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# Important Math Question before Blizzcon

Discussion in 'Diablo 3 General Discussion' started by cacophony, Sep 26, 2010.

1. ### cacophonyDiabloii.Net Member

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Important Math Question before Blizzcon

Okay, so going over some of the stuff in the wiki, I have some questions about gear/skill scaling. I can't make it to Blizzcon, but was hoping someone could answer a couple of math questions for me.

To start, let's define some terms. Let's take an average wizard, casting an average spell, Arcane Orb. Let's also take an average barbarian, using an average skill, Cleave. Here comes the algebra soup:
A = final damage of arcane orb
C = final damage of cleave
B = base damage of arcane orb, goes up w/ points in the skill
W = base weapon damage for the barbarian, goes up w/ better weapons
S = gear scaling factor for spells, let's call it spell power, and it is found on gear, normally
P = gear scaling factor for melee skills, let's call it attack power
X, Y, and Z are constants. They increase based on skill, how many points in the skill, and passives.

Here's the standard way most games do it.
A = B + X*S
C = Y*W + Z*P
Pretty easy to handle, pretty easy to add in crit/haste damage calculations, too.

Here's what it looks like D3 is doing.
A = B + X*S*B = B[1 + X*S]
C = Y*W*Z*P

Am I reading the wiki wrong? Is this really how they are handling gear scaling damage?

2. ### FoodspiceDiabloii.Net Member

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Re: Important Math Question before Blizzcon

Unless I am completely misunderstanding your post, you're saying damage increases faster with more skill points and better gear than 'most games'. I see nothing wrong with this provided that difficulty (monster numbers and hp) scales accordingly. Am I missing something?

3. ### NekoraDiabloii.Net Member

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Re: Important Math Question before Blizzcon

It depends on whether Spell Power is a percentage or a number.

If Spell Power is a number, it will look a little more like this:

N = Skill-dependent Spell-Power scaling factor, different for each skill

A = V*B + X*S*N

In this way, a skill like Frozen Orb might not get as big of a boost per point of spell power as a single-target spell, for instance.

I think you mostly have melee right though, depending on whether skills add a base amount of damage to a normal attack, or enhance/detract from normal attacks by a percentage.

4. ### cacophonyDiabloii.Net Member

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Re: Important Math Question before Blizzcon

That N number is redundant. X is the scaling factor, it is skill dependent, passives dependent, and skill point spending dependent. In WoW, it used to be character level dependent, too. There were also special gear set bonuses that could raise that coefficient when you collected most of the set. That coefficient is usually pretty small (almost always less than 1, mostly less than 1/2) for most fast AoE skills, and pretty large (greater than 1 sometimes) for slow, high cooldown single target nukes.

But again, my question is this; if you have two characters of equal level, equal skill build, etc, and one has a better set of boots, is that difference now an exponential growth, instead of the linear growth we mostly see?

5. ### NekoraDiabloii.Net Member

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Re: Important Math Question before Blizzcon

I didn't realize you were folding ALL of the coefficients into one number. If that's the case, then yes, N is redundant.

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Re: Important Math Question before Blizzcon

I'm not paid to worry about math of a higher level than is sufficient to baffle store clerks by handing them say, \$11.07 for a \$5.83 bill.

But in regards to the calculations above... we don't know enough yet, about how stats, skill levels, clvl, +damage, and +%damage factor in. The only real big D3 change we know for sure is that +%spell damage is a very common mod, and one casters will have to stock up on, as or more avidly than melee chars want +%weapon damage.

7. ### cacophonyDiabloii.Net Member

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Re: Important Math Question before Blizzcon

That's kind of the question I'm asking. The way it's worded (% spell damage) leads me to believe it's the geometric scale (A = B[1 + XS]) versus the old WoW spell power system of linear scale (A = B + XS). It will also be interesting to see how they handle the naturally geometric stats (critical strikes and faster attack/cast speeds), whether they go to the combat rating system (a level 50 character needs X crit rating to get 10% extra critical hit chance, while a level 60 character needs (X + n) crit rating to get 10% extra crit chance).

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Re: Important Math Question before Blizzcon

It doesn't really matter how the calculations are executed, from the player's end. Most players will never know the formula or want to know them. Players just need to see the numerical inputs that matter, and have some idea of their relative importance.

I'd imagine the D3 team realizes that, and plans accordingly. Perhaps the attributes will have tool tips that say, for instance, "Raising your dexterity increases your to/hit, damage with ranged weapons, defense, and spell accuracy."

It seems that the listed skill damages are basically like the listed damage on a weapon. e.g., you pick up a short sword that does 2-6 damage, and then it does 14-30 on your character, once skill bonuses and stats are factored in.

The only hard facts on this, that I know of, came from a brief observation I made on the WD, last year. From the spell damage wiki article.

That was with, at most, +50% spell damage from gear. So clearly the stats were a major factor

If I have a chance this year, I'll try to note the damage listed on some spells and see how it changes with another point in the skill, a level up, a +stats item, etc.

9. ### cacophonyDiabloii.Net Member

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Re: Important Math Question before Blizzcon

I have to mildly disagree. The scales matter in terms of PvP balance and a little also in terms of the game's pace.

Let's take two wizards; equal level, equal build and runes, equal gear, except the second wizard has a little bit more spell power on her gear. Here's the math.
WoW, linear form.
A1 = B + XS1, A2 = B + XS2, where S2 > S1;
A2-A1 = X[S2-S1]. Linear, easy.
D3's potential system.
A1 = B[1 + XS1], A2 = B[1 + XS2], S2 > S1;
A2 - A1 = BX[S2-S1]. The difference is proportional to the initial value of the spell.

At higher levels, this proves tricky. A slight edge turns bigger and bigger as time goes on, making PvP balance even harder; you'll need the "best" gear almost immediately if you have any hope of competing (this also leads to a "defensive arms race" where defensive stats also scale exponentially). For PvE, when you try to tune the monsters and their difficulty, it is also tricky; a challenging area becomes a joke when you pick up a tiny little bit of gear, or alternatively you easily clear an area, get no upgrades, and then get smashed in the next area.

Simply put, as B gets larger (towards the end game), the effect of each gear upgrade becomes massive; even if defensive stats and health pools scale to compensate this, it requires razor thin balancing, which is more difficult than in a linear system.

10. ### permaximumBanned

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Re: Important Math Question before Blizzcon

Cacophony is right.

If that formula is true end game PvP will be really really hard to balance as minor looking differences in the gear translates to huge differences in the combat.

Small 5% more spell damage may translate to enormous damage boost for a caster that already has a great gear.

But imo this won't be the case... It would be a huge mistake and Blizzard is not that bad.

11. ### The RockmanDiabloii.Net Member

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Re: Important Math Question before Blizzcon

Ok I see you getting confused, it's because weapons skills are % weapon damage you missed this point its 1+X% boost to attacks.
See it makes spells = to weapons power wise it just that items and skill switch places in terms of what the multiplier. For Spells items are a +% booster and skills are a flat number.
Whereas for weapon attacks items are the flat number and skills are the +% booster.
Both use this formula A=B[1+X*Y] where A is damage dealt B is base damage X is stat damage boost and Y is weapon % boost from skill (convert it to 1+X%) or spells gear % boost.

There's no need for a staling factor for skills as it should already be built into the skill (for spells single target skill more damage etc or a higher % multiplier for weapon skills etc) gets rid of one of your constants.

cacophony what the difference to a warrior vs warrior fight when one got a better weapon? So you want it where a wizard with no items does maximum damage 100% of the time, weyhey I can go kill everyone naked with my uber spells of DOOM!!!

Last edited: Sep 30, 2010
12. ### cacophonyDiabloii.Net Member

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Re: Important Math Question before Blizzcon

Okay, let's start looking at melee characters and weapon damage.
Usual damage equations look like this (C = final damage, W = base weapon damage, P = attack power (on gear), Y and Z are skill/passive/etc dependent coefficients.
C = Y*W + Z*P, this is the linear form, standard WoW skill.
C = Y*W*Z*P, this is a geometric form, and if I'm reading the gear affixes in the wiki correctly, this is how D3 does the calculations.

Let's take two barbs, equal level, skill build, etc, except the second one has a better piece of gear that is NOT a weapon, so P1 < P2.
Linear WoW form.
C2-C1 = Z*(P2-P1)
D3 form
C2-C1 = YW*Z(P2-P1); much different, and becomes insane late in the game when W becomes large.

Now let's change JUST the weapon damage, W1 < W2.
C2-C1 =Y(W2-W1), simple linear form
C2-C1 =YZP(W2-W1), proportional to your other gear, which gets very large late on

Changing both weapons and other gear becomes trivial.
C2-C1=Y(W2-W1) + Z(P2-P1), linear form
C2-C1=Y(W2-W1)*Z(P2-P1), geometric form

As you can see, it's pretty analogous to the spell situation, except now gear differences and weapon differences are part of the equation. As an aside, usually a developer picks out averages for weapon damages per level, and sort of "pegs" spell base damages per level around those weapon damages (or at least try to). Either way, the geometric form is a tougher balance job, b/c small differences get magnified late on. Any mistake in itemization by the developers could result in huge imbalances.

13. ### The RockmanDiabloii.Net Member

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Re: Important Math Question before Blizzcon

Glad to see you agree that its kind of the same with a difference (according to you post), which is the point I was making.

What I was saying is there's a flat damage component and a % booster, all what changes if what does what out of skills and gear.