where I first thought you would have the same system aswell, meaning you would need 500 attack to deal 500 damage or 800 defense to reduce 800 damage to 1. And when I found out that it is not like this, that was when I first thought about this kind of balancing the first time. Ever since then, I am very interested in how a game I start to play may be balanced. Is it percentage-based? Or simply 1 by 1 based? Ever since my first RPG I have encountered many different ways of damage formulas, where my newest game "Diablo 3" has the most ridiculus one starting at 3 to 4 damage per attack on level 1 and demanding a lunatic 99.999.999.999.999.999 damage (more than a quadrillion) from you per attack to even beat normal enemies in a few shots on a level-140 great rift. xD So, yes, the numbers thrown around mean a lot to me. Too high numbers are just screentrash, while too low numbers can be too simple - thus, boring for me.

When I start to think about balance and numbers, I take these following things into my approach of such topic:

-Is my game meant to be for those who like to win battles with a lot of tactical approach, like buffing/debuffing, exploiting elemental weaknesses, etc? Or are they rather meant to have an easy time a la Final Fantasy 5/6/7 where I can never really be underleveled and where I can choose the skills I prefer to win with.

-Is my game meant to be a wannabe-die hard, where I lose by doing two mistakes back to back, or rather easy and soft?
Do I like a nice and warm balance between giving possibilities and handing restrictions aswell, like the player being able to grind their way to victory if they so desire, or do I hand them caps everywhere?

- Do I like a simpler way of putting values into everything, like having only 30 HP at level 1 and deal only around 10 damage, while capping it out at three-digits in the endgame at most? Or do I want to have walls of numbers flying around for no meaningful reason, like sand in the desert?

I think of what could be interesting to have and what is not really common in other games. I dislike digital salad or damage trains, so my personal preference, for example, is to begin with around 80 HP, 60 MP and a dealt damage of around 12 per normal attack at level 1 and letting that grow towards around 3500 HP, 800 MP and a dealt damage of 2200 per normal attack at level 100, while also using damage caps through plugins.

A damage formula I am using, is:
Code:
500 * a.atk * 0.02 * a.level * 0.02
With this formula a level 10-character will deal 20 damage while attacking with an unarmed 10 base-ATK.
Of course, this is just the offensive part and the part that takes the opponent's DEF into account has to be added, but this is the simple idea behind it.
This code may be simplistic, but it is easy to understand even for people like me who know nothing about algebra and programming so far. :p (but I am willing to learn, as this is the only way I could even do an RPG on my own)

Since it has it's own base value (the 500) the "a.atk" becomes free to be used as a multiplier instead of being the base value.
It also uses the character's level to further multiply the damage in a way that it will become more useful the more levels you have.
So, depending on your preferred gamestyle, you may find it useful to increase the use of every ATK-point over the course of the game to prevent the need for higher statboosts just to have a meaningful impact on the damage output of a skill or weapon. A simple "ATK+6" already might do it.
 

Aoi Ninami

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A damage formula I am using, is:
500 * a.atk * 0.02 * a.level * 0.02

I'm not sure why there are three constants in there. Quantities multiplied together give the same product regardless of order, so you could just have written "0.2 * a.atk * a.level" or, even simpler, "a.atk * a.level / 5".

This may work for your game, but one thing I immediately don't like about this formula is that for low-level characters, increasing their ATK does nothing unless it reaches a multiple of 5. For instance, your Level 1 hero has 10 ATK and sees a +4 weapon in a shop. That looks like it should be a good buy, but it's not increasing his damage output at all. How do you get around this problem?
 

Prescott

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Here's what I did. This may not be the best way to do it and I definitely have a little bit more balancing to do because a little bit is based off assumption of where the party will be at strength wise at a given point in the game, but it provided an amazing start point for someone who has technically never made an RPG in RPG Maker before xD

I basically used a lot of math and a linear regression calculator to match up a party's average damage output per turn (with 9 normal attacks tested and 1 critical since it's a 1/10 chance to crit in my game) to the enemy's HP. I did this for the party being at level 1, 10, 25, 50, and 80. The linear regression came in to play when I was scaling the numbers in between those levels instead of having to do test battles to get averages for every single level. Then, I decided how many turns it should take to defeat an enemy and at what level and what size of party, multiplied that by the damage output of the party, and made that the enemy's HP. I then found the other parameters (def, agi, etc.) that worked for one enemy that was meant to be mid-level, and then calculated the percentage between that and the HP. Used the same formula to apply to the other enemies. I've been alpha testing recently and I've only had to balance a few things, only slightly nerfed 1 enemy and greatly buffed a bunch of the skills. I only did the average party damage thing with normal, physical attacks, meaning that I wanted the amount of turns it would take to defeat the enemy to be without anything equipped, so skills and better weaponry would help a lot more especially in battles with more than one enemy.

That's a pretty long way to go about it, but it really did work wonders. I have a lot of enemies and a lot of different weapon/armor configurations in my game, and so far it's worked almost perfectly for all of it.
 

Sednaiur

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I'm not sure why there are three constants in there. Quantities multiplied together give the same product regardless of order, so you could just have written "0.2 * a.atk * a.level" or, even simpler, "a.atk * a.level / 5".
I did not write the full formula, because I gave a simpler example, but I see your point regardless.
The full formula I use for my basic physical attack is
Code:
20 + (500 + v[x] * 3) * a.atk / 50 * a.level / 50 - b.def - (b.def * b.level / 50)
I just recently included the variable into my formula, but it was always meant to contain a variable, I just didn't know earlier, how to do that. :p
My idea behind this formula is as follows:
20 raw base damage so there is someting to be dealt.
The 500 after that is the base number meant to be increased by a variable used for this kind of skills only. The variable itself is increased by different means, like solved quests, learned skills, etc. There is no need to ever change any of the multipliers after it in any basic formula, save for special attacks that use totally different formulae anyways.

With my formula, you increase your actor's dealt damage by:
The actors level
The actors equipment
Stat upgrades along the lines of +1 consumables
Raising special variables due to reached archeivements with quests etc.

I may be inexperienced but formulas like "a.atk * a.level / 5" just dosn't cut it for me.

This may work for your game, but one thing I immediately don't like about this formula is that for low-level characters, increasing their ATK does nothing unless it reaches a multiple of 5. For instance, your Level 1 hero has 10 ATK and sees a +4 weapon in a shop. That looks like it should be a good buy, but it's not increasing his damage output at all. How do you get around this problem?
My characters may have only 10 base ATK but they come equipped with a weapon of at least additional 10 ATK each, meaning they start with at least 20 ATK. With the above formula...
a level 1 actor with 20 ATK (10 base + 10 equipped weapon ATK) deals 19 damage to a target with 4 DEF.
a level 3 actor with otherwise same stats deal 27 damage to the same enemy, meaning a 4 damage increase per level.
a level 3 actor with 24 ATK (10 base + 14 equipped weapon ATK) deals 30 damage to a target with 4 DEF, so a +3 for a weapon with 4 more ATK.
I wouldn't say that it is a huge difference while being on level 1, but realistically speaking you reach level 3 in mere minutes, meaning a damage increase by 1 for each point of ATK. Still, it depends on many factors like the skills you have, as other skills also may have other formulas, like a roundhouse strike hitting all foes, dealing only around 60% damage, or a charged hit that may come in last but dealing around 170% damage.
 

Dagothe

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A funny damage formula I use that scales the max damage with max Hp;

Math.max(1, b.mhp * (1 - (b.def / (a.atk*1.5 ) ) ) )

What this does is make your minimum damage 1 to avoid negative numbers against high def enemies with low atk score, and max damage will be a stat modified percentage of defenders max Hp.

Say A, Hp = 120, Atk = 24, Def= 24
Fighting monster B, Hp = 150, Atk 30, Def = 30

A attacks B, doing 25 Hp dmg (if B had 120 Hp, the dmg would have been 20).
B attacks A, doing 56 Hp dmg (if A had 150 Hp, the dmg would have been 70).

Say C, Hp = 600, Atk = 120, Def = 120
Fighting monster D, Hp = 10, Atk = 130, Def = 130

C attacks D, doing 3 Hp dmg.
D attacks C, doing 231 Hp dmg.

If C attacks B, it does 125 Hp dmg.
B attacks C, doing 1 Hp dmg.

This formula allows the attack damage to grow in strength as enemies become stronger as well as yourself even if the difference between your attack and enemies defense is still the same as lower levels, it prevents killing strong enemies with low Hp from dying in 1 hit to remain a challenge, but it also allows for 1 hit kills if the difference between defense and attack is great enough. One down side I suppose is enemies over 10k Hp can recieve over 9999 damage, but Math.min() function easily lets you cap it at a desired number.
 
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Milennin

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For stats, I do like to start off in the low double digits (between 10 to 30), and then generally multiply by 10-20 times that value at level 99, depending on how much I want the level ups to count. Starting too low (basically everything in the single digits), I find that every single point of growth can add so much power that it can easily throw the balance off. Low double digits working best, in my experience, and still leaves plenty of room for growth.
In the end, pretty much anything could work, since what really matters are your damage formulas.

For my most recent game in MZ, I went with "a.atk" as my base damage formula for Attack. I'm not even going to bother with defence, because honestly, it doesn't really matter since it's an invisible stat anyway, and I never differentiate between different types of damage in my games. Characters always hit their attack stat as the default value, which feels right. The heavy hitters still hit hard, and the supports hit less. No need for defence to add that extra layer of nothing.
For Magic Skills, it really depends on a lot of variables, but my basic single-target damage skill is basically like "a.atk*2.5", while the AoE version of that for the same MP cost would be more along the lines of "a.atk" or "a.atk*1.5", kind of depending on the secondary effect of that Skill. Can't really set a strict baseline for what the right multiplier is on Skills, because MP cost, targeting, conditional damage and secondary effects must be taken into account. I generally just go by feeling, then test it out, and fine-tune the numbers if needed.

For monsters, it's pretty similar to actors. You look at how many turns you want the average monster to survive basic attacks from at the level you expect actors to be at when the monster shows up. Then how many skills they should be able to take before dying. Adjust HP accordingly. There's no right or wrong, it all depends on your combat system. For quick, grindy combat, you want to set it to die fast, for combat that relies on comboing skills, you want them to last at least a few turns.
 
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Seacliff

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Depends on the game and all that.

I liked Yanfly's solution to using the League of Legends damage scaling. Damage = a.Strength / (100 + b.Defense). It features decreasing returns when min-maxing both strength and defense, so it's easier to balance around.

Lower numbers work, but when you're working with lower numbered stats, small changes have really big effects. To work around this, I tried using the Dragon Quest formula of using division in damage formulas rather than multiplication. (Attack/2 - Defense/4 as opposed to Attack*4 - Defense*2). This works pretty well, as it features lower numbers that are easier to manipulate.
 

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