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2. Fire Emblem Heroes
3. Quick and Dirty Damage Mechanics (not actually quick or dirty)

#### User Info: Reimys

Reimys
4 years ago#1
I'll lead off with a disclaimer: I'm pretty sure I've managed to figure out the order the game does things in and how it goes about doing it, but if you can prove me wrong I'd be happy to hear/see it.

You're going along, doing your usual stratum training or arena thing. You, being a connoisseur of Fire Emblem, decide to think a few turns in advance, sipping at your classy drink of choice. 'Ah,' you decide, 'This unit can take this much damage when the enemy comes to attack, and survive with just enough HP to go on to kill another!' You pat yourself on the back for #StrategeryWellDone.

Except what's this? The enemy does more damage than expected when they move in, and you do less than you thought you would. You thought you accounted for all the modifiers! Doesn't everything round down in this game? You did all the multiplication and rounded your numbers, so what gives?

Well, it's that Fire Emblem Heroes really, really hates decimals, that's what. The short of it is that you are possibly losing... or gaining! Damage because the game rounds- truncates, rather- between steps, and stuff like weapon effectiveness and weapon triangle advantage is done in different steps. Also, Weapon Effectiveness comes before Weapon Triangle Advantage/Disadvantage. This sounds ridiculously nitpicky, given that we all learned about the commutative property in basic algebra, but does make a little bit of a difference.

Let's start simple.

THE BASICS

With a neutral matchup,

Damage = Attack - Defense (or Resistance, if attacking with a mage or Manakete)

Cool, everyone knows that. No decimals here to be screwy. But what if we throw in... hm, a Luna on an enemy with odd defense?

https://i.imgur.com/s6AKKTg.png https://i.imgur.com/xYPAPnH.png
https://i.imgur.com/OrhmeW3.png
50-23 = 27. Neato. The Luna hit actually does 38 damage though, as seen by Virion's 42 hp dropping to 4. So that's +11 damage from 27. 23*0.5 = 11.5, but who needs decimals? It rounds down. Remember that. Fire Emblem Heroes hates decimals and everything gets truncated. That's actually 11. So Virion only loses 11 defense and has an effective defense of 12 when Luna goes off. The defense subtracted is the number that gets rounded down, not the final defense. You can't just divide by 2 and then chop off the .5, okay?

MIXING IN WEAPON TRIANGLE DISADVANTAGE (or advantage, but I forgot to get screens of relevant numbers and with the 'round down' knowledge everyone has nothing much really changes there)

Wait, you just do 120% of your damage on WTA, and 80% on WTD, right? Well, yes? Kind of?

So we have this Tiki.
http://i.imgur.com/i36KXQf.png
She's kinda hurting, but that's okay.
http://i.imgur.com/yeX0PBs.png
We have this knight guy. Quick, how much damage will this green knight do to red dragon Tiki?
Well, that's easy, guy has WTD, so clearly it's floor(19 * 0.8) - 12 = floor(15.2) - 12 = 15 - 12 = 3, right? God that's a lot of redundancy, but this is just so you can clearly see the steps I'm taking.
http://i.imgur.com/3UsD76v.png
And as it turns out, no, it is not. Knight guy does 4 damage, not 3. Knight guy is also all alone. No random spur buffs from friends here.

Here's the thing: remember the thing about WTD being -20% attack in the in game tip? Yeah, remember the Luna thing above? You know where this is going. That -20% is the one cut off, not the '80% final attack'. So.
damage = [ 19 - floor(0.2 * 19) ] - 12 = 19 - 3 - 12 = 4

There we go. So now we have for WTA:
damage = [ ATK + floor(0.2 * ATK) ] - DEF
and for WTD:
damage = [ ATK - floor(0.2 * ATK) ] - DEF
Replace 0.2 with 0.4 if Triangle Adept.
3DS FC: 4656 - 7963 - 4906;
IGNs: Y Mimosa (????); AS Cinquefoil (????); M Emii (1328)

#### User Info: Reimys

Reimys
4 years ago#2
WEAPON EFFECTIVENESS AND WTA/WTD

http://i.imgur.com/mcRylM2.png
Boy I love having dragons tank Falchions.

Anyway, here's a Chrom in training tower. Stratum 9 I think, I don't remember it doesn't matter.
http://i.imgur.com/3XviFnR.png

There's a nice spot right there for me to shove Corrin or Fae into to demonstrate damage done to them. They'll be getting buffed by Lucina's Spur Attack +4 attack, so mind that if you want to goggle at damage. Chrom on the other hand is all alone and isn't getting buffed by anyone, and currently has Fae's Threaten Attack on him for that nice 45 damage. Poor guy.

So here's Fae.
http://i.imgur.com/FzWsIgf.png

Aaaand here's Fae against Chrom.
http://i.imgur.com/guAg4GP.png

Ow. But let's put our damage formula to work. Two possibilities here if you ignore what I said in the first post about operation order: either WTA boost happens first, or Falchion's dragon slaying effectiveness happens first. Remember that weapon effectiveness is +50% attack, and that we never multiply directly; treat all attack modifiers as a separate added value to the stat so you know when to round/truncate things.

Let's math out WTA boost first:
attack after WTA = 45 + floor(0.2*45)
= 45 + 9 = 54
attack after weapon effectiveness bonus = 54 + floor(0.5*54)
= 54 + 27 = 81
Actually, we never even had to round at all because those were both a flat integer- 9 and 27. Except...
Damage = 81 - 25 = 56
And as we can see, Fae takes 55 damage. That can't be chalked up to rounding error or any weirdness like that.

Let's try effectiveness boost first instead:
attack after weapon effectiveness bonus = 45 + floor(0.5*45)
= 45 + 22 = 67
attack after WTA = 67 + floor(0.2*67)
= 67 + 13 = 80
Damage = 80 - 25 = 55
Oh, hey, there we go.

Anyway, here's wonderwall- I mean Corrin.
http://i.imgur.com/w781btl.png

Here's Corrin against Chrom.
http://i.imgur.com/figh0GL.png

Math.
atk after eff boost = 45 + floor(0.5*45)
= 45 + 22 = 67
atk after WTD = 67 - floor(0.2*67)
= 67 - 13 = 54
Damage = 54 - 34 = 20
Checks out. This is actually an example where it doesn't matter if you do WTD first because the numbers come out even enough to end up at 54 anyway. However, at 44 attack, there's a difference, and in fact 44 attack is what that Marth going against Corrin up above had.

Reimys posted...
I have one flat number of Marth doing 19 damage to neutral fCorrin, screenshotted, so that's -Atk (44). There's a couple ways to do the math internally, but so far I've only gotten one method to come up with 19. Given my damage taken, I'm looking for a method that gives Marth an effective attack of 53.

The standard thing we all were doing was floor(44*0.8*1*5)-34, but... floor (52.8) = 52, 52 - 34 = 18, one short. This one's wrong anyway, bc it assumes rounding takes place only after all attack modifiers do and that's not how it works.
If we do WTD first:
44 - floor(0.2*44) = 36
36 + floor(0.5*36) = 54, 54 - 34 = 20 dmg, one too high.
If we do effectiveness first:
44 + floor(0.5*44) = 66
66 - floor(0.2*66) = 66 - 13 = 53. Perfect.
3DS FC: 4656 - 7963 - 4906;
IGNs: Y Mimosa (????); AS Cinquefoil (????); M Emii (1328)
(edited 4 years ago)

#### User Info: Reimys

Reimys
4 years ago#3
SPURS AND YOU

By the way, fun fact about Spur Atk/Def: they add to the stat. They don't cause a flat +4/-4 in damage dealt/taken. Look at Fae, look at Chrom.
https://i.imgur.com/FzWsIgf.png

Fae has 43 attack, attacking into WTD against 19 res. Due to WTD she has 35 attack (43-8), now... if Lucina wasn't there, she'd do 16x2 into Chrom. But if Spur was a flat +4 to damage, then she should be doing 20x2. Instead, she's doing 19x2-- or effectively attacking with 43+4 then penalized by WTD attack.
atk = 47 - floor(0.2*47)
= 47 - 9 = 38.
damage = 38 - 19 = 19.
I only bring this up because I've seen it mentioned sometimes that spurs/goads/wards are a flat addition/reduction after everything else; that's not the case here.

There was a misconception a while back that the buff damage the -Blade tomes Nino/Tharja/who?(well okay Odin) use were flat damage. No, it's just added to attack.

http://i.imgur.com/Y3BA3il.png
So here we have a Nino doing her best. She's at +3 Atk and +4 Spd from Eirika.

http://i.imgur.com/MkhteuH.png
Here's a Takumi looking like a Takumi.

http://i.imgur.com/8q4uoTG.png
And here's him getting rekt.

Damage = ( Displayed Atk + Total buffs ) - Res
or in this case
Damage = 46 + 7 - 13 = 40.

But wait, Rei, how can you prove it's just added to attack? That would have worked out the same way with just a flat +7 on after Nino did 33 damage! Well, then, fine, here.

http://i.imgur.com/t6aRzf5.png
Behold, a Shanna, who has 23 res and WTD against Nino.

http://i.imgur.com/SSbl5Bq.png
And here's her taking also 40 damage against Nino, which implies that Nino is attacking at either 63 effective attack, or 56 effective attack, then with a free +7 true damage tacked on.

If it's true damage added onto the end and doesn't affect attack:
Atk after WTA = 46 + floor(0.2*46)
= 46 + 9 = 55
Damage = 55 - 23 + 7 = 39
Nope.
If the buff values are included in her attack:
Atk after WTA = 53 + floor(0.2*53)
= 53 + 10 = 63
Damage = 63 - 23 = 40
Ey.

PROC SKILLS A LA GLACIES/IGNIS AND YOU, OR: NO IT'S NOT DEFENSE PIERCING PER SE

So here I have a sad Felicia who got pretty beat up by Takumi while she charged her special. :(
http://i.imgur.com/224gr7Y.png
And here's a tower Robin.
http://i.imgur.com/TRVfDlq.png

Poor Felicia is at 20 effective attack against Robin's 23 defense due to Blarraven's effect, yay WTD.

Here's Glacies proc.
http://i.imgur.com/HtqBzQZ.png

Robin takes 27 damage.
floor(0.8*38) = 30
Glacies, if it was defense piercing, should do 30. It is not doing 30. Therefore it is not defense piercing.
With 20 attack vs 23 defense, you can imagine that Felicia is currently doing -3 damage, displayed as 0, because healing on attack would be silly. Glacies adds 30 damage to her -3, so -3 + 30 = 27.
Alternatively you can imagine that it's +30 attack after WTD/effectiveness (see: niles) has taken place, because the difference between +30 attack and +30 damage is... well, nothing if the attack is added after all other modifiers have already resolved. 20 + 30 = 50, 50 - 23 = 27.
3DS FC: 4656 - 7963 - 4906;
IGNs: Y Mimosa (????); AS Cinquefoil (????); M Emii (1328)
(edited 4 years ago)

#### User Info: Reimys

Reimys
4 years ago#4
There, now I've satisfied my OCD. Maybe now that it's all written up somewhere I can stop fiddling with it and compulsively taking screenshots. @_@

I just hope I didn't accidentally write up nonsense somewhere due to sleep deprivation, bah. Please tell me if I did.
3DS FC: 4656 - 7963 - 4906;
IGNs: Y Mimosa (????); AS Cinquefoil (????); M Emii (1328)
(edited 4 years ago)

#### User Info: Krentaris

Krentaris
4 years ago#5
That's actually awesome. I'd even request sticky for this, it's well written, thoroughly explained and even has visual evidence.

Yeah screw it, sticky this, it's excellent.
"Perfectionism becomes desirable when it stimulates the healthy pursuit of excellence."

#### User Info: AntiAir

AntiAir
4 years ago#6
Cool.

Sorry to ask since you're tired, but how is the bonus from gem weapons/triangle adept? Does it add/substract floored 0.2 Attack twice? Or does it go straight for +- 0.4 Attack?
Destroyer of aircraft.

#### User Info: CyclonSilver

CyclonSilver
4 years ago#7
There's mooooore~

Double WTA is attack x 1.4(or 0.6), not x 1.2 x 1.2(or 0.8 x 0.8). Also, triple, quadruple or quintuple wta don't exist(triangle adept and jewel weaponry do not stack with each other, basically), though admittedly I have yet to run in a situation where even a quadruple could be a thing. But if two such effects are involved(two opposing jewels, two triangle adepts, or one of each), they don't stack.
Kurt Hectic never wanted to be a hero. He was content with his life, and wanted to live out his years in quiet dignified anonymity.
Sadly, it was not to be.

#### User Info: Reimys

Reimys
4 years ago#8
CyclonSilver posted...
There's mooooore~

Double WTA is attack x 1.4(or 0.6), not x 1.2 x 1.2(or 0.8 x 0.8). Also, triple, quadruple or quintuple wta don't exist(triangle adept and jewel weaponry do not stack with each other, basically), though admittedly I have yet to run in a situation where even a quadruple could be a thing. But if two such effects are involved(two opposing jewels, two triangle adepts, or one of each), they don't stack.

I have a tiny thing at the bottom of the first post basically saying the same thing as the first thing you said, haha. I think I would have elaborated except I was running into character limit.

Admittedly it did not occur to me to have a blurb about 'no, you can't get 0.6 or 0.8 extra damage to happen' though!

AntiAir posted...
Cool.

Sorry to ask since you're tired, but how is the bonus from gem weapons/triangle adept? Does it add/substract floored 0.2 Attack twice? Or does it go straight for +- 0.4 Attack?

Second one I'm pretty sure, I only don't say it as an absolute because I don't currently have screenshot proof of it with relevant values. Still, if it's added/subtracted twice in different steps that'd effectively be a multiplicative modifier (1.2*1.2 =1.44 instead of the 1.4 it should be). Same step, well...

I can do a little bit of hunting around with Sanaki to try to exactly pin it down/prove it if you want though. o7 I do understand there's still the chance of a difference between say, adding floor(2.6) twice and adding floor (5.2), which is what I think you were getting at, right?
3DS FC: 4656 - 7963 - 4906;
IGNs: Y Mimosa (????); AS Cinquefoil (????); M Emii (1328)
(edited 4 years ago)

#### User Info: CyclonSilver

CyclonSilver
4 years ago#9
Reimys posted...
CyclonSilver posted...
There's mooooore~

Double WTA is attack x 1.4(or 0.6), not x 1.2 x 1.2(or 0.8 x 0.8). Also, triple, quadruple or quintuple wta don't exist(triangle adept and jewel weaponry do not stack with each other, basically), though admittedly I have yet to run in a situation where even a quadruple could be a thing. But if two such effects are involved(two opposing jewels, two triangle adepts, or one of each), they don't stack.

I have a tiny thing at the bottom of the first post basically saying the same thing as the first thing you said, haha. I think I would have elaborated except I was running into character limit.

Admittedly it did not occur to me to have a blurb about 'no, you can't get 0.6 or 0.8 extra damage to happen' though!

Woops, missed it. That being said, the important part of what I said is that while effectiveness is multiplied by wta, double wta is just... wta, x2, as in 1.4 and not 1.44. That's not necessarily self explanatory. And there are the jewel weapons on top of triangle adept, but otherwise yeah, I totally missed that one part.
Kurt Hectic never wanted to be a hero. He was content with his life, and wanted to live out his years in quiet dignified anonymity.
Sadly, it was not to be.
(edited 4 years ago)

#### User Info: Reimys

Reimys
4 years ago#10
@AntiAir Here you go!

ELABORATION OF TRIANGLE ADEPT/GEM WEAPON EFFECTS

So, here's a glorious +Atk Empress of Begnion, Sanaki.
http://i.imgur.com/a5djM6B.png

She's at 54 attack, which is a useful number here given that we're running Triangle Adept 3 for 20% extra damage when WTA, and 20% extra reduced when WTD. The question is, does that make the bonus 40%, or does it simply do 20% twice in the same step? Thanks to 54 attack (20% of it is 10.8, or 10... vs 21.6->21 if it's a 40% bonus), we can find out!

Here's Minerva.
http://i.imgur.com/GQIkMNf.png

She is not very magic tanky.

http://i.imgur.com/8WBAQgY.png
Very much not so.

Alright, so it looks like Sanaki is attacking with an effective 75 magic, dear sweet Ashunera. Let's see what that turns out to be!

If Triangle Adept simply applies the 20% bonus twice:
Atk after WTA = 54 + floor(0.2*54) + floor(0.2*54)
= 54 + floor(10.8) + floor(10.8)
= 54 + 10 + 10 = 74
Damage = 74 - 13 = 61
Oops, not quite.
If Triangle Adept changes that 20% bonus into a 40% bonus:
Atk after WTA = 54 + floor(0.4*54)
= 54 + floor(21.6)
= 54 + 21 = 75
Damage = 75 - 13 = 62
Blammo.

It is not remotely multiplicative. If it was, it'd be:
Atk after normal WTA = 54 + floor(0.2*54)
= 54 + 10 = 64
Atk after Triangle Adept boost = 64 + floor(0.2*64)
= 64 + 12 = 76
Damage = 76 - 13 = 63
That's a no go.

We don't really need to go further with this, but here's Est anyway.
http://i.imgur.com/qDyAHVF.png

It's just 10 more res on top of WTD, right? How bad could it be?

http://i.imgur.com/DKDNaCd.png
Oh. Mind you, Minerva did have a fliers buff of some sort, but as you can see she's not in range to be buffing Est.

Atk after WTD = 54 - floor(0.4*54)
= 54 - 21 = 33
Damage = 33 - 23 = 10
Yikes.

You'll note that changing the modifier itself into 40% gives the potential for an extra +1/-1 damage difference compared to if Triangle Adept was just adding/subtracting the base 20% modifier twice in the case that the value for 20% of your attack is x.5~x.9 pre-rounding.
3DS FC: 4656 - 7963 - 4906;
IGNs: Y Mimosa (????); AS Cinquefoil (????); M Emii (1328)
(edited 4 years ago)
1. Boards
2. Fire Emblem Heroes
3. Quick and Dirty Damage Mechanics (not actually quick or dirty)
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