Observations about character stats

[Xaos]

This thread is not a suggestion for LoE, nor is it about any particular game, its just about my thoughts concerning game design in general.  There may or may not be anything in here worth spending your time reading.   Proceed at your own discretion.

A while back, I observed that the characters and their minions in Final Fantasy 12: RW have a tactical Rock-Paper-Scissors as well as an Elemental one.

Of course, its not like your normal weakpoint where the inferior (in the cycle) unit just takes double damage.  The way the unit types interacted with each other was....odd:

*-Fliers drop like well, flies when fighting ranged units, often never closing the gap and not accomplishing much when they do.
*-Melee units shrug off arrows and spells alike, closing the gap and crushing ranged units
*-Flying units dodge most of the attacks of Melee units, and tend to come out on top.

Indeed, it wasn't until long that I figured out that this system could've been interpreted entirely through their stats:

*-Melee units have high defense and low accuracy.
*-Ranged units don't just have "not-awesome" attack power, but incredibly low damage since melee units can take shot, after shot, after shot.  They also have enough accuracy to reliably hit fliers.
*-Flying units have high evasion and, we can infer, low defense.

Following this, I noticed something about statistics.  I am, of course, assuming that all stats have a

low defensive stat>low offensive stat>high defensive stat>high offensive stat


Now, its important to note that a merely "average" offensive stat can stand up to a high defensive, so long as the guy with the "average" stat has a large advantage somewhere else.  For example, the flyer's attack power is not exceptional, yet the melee guy's accuracy is SO low in comparasion that he will miss enough times for the flyer to widdle down his hit points.

Therefore, you can make all sorts of triangles, from the Revenant Wings version:

Melee (Def +, Acy -) > Flying (Eva +, Def -) > Ranged (Acy +, DPS -) > Melee

to similar ideas that follow the same rules:

Rock (Def +, Eva -) > Brute (DPS +, Acy-) > Gnat (Eva+, DPS-) > Rock



NEW STUFF:

The above ideas were all posted back on the old forums, in another post.  From here on in, this is the other revelations.

Effective hit points-

I got this concept from this guide and its a very useful tool for anyone making a balanced system.

Its not too hard to grasp, but its basically combining ALL defensive stats a character has (armor, evasion, etc.) into a single numerical value.  There's your hit points, but all these things PROP UP your hit points, so the real value of your hit points is much higher.

eHP = bHP * (100/(100-ev%)) * (1+(arm*0.06))

bHP = Base HP
ev% = Evasion percentage (100% means you can't be hit, duh.)
arm = Armor of unit. (armor in WC3 reduces the damage by 0.06%)

I have a formula for calculation pure Damage reduction instead of percentile reduction, but I'll get into it later.

The anatomy of Damage per second-

Lots of things can improve how much damage you do, not just the raw damage of your normal attack.  There's the rate of cooldown

And of course, there are magic spells and other "active abilities" which either grant static bonuses (or inflict static debuffs and conditions on enemies, but those usually either miss a lot, or have their effects or duration nerfed to the point of being trivial.  Damage-over-time is an interesting hybrid of the latter debuff and direct damage) or do static damage.  A big problem is that weapons end up granting a bonus to damage (and armor to defense, and accessories to other stats) while spells are self-contained and cannot be improved by anything you equip, you have to level up or learn a bigger spell to do more damage.  This is why its hard to balance fighters and mages.  Well, "blasty mages" in any case."  Because Fighters are usually based on STATS while Mages are based on SPELLS, this creates a dynamic.  Fighters improve by leveling up AND getting better gear.  Mages mostly just improve when they level up IF even then!  (Dungeons and Dragons 3rd edition is notorious for this.  Most notably, there is a guide for a computer game that uses the system, Neverwinter Nights 2, that explains how access to magic weapons in a server -or setting if you are doing it table top- can make that normally too-inaccurate-to-matter fifth attack fighters get REALLY powerful.)

Now, making buffs from spells % based will keep and having a weapon system like Zodiac where the active abilities not only improve damage based on weapons equipped, but weapons also improve magic damage the same way they improve physcial damage.  Determining what class of weapon you use plays a big role in how your character fights in that system, and this idea could be applied to other games.


Calculating critical hits:

Average base damage * (Crit chance * (Crit multiplier -1))

I had to work this one out for myself, but it was simple enough.  Here's my work:

100 attacks with a 40%/*2 weapon, a single attack does an average of 2 damage.

200 base damage.  (100 x 2 = 200)

40 attacks do +2 damage  (40% crit chance, double damage)

Those crits will yield an extra 80 damage (40 x 2 = 80)

Combined with the base, the new damage is 280 (200 + 80 = 280)

finally, divide the new damage from the base damage (280/200=1.4)

Therefore weapon that has 40% chance to do double damage has a value of 140%.  It will do 40% more damage others.  And if it did triple damage, it would be +80%.  And quadruple would be +120%.   And quintuple would modify the average damage by 150% and so on.


"Raw" and "conditional" offense and defense-

Really, aside from evasion, the only defensive stat you need is Hit points.  Final Fantasy tactics segregates armor availability by job classes, but all any armor is going to do for survivability in that game is raise your hit points.  And this works.  It gets weird when you try to figure what exactly happens in the game world when an armored knight is healed, but not quite up to full HP (because the armor raise Maxhp so dang high), I mean, is healing spell also healing the dents in the armor?  But Mechanically speaking, that

And assuming you can only make one attack per turn (or attack animation in a real-time game), then the only OFFENSIVE stat you need is how much raw damage the attack does to the enemy's hit points.

Of course, there are other stats which influence damage.  Armor Penetration, Rate of Attack, Critical chance, elemental weaknesses, etc, etc.   Depending on what your game system uses, you might have all sorts of statistics that determine your ability to take and dish out punishment in combat.

Lets discuss four (which AREN'T critical hits or elemental weakpoints), shall we?

Armor:  It has many names.  Defense.  Damage Reduction.  Protection.  But all does one thing- protect hit points from harm.  If this is high enough to overtake the enemy's offense, the enemy might not be able to harm you at all!  (or maybe it will just do 1 damage, in the name of "fairness" or something.)

Penetration: As in "Armor Penetration."  It ignores some amount of the enemy's defense, propping up your damage, but if you have more penetration than the enemy has armor, that extra penetration goes to waste.

Regneration: Restores hit points without the aid of items or healing abilities.  Usually its either too slow to help in combat, or it stops while you are in combat/taking damage.  But if it is persisent AND powerful enough to recover hit points while you are losing them, it basically acts like defense.  Only, you know, retroactively.  It IS possible to be reduced to 0 hit points and die, even though you HAD some healing on the way.  And that really sucks, ask any WOW player who went down while he had a Heal-over-time buff cast on him.  On the plus side, Armor Penetration has got NOTHING on this.

Rate of Fire:  The reason damage is often called "DPS" is because sometimes you get more than one attack in a certain period of time.  The more attacks you can wail on someone in a single combat round, the more damage you do.  However, just remember that each attack has its damage reduced by defense.  Its effectively multiplying defense.

There is even a Rock-Paper-Scissors between these stats, see if you can figure out how it works:

Rate of Fire>Armor>Penetration>Regeneration>Rate of Fire

Numbercrunching Snags-

A common, indeed necessary, practice used by players of most RPGs or Monster raising games that force you to devote limited resources (Perk points, D&D point buy, time in Monster Rancher before you Rabbit-thing croaks, etc.) is Min-Maxing.  (Well, technically, its creating an outright BUILD for your character.  Planning out every. little. thing. about the character in the name of finding the shortest route to the cheese.)  Min-maxing generally works unless your system has something built in against it*.

However, let's say there is an MMO out there which allows you to build pure evasion or pure offense or whatever type of characters you want, but the designers are sneaky and want to design certain rare monster types that challenge characters that have number crunched.

Things that overcome one stat and might make you wish you had put points in others:

% attacks, bane of Hit points and defense:  These enemies deal damage based off a % of your current Hit points (or in FF12's "Zeromus the Condemner's" case, your max Hit points).  They usually halve your hit points and halve and halve and halve and once your hp pool is itty bitty, they will finally release an attack that does normal damage and kills you off.  Evasion would've helped dodging these attacks more than hit points OR defense, and Accuracy/Damage would've helped kill them off before they could kill you...

Suicidals, bane of Attack power: These nasty creatures throw themselves at you and blow you up.  They are fragile (or perhaps attacking them at a distance would blow them up before they get to you), so all of your offensive power?  Redandant.  Accuracy helps you one shot them, and any defensive stat at all

The Automatic hit, bane of Evasion: These attacks are not even UNCOMMON in games, and they are why evasion is usually not respected.  That, and Evasion is a pretty binary defense.  If you are all evasion (but not 100%) and no defense, then the only fight you are not going to always be one lucky hit away from death is versus the percentage damage guy.

???, bane of Accuracy: Sorry, no clever solution here.  I do have to say that the accuracy in question is MAGICAL accuracy (another idea from zodiac), which determines how well your Debuffs hit, then obviously status immunities will take care of that.  But making ANY kind of character who revolves around an element or status ailment that any monster out there could be immune to (and ALL boss monsters usually are), without any diversity in your attack options is not a very good decision.  At all.

*-in Monster Rancher, I had my Pixie do Mailman jobs, which improved her iINT and SKILL stats at the cost of points in DEF.  I had super high evade, and I thought that if my LIFE stat was high enough, my hit points would carry the day.  But no!  0 Def automatically makes ALL attacks do 999 damage, crushing even the healthiest of monsters!  There is no penalty for having super low power if you specialize in magic attacks, however...



The Final value-

So...now that everything has been made so complicated, how do you determine what unit beats what?

Well, go back to where I said all you need is Hit points and Damage.  If you can calculate an attackers total damage in a single combat round (where as a combat round also has a good representation of the number of attacks as well as regeneration...) as well as a defender's Effective Hit Points, you can determine how long it will take the attacker to take down his enemy provided the defender doesn't counter attack.

Accuracy reduces Evasion (evasion is usually, but not always propped up to be higher than accuracy so you always have a good miss chance), and Armor/Defense reduces damage.  # of attacks multiplies the total average damage, but it also multiplies the Armor/Defense.  Penetration reduces armor but doesn't do

Once the round has passed, regeneration kicks in and heals some of the damage.

Now, have the defender damage the attacker.

Whoever deal more damage to a larger PERCENTAGE of the other's effective Hit Points is likely stronger and the favorite to walk away....as long as stuff like teleporting or stunlock or ranged attacks don't make things complicated.

But I'm not going to tell you how to work out and balance THOSE incomparables...we could on forever.  Literally forever.    As long as somebody comes up with something new to throw into games, we'd have to factor them in, and imagination is endless...

[Xaos]

Huh.  You know, maybe I should've posted this on a forum with less traffic...



EDIT:  Actually, on the "I can't find a good counter for high-accuracy" characters thing:

In general, all enemies that have a low opposing stat but the other stats are high is a good thing.

A High power, low accuracy dude can CRUSH a low defense character, but if they simply treated defense as their dump stat, and put a high, high HIGH amount of points in evasion...

Well, then, Sluggo is actually an EASIER foe for Dodgy to fight.  Because Dodgy is made of glass, then EVERYBODY can one shot him, and he only survives by dodging (or stun locking, explosive sneak attack damage, etc.) Power doesn't matter when fighting Dodgy, only accuracy does.  Which means that any kind of numbercruching can come back to haunt you (unless you can go an entire game without using a particular stat or skill or something.  Like neglecting your physical stats or weapon perk trees because you specialize in magical damage.)

So low defensive stat actually BEATS high offensive stat.  The cycle is circular!

Low Defensive (Assuming numbercruched and not just lower leveled)> High Offensive> High Defensive>Low Offensive> Low Defensive