How do you begin to balance your numbers and formulas?

@Aesica Ooooh. Yeah, I mathed that all wrong. Yeah, yours is probably the best for what he's asking then. At least, for someone like me who likes a system that has that self-explanatory feel. In fact... I may tinker with these numbers and use this instead... if ya don't mind ^_^;; I like the built-in diminishing returns aspect.

I just... don't trust things to do PEMDAS right! Also I feel better about compartmentalizing things. Like if I want to add a modifier here and there later on I can keep things separate (and add more and more parenthesis!) and make sure the new bonus/resistance happens where I want it to.
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You can pretty much make any kind of growth curve match 2 specific points, this should not be the issue here.

Also, you can still choose the impact of DEF on the formula, if you are planning to use that stat in the first place. Some creators may favor a damage formula where ATK and DEF offset each other, so using the same spell against a target whose DEF matches the attackers ATK will always do the same damage.

Using Jesse-PVGames' formula as an example:

(a.atk / 2) * (2 * a.atk / (a.atk + b.def))

Assuming attackers ATK and defenders DEF are equal, that formula would result in a.atk/2 damage, proportionally increasing with stats. Now, if you want the damage to 80-fold while the ATK only 10-folds, one way to do that could be adding an exponent to a.atk. Find out to what power you have to raise 10 to to get 80 (-> log10(80) ) and you have your formula:

Math.pow(a.atk, 1.9) / 2 * (2 * a.atk / (a.atk + b.def))

Right now, the formula results in 226 damage at 25 ATK, which is a bit much, so you could add a factor to bring it back down to 80:

0.177 * Math.pow(a.atk, 1.9) * (2 * a.atk / (a.atk + b.def))


This result is probably not really suited for very low ATK values (values below 3 will mostly result in 0 damage), which you may not need in the first place. Since the damage is mainly determined by the attackers ATK in this example, this stat now has significantly more influence in the damage formula than the defenders DEF. If this turns out to be a problem in your game, you could consider to factor in level or skill rank instead of raising ATK.

 

There's a school of thought that asserts this is not diminishing returns. The concept is sometimes called "Effective HP", and the theory is that in your system, for example, if you can take X hits with 0 defense before dying, every 100 points of defense will allow you to take X more hits before dropping. So if you have 10000 HP and the enemy is dealing 1000 damage:

• 0 defense causes you to take 1000 / 1 = 1000 damage, so you can take 10 hits.
• 50 defense causes you to take 1000 / 1.5 = 666 damage, so you can take 15 hits.
• 100 defense causes you to take 1000 / 2 = 500 damage, so you can take 20 hits.
• 200 defense causes you to take 1000 / 3 = 333 damage, so you can take 30 hits.
• 300 defense causes you to take 1000 / 4 = 250 damage, so you can take 40 hits.
• 400 defense causes you to take 1000 / 5 = 200 damage, so you can take 50 hits.
• and so on. +100 DEF = 10 extra hits that you can absorb.

If you think of it this way, it actually makes a lot of sense to consider DEF as a linearly-useful stat, rather than as one with diminishing returns. It also holds up when considering Healing: a 1000 HP heal will increase the # of hits you can take by 10% of whatever it already is (so 1 hit at 0 def, 2 hits at 100 def, and 5 hits at 400 def). I think it does get muddy when characters have multiple defensive stats (like DEF and RES), and there I think returns do diminish based on how far ahead one stat is over the other stat. But partially for this reason, I generally stick to a single defensive stat when designing my games.

This probably seems awfully pedantic, but I really think it's a fascinating way to look at it when designing formulas (and I think it's one of the reasons why your formula is good)!

 

While you're right about that, it really only applies in a vacuum where healing isn't a factor. Once you factor healing in, everything changes since it's going to heal the same amount regardless of your defense. The amount cut from that 1000 damage attack vs 0 and 50 defense is 334 damage. This is actually more than the amount cut between 100 and 400 defense, which is only 300 damage. Between 400 and 500, that's only a 50 damage difference, and if your healer can restore, say, 400 hp per turn, that 50 damage difference is pretty inconsequential comparedd to the 334 difference.

I should've probably specified that I meant diminishing returns in the practical sense, not in the mathematical sense.

 

@Aesica
Rather unintuitively, healing actually swings the equation in the other direction (at least in theory). If you look at healing as if it were a flat 400 reduction from the damage numbers taken each turn, the number of turns you can survive grows now grows exponentially (rather than linearly) with each point of DEF, to the point where at 150 DEF the character would never finish a turn below max HP (after taking damage and then being healed). Beyond 150 DEF, they'd gain HP each turn after the heal. This goes against everything we'd expect, since the absolute numbers are being cut by so much at the low end (e.g. 334 compared to 50).

I tried for a little while to think of scenarios where this mathematical efficiency wouldn't equate to practical efficiency, and - aside from perhaps a scenario where the numbers presented are for a Tank and the tank's ally Squishy the Mage was going to get one-shot anyway, or a scenario where the boss is actively healing itself - I couldn't think of anything. Every other scenario I thought of that included healing, allowed the player to deal more than twice as much damage before dropping, by doubling their DEF.

If I've thought this through correctly, the upshot is that such a formula wouldn't prevent against overspecializing in the defensive stats, and to do so you might need to introduce a mechanic like square-rooting the raw value before applying it to the formula.

I could definitely be missing something, though. I'm pretty tired right now and might be overlooking some obvious element of party combat. x.x

 

@Wavelength
I suppose it depends on how you plan the rest of your game's battle system. In mine, I plan on having healer-types able to cast their healing spells pretty much every round in harder battles (this is to make raising dead allies, despite being cheap, a tricky thing to do) and these spells come in both aoe and single target format. So if my aoe heal is being used every turn to counter the effects of a boss using its 1000 base damage aoe every turn, the 300 DEF tank is still going to get healed along with the 100 DEF rogue. In such a case (and I should've probably stated that this is the main situation I was thinking of) the tank gains more of a benefit from upgrading from 300 to 400 than from 400 to 500.

It did just occur to me that the type of boss encounters I plan on using aren't the RM norm. I like the idea of bosses that deal several attacks per turn rather than just 1 big wallop due to the added layer of strategy it demands. So if the boss deals that 1000 damage aoe as well as several single target hits against random party members (which the tank should be taunting for the sake of Squishy and pals) having both a tank with high DEF and an aoe heal is important, even though the tank just needs enough DEF to be able to come out neutral or positive after the damage is applied and the heal lands.

That said, stat overspecialization is really only a problem when you let players freely allocate stats--something I dislike so it won't be a problem in anything I produce. The best they can do (in fact, what they should be doing) is to pile all the best DEF, RES (MDF), and HP gear they have onto their tank.

 

Personally, I never went anywhere to "learn good formulas" or "learn good ways to balance things". I started with the basic supposition from a Player's Perspective. How powerful something is in comparison to the player is not how much damage it does, but in how quickly things die.

What do I mean? Most players don't really care what the damage numbers say. Exceptions being damage that is significantly higher or lower than what they've been seeing for most of the game. What most players are doing is counting hits. How many hits will this kill my character in? How many hits can that monster endure before I kill it? Using this as a baseline... I've found that it doesn't really matter what formulas you use, as long as you're setting some "hard and fast" rules about what those formulas must accomplish.

So, first, you need to define what "balance" in your game actually is. Because your definition there is going to determine how you use your formulas, stats, and skills.

My personal answer was, "if the player knows nothing about this creature, it should take 4 hits to take out. If they are fighting this creature as a repeat, it should die in one hit". To that end, I've balanced all of combat around that... eschewing using strictly formulas to accomplish it. But, that all played into a design philosophy I wanted to explore and use.

But, here's the basic problem: No matter what you set your formulas for... you have to balance around them. All of combat needs to conform to the basic idea behind whatever formula you've settled on. So, you need to decide, "what am I trying to accomplish?" and then decide how best to accomplish that.

Many people on these forums use multiplication and division and swear by how good they are and easy to balance they are. I've never found that to be the case. I've found that the more complicated I've made formulas... the harder they are to balance in any reasonable sense. Especially when you must take skills, equipment, player stats, enemy stats, states, elements, game features, and intended difficulty into account. As a general rule, the more "moving parts", the easier something is to break. Some people just achieve their desired results using multiplication and division. I find nothing wrong with that. However, as a video game player, I've found systems that do that to be among the easiest to exploit and allow players to most easily break any planned difficulty in a game. Especially with default formulas. The default formulas essentially communicate to the player that they should ignore putting any points into Defense and put them all into Attack since you effectively need twice as many points into Defense to nullify something. For every 1 damage dealt to you as a player, you need to invest 2 points into defense to get rid of it. Which effectively makes most defensive equipment pretty useless. Unless you're scaling back enemy Attack in order to make damage reasonable for the Defense Levels. Even then, once you get into the realms where anyone has 500 Attack Power... You need 1000 Defense to nullify it... which means you will always be doing some damage, and so will enemies. Personally, I do not want to deal with crazy ratios like that, or multiplicative formulas that nullify the point of half of a combat system... or allow easy exploits. I can't make it work properly to allow it to balance or scale easily, so I don't muck with it. Let those with more talent or drive figure out how to make it work. I don't want to work that hard.

What I decided to use, because I could more precisely control the power of any given character... was a strict "one to one" ratio of formulas using addition and subtraction. One point of defense nullifies one point of attack. It's pretty boring and allows for little strategy, however, so I also put in "base damage" for every Skill. I also split off my stats into 3 attack stats and 3 defense stats. That way, even if you had 999 Defense... an enemy using Agility to hit you, would still have a chance. Multipliers take effect only with the "Limit Breaks", some special Skills, or with Elements. I found a 1 to 1 ratio actually made my own combat very easy to balance. At any given point in the game, I know how many of each stat a given character is able to have. Though, to accomplish this, I did also remove stat gains from level ups... not to remove grind, but to prevent the use of grind as a means of breaking combat. So, the only stats any character has are those they've earned from the Quests they've completed or those they've gained from any given piece of available equipment. I set simple "thresholds" based on these stats. What's the minimum and maximum stats the player will have at any given point in the game? I find it far easier to tweak for a few points of a stat than to try to tinker with an entire formula to get the desired effect. My most powerful skills have a Base Damage of 100... they are guaranteed to have 100 extra points into their usage. It can still be nullified by enemies based on type, stat used for the skill, and many other factors. But, this base damage prevents players who have the same attack/defense as the monsters from simply doing no damage while expending MP. Being massively outclassed still results in usage of MP for no result... But, an "even match" is basically an advantage for the player. For perspective, my "Fire" skill at its base level is (a.mat + 10 - b.mdf). The enemy must have 10 more defense than the player has attack in order to nullify the damage. At higher levels of the "Fire" skill, the enemy must have more and more defense to nullify the attacks.

Please note... my system works for what I'm doing. I have no doubt that anyone implementing it "across the board" with a different intent for combat than I have could and would make it easily fail and be difficult to balance. For example, just letting players gain stats via "level up" can potentially unbalance the whole system and formulas I'm using.

The point is largely, "design formulas for your combat based around how you want that combat to look to the player". Or... you could do it the easier way. Pick a formula... doesn't really matter too much which it is, unless it's super complicated... and balance the rest of your game around it. Add/remove stats as necessary to monsters/characters to get the desired effect.

Playtest often. Constantly. Realize that some players will break your intended balance. Realize that's okay to do. So long as players cannot break your balance "unintentionally", IE... they're not trying to do so... you've done a good job balancing the game.

 

It's possible that things may work out differently in your game somehow, but from the point of view of my game at least, this is completely wrong.

Of course it's true that with the default (4 x ATK - 2 x DEF) formula, or the additive formula I previously used (which was just half of the default), every 1 point of the enemy's ATK needs 2 points of player DEF to nullify. But when comparing player ATK versus player DEF, you have apples and oranges.

Player ATK does nothing except when it reaches certain thresholds, at which particular monsters are now killed in one fewer hit, and the locations of those thresholds depend on the monsters' HP and DEF. Player DEF, meanwhile, reduces the damage from every hit you take by 2 (or 1).

I've played a lot of DROD RPG. In that game, there is no variance whatever, so gaining 1 DEF means you are guaranteed 1 less damage from every hit. After playing some long holds, you really get a feeling for how much investments in DEF pay out in the long run. And statistically speaking, this will still be true with variance taken into account.

Let's use some numbers from my game to illustrate. Before the second dungeon, you reach Level 2, giving you 12 DEF. You start with clothes (+2), and the first dungeon contains a shield (+4). So, the player could ignore these and go in with 12 DEF, but realistically, minimum DEF at this stage of the game is 18. There's also a shop before this dungeon, and you have the ability to buy a better shield (+8) and better clothes (+8), so you could have up to 28 DEF.

That means that if I'd stuck with an additive formula, all enemies with 14 or less ATK would now do zero damage, and even 19 ATK (the highest from the first dungeon) would barely scratch the player. So all enemies from the first dungeon would already be obsolete. And if I continued the pattern of allowing the player to shop between dungeons, that would probably be true from the second dungeon to the third as well, and so on. That may not sound so bad to you, but the first dungeon is a short tutorial. I don't feel the player would be bored of seeing the same monsters yet, when simply combining them into different troops can challenge the player to come up with new tactics for each one.

For me, the virtue of a multiplicative formula -- I've found this out after a very short time of playing with one -- is precisely that it avoids DEF being overpowered. The player still gets a lot of benefit from raising their DEF from 18 to 28, but it doesn't break the game.

 

@Tai_MT : You actually forgot to factor in max HP when you did that, as unless your players max HP never goes up, you actually need the system to be in such a way that the damage they take is going up per dungeon. That can be sort of handled with the default formula just because equal stats still means you take 2 * the stat's damage (4 * a.atk - 2 * b.def always returns 2 * a.atk if a.atk = b.def). It can get trickier with other formulas though.

As for how I did my balancing, I started out by figuring out what an average # for the stat was in each of my stats at level 1, and 99. Then I decided if each class was bad, poor, average, good or great in each stat, and set the curves from there. I had to edit it once as I used too low an HP curve for all characters, but overall it worked pretty well.

Then I recorded average stats without equipment at all levels. Excel was good for this. I also set it up so I could have it calculate my stats with specific equipment, so I could see the player stats at x point in the game. So if I knew the player was going to be level 48, I could see what the average stats were, and could tell it the equipment to have then, and it spat out the stats at that point in the game (BTW, this took a while to set up in excel, but is really handy once you do set it up).

From there, I had the system calculate how much damage an average character with that equipment would do to a monster with that DEF. I decided then how many hits with standard attack I wanted it to die in (early dungeons were 1 - 2, late game dungeons 10+), and used that to compute what average monster HP should be. For monster ATK I had to play with it some and use the formula to see how much damage they did to a player with average stats, and one thing I noticed was late game, most monsters needed to have higher ATK than the player just to offset your high HP late game, and to make then actually a threat, else this could happen "That dragon did 500 HP. Yawn. I got 6000 of them". Though that is probably an artifact of my damage formula too.

MAT took a lot of playing and occasionally nerfing or buffing monsters, due to how many magic skills used MAT.

BTW, for the curious person, my formula ended up being:

[(a.atk) * (a.atk + strength of the attack + a.level)] / (b.def + 20) all times 2 then plus a.level.

The + a.level means your minimum damage is equal to your level in the end. It's not much, but it does prevent you from ever doing 0 damage, and even goes up a teeny bit through the game. The * 2 is because I found the numbers to be way too low until I did that, the * 2 with the add-on of the a.level in the numerator seemed to balance it out right to work with my HP curves. And yes, I did add a script so that enemies have levels just so a.level meant something for them as well.

 

@Aoi Ninami

I understand where you're coming from in terms of design perspective. However, I simply can't agree. Most players don't play "defensively" anyway. They play "I need to land as few hits as possible to end the game as quickly as possible". Players often invest in defense purely as something they always do. I'll buy the new equipment simply because it's new and makes my stats go up. But, if given the option between "more attack" and "more defense", the vast majority of players will pick "more attack" unless having more defense actually keeps them from dying in the immediate sense.

For example, in every Zelda game I've ever played, I pick attack over defense. Except Link's Awakening. Why? Because there's a "secret ending" if you complete the game without dying. Having to take twice as many hits to die from all sources is fantastic insurance to getting that ending.

But, that's the trick, isn't it? If I can kill enemies in one hit, that's more valuable than if they can kill me in 4 hits or 3... because realistically, they won't get 4 hits in if I go first and I kill them in that first turn. That's not even getting into Dedicated Healers to undo damage you've taken either and how powerful they typically are. Even as @bgillisp says... it doesn't even take into account HP gain.

That's the rub. Unless you're designing a game in which defense is actually very important... players won't worry about it much at all. They'll buy the new weapons first from your shop, if they got cash, they'll buy your defense items, and move along, unless they want all the new stats. Defense in most RPG's is already not that important or useful by default. The most efficient way to play any RPG is to boost your damage as much and as quickly as possible to avoid taking more hits than necessary (or getting to the point where you take no hits). All that happens when you use the default formulas for damage (needing two defense to nullify a single attack) is massively over-inflating stats just to balance something. I mean, why bother at that point? You won't have to inflate the character's attack stat to kill enemies (in fact, you make it pretty easy to obtain overkill with the default formulas), but if you want any sort of defense against what the player has, you now have to throw twice as many stats into defense as you otherwise would.

My personal philosophy is two-fold. "KISS" (Keep It Simple, Stupid) and "Why use two when one will do?". I simply see no need to complicate something if it isn't necessary.

I just prefer the way the combat stats work better the way I do it. Whether that's better or not probably largely depends on preference and goals for a Combat System.

But, just for illustration: If one of my characters gains an extra 14 points to attack, they do an extra 14 damage to enemies they've been fighting. If one of the characters using the default formula gains an extra 14 points to attack, they do an extra 28 damage to enemies they've been fighting. My system allows me to use a "gradual scaling" method for my equipment and monsters. The default formulas actually require pretty massive growth in terms of stats just to "stay where they are".

I can keep combat to "kill things in 4 actions" with relatively low stats all through the game. But, with the default formula? Keeping to the rule of "kill things in four actions" becomes much more difficult to pull off as you now need to begin massively scaling your stats up based on the stats of the players. I can keep the stats of my monsters relatively close to that of my characters with my formulas. I can balance down to a single HP if I want to or need to (I don't often do this, but having the ability to control combat so precisely allows me to balance it much more easily). Whereas, using a multiplicative formula... I can only target an "array" of numbers and hope that I've managed to balance combat for "the majority of my potential players".

That's just not something I want to deal with. I find it too complicated and time intensive. My method allows me to cut out all the clutter and complications of normal battle. Essentially, I just adopted what Tabletop D&D has done. Whatever your stat is plus whatever weapon dice you roll, that's your damage... provided you hit. Small numbers is what you'll usually get, which means enemies can be far less complicated in terms of their "stat blocks" and won't suffer "inflation".

Some people like the multiplication and division and the complexities that implementing it brings.

But, I mean, why use the default formula when I can just type in there "a.atk + a.atk - b.def" and get the same result? Or "2 * a.atk - b.def"? To me, it's all needlessly complicated for no real reason at all. If you desire simple results, use formulas without multiplication/division. If you desire more complicated results that enact versions of "scaling", then use your multiplication and division.

 

Absolutely! The first time I played DROD RPG (or its predecessor Tower of the Sorcerer), I loved ATK and the way it let me take fewer hits to kill everything. It took a long time before I realised just how powerful DEF is in that game. But it's still true that DEF is powerful, whether players realise it or not. And I want to balance things so that the game doesn't feel broken, whatever choices you make for upgrades.

 

A system where all enemies are based around taking an exact number of turns to defend normally -- but can be one-shotted if the player already knows how -- sounds wildly imbalanced.

That's not the default formula at all for later versions of RPG Maker. And even with such a formula, what matters is what percentage of a character's HP each point of Defense reduces damage by. If 10 points of Defense reduces damage by 10, that means a whole lot different in games where you have 50, 500, or 5000 HP. In the typical RPG, even with increasing Attack and Defense stats, the damage dealt still steadily increases -- because HP is also a factor.

Also...why would you want a system where you could get enough Defense to completely negate the damage done by an end-game enemy with 500 Attack?

"My warrior smashes you with his gigantic battle-axe of killing."
"Ha! Sucks to be him, I have 999 Defense! My hero's armor is impervious!"
"Then my unarmed rogue swiftly delivers a simple punch."
"...crap."

 

This is an interesting assertion. I'm not sure whether or not it's true and I'd love it if you and everybody else could think through it with me!

In a straight-up 1v1 "slugfest" without multiple party members, healing, revives, one-shots, multiple damage types, or the need to make it through an entire dungeon alive, you are definitely correct. Investing in Attack over Defense would objectively increase your damage differential over a single enemy by twice as much as investing in Defense over Attack (using the default formulas).

However, things get really fuzzy when you factor in all of these other "common" RPG staples. For example, when you take into account the existence of AoE heals, and the enemy's attacks are (randomly) being distributed among multiple members of your team, I think it becomes more efficient to have your low-DEF members invest in increasing their DEF so as to allow you to get your entire party back to near-full HP at the same time with the AoE heal.

Similarly, DEF becomes invaluable in avoiding one-shots by bosses. Depending on how "costly" death is (this thread provides additional discussion starting from Page 2), increasing DEF above the threshold where a character can be one-shot might be an absolute requirement to surviving boss fights. So while raising ATK might be more "efficient" in general, allocating some points into DEF might be the price you need to pay to play.

Party and troop size come into play for sure. Every turn, each battler gets one action. If there is one enemy using single-target attacks and you have four party members, each point of DEF in the (a.atk * 4 - b.def * 2) formula will save you from taking 0.25 damage per turn. Each point of ATK will let you deal 2 extra damage per turn. Meanwhile, if there are 8 enemies in play and only 2 party members, each point of DEF will save you an average of 0.5 per hit, meaning 4 less damage per turn... whereas increasing ATK by a point will still only provide 2 extra damage per turn.

Damage types also factor in. The player can choose what types of damage he dishes out with each character, so increasing ATK or MAG can generally be useful on every turn as long as you're choosing just one of those two stats to increase for the entire game. For DEF and MDF, on the other hand, each will only affect half of incoming attacks/skills, and you need to improve both in order to keep your defensive capabilities up. In your case, Tai, since you have three different types of ATK and DEF, the ATK gains a whopping 3x advantage over DEF in its efficiency unless you have ways to force the player to invest in all three types of ATK instead of just one.

Now, as for the effect of raising your ATK or DEF stat in the lens of surviving an entire dungeon, where you have (limited but reasonable) healing and consumables... I think that this would still follow the "efficiency" rules, as modified by the above elements? I'll admit my mind bends every time I try to figure this one out. Does DEF become the better option throughout a long dungeon, does ATK stay generally preferable because killing enemies quicker = fewer hits taken, or does it depend on things that I didn't even mention above?

I always respect simplicity in damage formulas because it provides for better clarity and player understanding about what their stats do. But I think that a well-designed multiplicative formula is just as easy to achieve this with, unless you're designing a competitive tactics (or card) game where the player should be reasonably expected to calculate the damage a move will deal one or two turns in advance.

I'll present my own formula once again as an example: (a.atk * s) / (b.def + 20) where s is the skill's power level (displayed on skill select). Really simple and clean IMO.

It's also got just 4 total terms (including 2 references to stats). I could even remove the "+ 20" by simply adding 20 to every battler's DEF stat, but I chose not to because of the effect it would have on DEF debuffs. (Some of the multiplicative formulas in this thread did use 5+ terms (with 3+ refs), but even they weren't too bad about clarity.)

Your given formula only has 3 (including 2 references to stats), which is admirable, but I think that once you add in the "base damage" you mentioned, it becomes 4 terms (still with 2 refs) for most moves, just like mine, correct?

Long story short, I feel that you're overstating the complexity of multiplicative formulas. Badly-designed formulas of either type are likely to be too complex, but well-designed formulas can be kept transparent and simple, even multiplicative ones.

Maybe it's a wording issue here, but it sounds like you think the default formulas in RPG Maker are multiplicative formulas. In fact they are additive formulas. The multiplication sign exists in them, but it merely increases the magnitude of stats' absolute effect on the amount of damage dealt. Multiplicative formulas use relative reductions (that can be converted into a percentage) for defensive stats.

Personally, I love being able to come back to fights from three or four dungeons earlier and being able to one-shot the enemies that used to give me a stiff challenge - or even being able to see enemies later in a dungeon and one-shot them even though they were giving me trouble at the beginning of the dungeon. It's a wonderful power fantasy (second only to the "Revenge Rollup" of Katamari Damacy).

So I think that what you're doing here sounds awesome, but I have to admit that I couldn't really follow how you got there. Could you spell out for me how you're making enemies take several hits to dispatch when you first run into them, but allow the player to one-shot them just a little bit later (with knowledge of their mechanics)?

 

I absolutely love this topic thus far! There has been a lot of useful and thought provoking information. I thought I would chime in with a different formula. Being an avid table-top gamer as well, I use this formula for a few of my projects (changing the '6' in the formula to the desired dice amount depending on the skills) :
if (b.def <= (Math.randomInt(20) + 1 + a.atk)) Math.randomInt(6) + 1 + a.atk; else 1
//I do not like 0 damaging attacks <_<.
I use formulas like this because I have an extensive knowledge of games like D&D and Pathfinder, and with these formulas, I am able to clearly see what kind of stats my characters and enemies need and can better adjust them.

However, I could see something similarly being used without the table-top references:
if (b.def <= a.atk) a.atk * 2; else a.atk / 2

 

@Seirein

Sounds wildly imbalanced, but it's also not an exact number. 4 turns is the "average". Which will depend on player knowledge, whether they got lucky and figured out how to defeat it first turn by using the correct strategy, and even stats/equipment. But, these are all for base enemies. The things you'll be encountering most of the game. I don't like when players one shot everything through the entire game by spamming their best stuff all the time and mitigating that strategy by simply downing consumables or casting "Cure". The idea behind it is that all basic combat is a lesson for the player to learn while the boss fights are the main test. If the player has already learned the lesson, I'd rather they be able to "move on" as quickly as possible by more efficiently dispatching enemies as they move forward (one shotting them).

BTW, you're right about the formula having changed. It uh... actually got worse. a.atk * 4 - b.def * 2. If you consider that your player may have 40 Attack and an enemy may have 20 Defense... 160 - 40 = 120 damage... That's pretty massive inflation. You'd have to jack up defense and max hp to cope with a simple TWENTY POINT DIFFERENCE in stats. Maybe someone out there is talented enough to get that to balance. I'm not that person. I would prefer never dealing with something like that. Not in trying to balance monsters and skills and everything else.

Also... yeah, it's different in games where you have a lot of HP. But, why do you have a lot of HP? So players can see large numbers roll into the game? Numbers they won't notice or care about? If your typical damage is 4 against an enemy, but you suddenly do 20 against that enemy... it's the same psychological effect as doing normally 400 damage against an enemy and then suddenly doing 2000. it's a massive spike that works the same no matter how large your numbers are. In fact, I'd argue that the larger you make those numbers, the more meaningless a "spike" becomes. Consider if you are normally doing 4,000,000 damage, but then you spike for 20,000,000. Is that still meaningful? What about 4,000,000,000,000,000 spiking into 20,000,000,000,000,000? Still meaningful? Or does it just become "noise"? Or, if you consider simply large HP pools... What is the functional difference between 4,567 damage in comparison to 5,678? Is there any? The more HP you have, the less meaningful damage actually becomes, unless you're trying to scale damage against it. Is there a functional difference between 4,567 and 4,568 damage? Or is that just noise? Have you turned some of those numbers in the damage into pointless numbers? If so, why? To what end? What purpose? That's always bothered me about Final Fantasy games. That massive amount of HP they give you... 3 or 4 thousand when you start. Why? Enemies will still take 30 hits to even kill me, so what's the point? Why not just give me 30 HP and have the enemies do 1 damage a hit for the same effect? I don't need all the "noise" on the screen of the unimportant numbers (anything after the first two numbers). Doing ,damage to me is doing "1,500 damage". I assume most people who play games feel this way. The first two numbers in any amount of damage dealt are the most important, all others are meaningless noise.

As for completely negating damage... Why wouldn't you want that to be an option from a player? Would you rather the endgame enemy do 20 damage? 1 damage? Is it better to have the endgame enemy always deal at least 1 damage to you instead of being able to negate that damage? 'Cause once the enemy is at 500 Attack, they're going to be doing 1 damage to you with your Defense at 999. The most that enemy will ever be able to deal to you is 499 damage. Is that better or worse? I don't know. Personally, I prefer to make my enemies teach the player things instead of just being beefier pinatas. So, stats aren't nearly as important as what they can do and what the player can do against them. If a player is hitting "Attack" in my game, I've failed in the design somewhere, as using that is meant to be strategic and not "the thing you do when you want to win easily without using MP".

As for your example about the warrior dying to speed. It is funny, but it's hyperbole. Ever see a boxing match? Where the small speedy guy goes up against the big beefy dude? If the speedy guy takes one or two punches, he goes down. Easily. But, he can dodge fast, land a ton of hits, and generally keep the big guy at range. His advantage isn't that he can hit harder. It's that he can hit more. He can get into "openings" quickly before they are once again covered and land blows that are potentially devastating. That's the idea. A guy wearing 600 pounds of armor, who is a living tank... can't do anything against someone who can get in quick, hit a weak point... a gap in the armor... and kill the guy inside it easily. My combat works a lot like that. Though, magic is far deadlier to those tank guys than the speed guys are. The speed guys are primarily for taking out the magic guys or the strong guys without armor. Make more sense now? Big guy in armor swings his axe and misses, he's got a ton of openings. Speedy guy finds a gap in his armor and hits an artery with his tiny dagger. Big guy dies.

@Wavelength

All very good points. Unfortunately, I lack the time to reply to them all this morning. I think your formula would probably work well. I'm not sure how easy it would be to exploit on the surface there. I'd have to see what other mechanics you have in play or tinker with the numbers myself. I lack the time to tinker with numbers at the moment.

I do agree about DEF though. I just have the one caveat. That Defense stat only becomes important for those boss encounters, even with your own example. However, that is because boss encounters last a while. A typical RPG has roughly 98% regular encounters and only 2% of fights are bosses (provided the player doesn't grind a whole bunch or waste a lot of time exploring). I am simply not partial to a stat being useless for 98% of a game, only to have importance later. It means I'm spending money on defense points (buying equipment) for only 2% of the combat. I understand that most players won't think that way, and most devs don't either. But, it's the way I think. I like to "cut the fat". If I find something that is mechanically very useless, I either try to make it useful or cut it entirely. In most typical RPG's, Defense is simply a treadmill. You "run and run as fast as you can, to go nowhere". I buy armor as a matter of course without ever noticing much a difference in damage I'm taking. Why? Because it's still the same amount of hits to kill me. I can go from 5 total defense to 900 defense, and it will still take 15-30 hits to kill one of my characters. But, I can go from 5 attack to 900 attack, and there's a noticeable difference... I can kill enemies in one shot now, where it used to take 2 or 3... or even 5 hits. I don't know whether that's intentional game design or whether players just notice their own power more than their defense (some sort of bias), but I don't really like it that much. I much prefer a system in which a player gets a few points in defense and it increases their overall survivability against everything. Where it reduces the amount of heals a team might need to do. Even across a long dungeon. The problem is simply that most dungeons consist of roughly... what... 35 encounters maximum? Maybe 50 if exploration is important? If defense isn't coming into play during those 35 encounters of 1 turn a piece... how important is it, really? If it's more important in the 15 turn boss fight at the end than the 35 turns it took to get to him... how important is Defense? But, that's my perspective and my personal bias on the whole thing. Players don't seem to mind all that much. It bothers me specifically though.

Yep, it probably is a wording issue. I use "multiplicative" anytime multiplication or division is involved. Just the way my brain works. It's pretty imprecise, I admit. But, usually I don't have a problem communicating what I mean despite this

As for my combat system in particular... You've got the 3 attack types. Every enemy in the game is weak to one of them (meaning, their defensive stats won't cover for one of those types of attacks). Figuring out which one they're weak to is pretty easy... at most it might take you 3 turns. That's not where it ends, however. If the player does not have access to one of those 3 types, then they can move on to "Elements" and try those. Some skills are "strength, speed, magic" elements regardless of what stat they're using (there are Speed skills that use Strength as an element and vice versa, these are communicated to the player so they aren't confused). So, the player can run down the basic list of those first three Elements if they're even more confused. They'll typically get about 4 hits in of "neutral damage" before the enemy dies. It takes like 8 hits of "not very effective" type damage (either through stats or elements). They'll get roughly 1 or 2 hits in of "pretty effective damage" before an enemy dies. So, the player is rewarded for initial experimentation in figuring out how to best dispatch an enemy by being able to quickly do it every single time afterwards. Not knowing what that particular weakness might be also ensures that the enemies can get at least one action off before they go down. Enemies only share a handful of weaknesses and a handful of resistances in my game, so most damage is simply "neutral". Which means, you do normal damage to pretty much everything, but figuring out the extras... the quick wins... is rewarding. Though, you can also just be "over leveled" for the area as well. That works in my game too, even though stats aren't awarded via level up. It's a lot more complicated in practice than I've described, but this is the basic gist of it. The formulas allow for me to balance quickly between the "4 hits" and "1 hits" on a single enemy within an encounter or two.

 

You'll see it reasonably soon Or at least if I can get rid of some really big bugs in my Game Over Retry system

So, again, I'm trying to get my head around whether (from an effective HP saved/lost standpoint) whether ATK or DEF are going to be better for a long dungeon run, and my current instinct is that it's likely the same as a single-turn or single-battle calculation. Which means that - yes, if the formula weights ATK more than it weights DEF (like a.atk * 4 - b.def * 2), then ATK will be more useful even in a long dungeon slog.

But then, as we agree, DEF is useful against (generic RPG combat) bosses because it stops you from getting one-shot, and also keeps you from taking so much damage over several turns that your healing can't keep up. Perhaps the default DEF stat is like the Place Kicker on an NFL team - he may only be on the field on 2% of plays, but you absolutely need him to win the game. Not needing him on 98% of plays is no excuse for not hiring a great Kicker.

From a higher perspective, maybe this suggests that we as designers should work hard to make sure that "regular encounters" feel more like "boss battles" (but a lot quicker), so that we don't run our players into feel-bad quandaries like needing to invest in a stat that's not particularly useful in 90% of battles.

Sounds like it. So I think I can infer that your problem was not with the use of multiplicative formulas being used over additive ones, but with any type of formulas that are using coefficients (like a.atk * 4) which cause stats to become comparatively more useful than other stats. I mean, that's certainly a reasonable opinion.

Ah, I gotcha. So the difference between 4 hits and 1 hit is achieved by filling a knowledge gap. Experiment, figure out the enemy's weaknesses, use that type of skill/attack from now on. That makes sense. Thanks for clarifying!

 

After some more thought, I'm a bit closer to agreeing with you. I still don't think "damage differential" is the right way to look at things, because of Health/Damage Asymmetry. Having each point of ATK deal 2 more damage instead of 1 sounds great; but if you compare two games, one with [2*atk - def] and one with [atk - def], and the first game also gives its enemies double HP, that 2 damage is worth the same as 1 damage in the second game -- whereas if player HP is the same in the two games, player DEF is worth the same amount.

Again I'll use DROD RPG to illustrate. This game has a very simple system where all combats are automatic; damage is [atk - def] and once you initiate combat, you trade blows one for one until one of you is defeated. Most mid-game enemies have HP in the low triple digits, but the Rattlesnake has 1200 HP, 180 ATK and 20 DEF. To kill it without taking damage, you need 180 DEF or 1220 ATK. But let's assume you want to kill it (because you need the reward it guards) before that point. At 100 ATK and 100 DEF, the expected damage from the fight is 1120 (14 hits, 80 damage per hit). At 110 ATK, 100 DEF, it's 1040; at 100 ATK, 110 DEF, it's 980. And the closer you get to that golden 180 DEF, the more strongly DEF is favoured over ATK.

In short, higher-HP enemies favour DEF more, while lower-HP enemies favour ATK more, and the designer can shift the balance by changing the relative frequency of types of enemy.

Now, there's one key way in which DROD RPG fails to represent jRPGs. jRPG combat is not automatic, and so you can't have regular enemies that take 14 hits to kill without boring the player. Only bosses can have HP that high. So ATK versus DEF is influenced by whether you care more about making the stages easier, or making the bosses easier (with the caveat that the designer still has some freedom to shift the balance within each category, without changing the formula, by changing enemies' HP). And that's going to vary from game to game.

I'm surprised by Tai_MT's estimate that bosses are only 2% of battles. In my game, I'm aiming for more like 5%. And since bosses take longer than regular encounters, that's more like 10% or 20% of gameplay. And since stages should be doable with any stat build, the player does have a reason to care more about making the bosses easier.

 

I look forward to seeing all your design philosophies in play You'll have to let me know when you've posted it for play.

I think if we're talking "standard RPG combat", which lasts maybe one or two rounds and then it's over, Defense is probably going to be less important all around. HP is probably going to be far more important than defense, just because HP allows you tank lots of hits... while DEF in general allows you to tank the big hits. At least, in general, this is how it works. Extra defense can give your HP budget more hits to work with... and extra HP can nullify the point of having more defense. I think in practice, the players are only managing many small hits across a whole dungeon using their HP while they're managing a few large hits using DEF in boss fights. They are definitely tied together and you can't separate them, but largely across every RPG I've played, this is how the stats tend to work. Especially since players tend to "heal up" after regular combat whereas in boss fights, they tend to "heal up" during it. Just my observation. You can take from it what you will. I'm not even sure it has any significance to RPG design.

I think this is a good example. I just have the one issue with it... Much of the NFL is based around a lot of player skill and team strategy. Many standard RPG's simply aren't based in that realm. Now, there are some that are. But, standard RPG design doesn't focus on these two aspects of a combat system. Because of that, I feel like the 2% issue just isn't enough usage of the stat. In a standard RPG, a player can employ a single strategy of just "overwhelming force" to win the game. Meaning, they may not even need that defense 2% of the time. If they've spent a lot of time grinding and kill a boss in 2 or 3 rounds instead of the typical 10 to 15 of most bosses, they might not have need of that DEF at all. In the NFL, that good kicker is pretty much necessary. Even for only 2% of the combat. But, in a standard RPG that doesn't incentivize DEF and instead prioritizes ATK over every other stat? It might be tricky to even justify DEF in such a game, for even 2% of the total combat, as the player could get by without having anything other than "the bare minimum" (what they might gain from gear two tiers below where they are in the game... we'll say roughly 50 missing points of defense compared to what the dev calculated they should have, just so we have numbers to work with... plus any DEF point they gained from simply leveling up). In those games, it's almost a lot better from the player's perspective, to have percentage reductions of Elements against you, as they're far more effective than any single point into Defense ever will be. I think to make the comparison pretty exact, you'd have to guarantee that DEF comes into play on every boss fight. You'd have to guarantee those large damage spikes each boss encounter. I'm just not sure how fair that might be for all players involved. We're not even talking about the "squishy" type characters like Mages either who often have far lower DEF stats than everyone else.

Just to throw a wrench into it here: With my own formula, the main character (who is a Warrior Type, but has Jack of All Trades stat distribution) does take less damage than my Main Mage does. MC has a DEF of 10 for the base, Main Mage has a DEF of 5. It's a difference of 5 damage at baseline monsters. It's a lot of excess damage when you start the game (especially with HP being anywhere from 10-20 on a starting character). But, as you gain HP or DEF, that gap closes very quickly. Much quicker than the a.atk *4 - b.def *2 formula. With just a few points into Defense, my mage no longer needs to worry about damage from those baseline enemies anymore. Or at least, nowhere near as much. They don't require Babysitting during combat (needing to be Covered, needing defense buffs, needing barriers and shields casted on them). They are also a bit harder to one-shot by Boss Monsters. But, in a standard RPG? They can be fairly easily one-shotted in boss fights. In fact, it's pretty interesting to see that most RPG's don't have enemies that will target your Mages... or often kill them first. I sometimes wonder if this is some sort of algorithm included in the game to prevent the player from just getting romped by losing their Dedicated Healers on the first turn... or during crucial points of battle except through "bad luck".

I am absolutely in favor of this. I want to be engaged during all combat!

@Aoi Ninami

I just made a simple calculation. Most games have roughly 20 or so "Dungeons" in them (caves, actual dungeons, castles, whatever, anything with a boss at the end). Each "Dungeon" contains roughly 25 encounters or so across 4 or 5 enemies. So... 25x20=500 battles or so? add in 20 extra for Boss fights? Not counting in overworld encounters... It's like what... 3.8%? But, if you count overworld encounters... which are going be a LOT of battles... it boils down to like... 2% of all combat? Conservatively?

 

Fair enough. My game doesn't have an overworld, so I forgot to take that into account.

 

Ooh, very interesting point!! So, we're saying that because the HP of enemies tends to be high and their Damage output tends to be low, that in an additive formula (like a.atk - b.def, or c + (a.atk * 4 - b.def * 2) where c is an arbitrary skillpower) DEF tends to be favored, because the absolute damage reduction will take your total damage sustained per turn (and thus throughout the battle) closer and closer to 0, right?

Where a multiplicative formula is used (like a.atk * 100 / b.def, or (a.atk * c) / (b.def + 100) where c is an arbitrary skillpower), Health/Damage Asymmetry becomes irrelevant except at extreme values, right? Or does it not? This is mindbending

Great use of an example! I'd like to try working it out with a few different parameters and see what happens...

Scenario B: Rattlesnake has 1200 HP, 80 ATK, and 80 DEF. The formula is a.atk * 4 - b.def * 2.

• At 100 ATK, 100 DEF (as the player), you deal 240 damage per turn and take 120 damage per turn. You kill it in 5 hits, meaning you took 480 damage (4 attacks, assuming you go first).
• At 125 ATK, 100 DEF you deal 340 damage per turn instead, and kill it in 4 hits, meaning you took 360 damage.
• At 100 ATK, 125 DEF, you take 70 damage per turn instead, and kill it in 5 hits, meaning you took 280 damage.

Scenario C: Rattlesnake has 650 HP, 80 ATK, and 80 DEF. The formula is 100 + a.atk - b.def.

• At 100 ATK, 100 DEF, you deal 120 damage per turn and take 80 damage per turn. You kill it in 6 hits, meaning you took 400 damage.
• At 125 ATK, 100 DEF you deal 145 damage per turn instead, and kill it in 5 hits, meaning you took 320 damage.
• At 100 ATK, 125 DEF, you take 55 damage per turn instead, and kill it in 6 hits, meaning you took 275 damage.

Scenario D: Rattlesnake has 1200 HP, 80 ATK, and 80 DEF. The formula is (a.atk * 200) / (b.def + 20).

• At 100 ATK, 100 DEF, you deal 200 damage per turn and take 133 damage per turn. You kill it in 6 hits, meaning you took 665 damage.
• At 125 ATK, 100 DEF you deal 250 damage per turn instead, and kill it in 5 hits, meaning you took 532 damage.
• At 100 ATK, 125 DEF, you take 110 damage per turn instead, and kill it in 6 hits, meaning you took 550 damage.

Interesting. The additive formulas (including your own, with the 180/20 example) seem to make raising your DEF look pretty rosy, whereas the multiplicative formula was more even, slightly favoring raising your ATK.

I picked somewhat arbitrary numbers and adjusted them slightly to try to ensure that the "break points" for number of hits to kill were fair across each type of stat raise. Maybe different numbers (like a highly defensive enemy) would throw out different results, and of course factors like multiple party members and healing will muddy the waters even more.

But I do find it interesting that raising DEF was so valuable, even in the a.atk * 4 - b.def * 2 formula. Definitely gives some credence to that idea of Health/Damage Asymmetry favoring high DEF (if that's what you meant in the first place).

Also makes a lot of sense. Even in my examples above, if were were to lower the enemy's HP a lot (to one-third or so of their current values), then wherever the extra ATK helps you reach a break point where you kill a monster one hit quicker, I think it ends up being as valuable or even more valuable than extra DEF.

Tai's own example below notwithstanding, I'd tend to agree with you that 4-5% feels about right for most games I've played. Sometimes I get lost in dungeons, and if there are random encounters then I end up with closer to the 2% ratio, but I think that bosses/minibosses representing 5-8% of battles is generally a good design target in a turn-based system. Some games with slower, more involved combat systems, like Trails in the Sky, will smartly make it more like 10-20% boss battles, since even the basic encounters take over a full minute to clear.

At the extreme end, my own work in progress timeblazer has boss battles represent a whopping 67% of all combat, since I've abstracted dungeons into more engaging non-combat activities

===

Will do, sir It's going to be a private round of playtesting since the game is going commercial (and is near completion), but I definitely want you to check it out as it will be so interesting to me to see whether you find it engaging given where we've had similar and different design philosophies.

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.

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

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.

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!)

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).

Methinks it's just the RNG at work, combined with the fact that your mind is expecting the enemy to do the "smart thing", when in fact most of the time it won't. I haven't really noticed AI patterns that bias themselves toward the player (above and beyond what a pure RNG would do) in most games I've played.

I'm with you 100%. The tricky part, for normal encounters, is to find ways to make them engaging, without using either the length or the difficulty that boss encounters tend to have. Lots of different ways to do this, but too often RPG games just toss weak enemies with regular attacks into a troop, have the enemies throw a bit of damage or maybe a status effect down before they die, and hope it's somehow engaging.