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