On Magic Amplification

To start off, I'd like to crunch some numbers related to a subject I covered in the Zeus guide: magic amplification.

You mean what you got called out on for calculating incorrectly?

Yeah. That one. I put some thought into it to make sure my numbers were 100% right after that, and the research gave me some pretty interesting ideas that I'd like to share. The main question we'll be asking today is... well, ok there are two. The first is: what is the maximum amount of magic amplification you can apply on a hero? The second, and arguably most important is: is the team composition required to make such a thing happen viable at all?

Prooobably not, just from what I'm doing in my head.

I'm inclined to agree with you, but I haven't crunched the numbers just yet, so let's see what we've got. For starters, it's best we lay bare some of the basic mechanics of magic amplification and resistance in Dota 2.

1)All heroes start off with a base magic resistance of 25%. There are, of course, a few exceptions to this rule, specifically two: Meepo, everyone's favorite micro skillz hero, starts off with a base magic resistance of 35%, most likely to compensate for how vulnerable a target he can be, and Visage starts off with a base magic resistance of only 10%, likely to offset the insane magic resistance he gets from Gravekeeper's Cloak.

2)Magic amplification does not remove this innate magic resistance. It's always calculated in. There's an exception to this rule as well, however. Ancient Apparition, to be precise. His Ice Vortex ability specifically reduces magic resistance, rather than merely amplifying the magic damage taken. This is one of the reasons he's such a strong pick-up, actually.

3)All magic amplification stacks multiplicatively, with no upper boundary.

There's an exception to this rule as well, I assume?

Man, do you know Dota. Of course there's an exception! Pugna and his Decrepify dont' stack with Ethereal Blade, as the game considers them the same effect. In cases where Decrepify and Ethereal are both cast on the opponent, the game will always consider Decrep over Eth, as it is the higher value of magic amplification (on enemies, anyways; if you Decrepify an ally and the enemy uses Ethereal Blade on them, they'll take the 40% increase as opposed to the 25%).

Now that the basic rules are laid down, let's make a massively, magically lethal stew! For this brew we will need:



Feel free to call me out if I'm forgetting a source of magic amplification, but I'm pretty sure I've got everything. Anyways, let's look at those numbers:

First off, Ice Vortex reduces magic resistance by 30% at max level, which makes our calculations a lot easier actually. Instead of having to multiply by .75 every single time we try anything, this actually gives most heroes a negative 5% magic resist, which is basically a 5% boost.

Natural Order of Elder Titan amplifies magic damage by a whopping 33%. This seems like a lot, but Skywrath Mage and his Ancient Seal amp up damage by 45%. All of them get beat by Decrepify however, which increases magic damage by a monstrous 50%.

I'm gonna say we give AA the Veil of Discord, just because he could use the tankability. That's another 25% tossed on top of everything. Ready for the number crunch? Gird your loins, cause here it comes...

100*(1+.05)*(1+.33)*(1+.45)*(1+.5)*(1+.25) = 379.67

Holy Hell. All I can think of is using Finger of Death and doing over 3000 damage.

Yeah. It's pretty impressive, alright. The question is... can we do better?

Um... no? You did say this was all the magic amplification in the game.

True... but you can crank more numbers out a spell without using straight magic amplification... bring on the next round of ingredients!



Cheater.

Shush. Orchid Malevolence and Soul Catcher off of Shadow Demon both don't technically amplify magic damage, they do soul burn, dealing all the amplified damage as a separate instance right at the end. For our purposes though, this actually works in our favor... one spell will deal three instances of damage, all of which will be amplified.

This is going to be insane, isn't it?

I sure hope so. Chen, while Penitence is an amazing skill that deals its amplified damage as physical just doesn't output enough to hang with the big kids: 32% isn't big enough to knock anyone off our dream team, and the fact that it's physical means it won't be amplified by everything else, making our calculations really, really difficult. Thank goodness his numbers are low, or I'd have to deal with them.

Someone whose numbers ARE big enough to knock someone off our team is Undying. With Aghanim's Scepter, Flesh Golem amplifies damage by 35% at closest range, knocking Elder Titan and Natural Order out of our cocktail, thanks to the five hero limit of the game.

So, to clarify, our final brew for calculation's sake will be:



Our ideal scenario, then, is as follows:

Our poor target is caught out alone by all five heroes at once. Veil is used, Decrepify is used, Ancient Seal is used, Ice Vortex is used, Flesh Golem is used, Soul Catcher is used, and Orchid is used. The first instance of damage dealt by a single, incoming spell, will be amplified by...

100*(1+.05)*(1+.35)*(1+.45)*(1+.5)*(1+.25) = 385.38%

After 5 seconds, the damage from Orchid Malevolence is dealt. Decrepify is no longer active on the target thanks to its 3.5 second duration, but a maxed Ancient Seal will still be active. Since Orchid deals magic damage as well (lol), we now have the following equation:

385.38*(1+.3)*(1+.05)*(1+.35)*(1+.45)*(1+.25) = 1287.16%

HOLY...

No. I'm not done yet. Stay in your seat and take my math.

Yes, sir.

After 12 seconds, the damage from Soul Catcher is dealt. Decrepify is off cooldown and can be cast again, as can Ancient Seal if Skywrath's fingers are quick enough. Let's assume they are.

The damage dealt, as PURE damage, mind you, thanks to Soul Catcher being broken, is:

1287.16*(1+.05)*(1+.35)*(1+.45)*(1+.25)*(1+.5)*(1+.5) = 7440.74%

Oh my god... it's full of numbers...

Keep in mind, this is just a percentage calculation, starting with a base of 100. If the spell cast is Pugna's Nether Blast, the hero will take more than 24 THOUSAND damage.

Why... why do teams not do this?

Well, I mean... look at the team comp you need. Who's the carry on this team, Pugna? Sure he can do it, but he's certainly not the best out there. This scenario also requires Undying to get an Aghanim's Scepter, and... there are much, much more important things for an Undying to get. There's also the slightly uncomfortable fact that all of this damage gets reduced to 0 if the enemy jumped on has the almighty Black King Bar.

So... the point of this article was...

... Numbers are awesome?

I hate you.

I know. <3

Thanks for sticking with me, if you're reading this far. I tried to be really careful in my calculations, but I am only human, and assume I made a mistake somewhere. Let me know so I don't dash any hopes, ok? Safecyn, signing out.

Correction:

It's been brought to my attention that Soul Catcher, in fact, deals an instance of damage for each instance of damage, rather than one at the end. After looking over combat logs, I'm inclined to agree that this is how it works.

So? What's the damage?

Our new scenario is as follows:

Initial Damage:
100*(1+.05)*(1+.35)*(1+.45)*(1+.5)*(1+.25) = 385.38%

First Tick of Soul Catcher:
385.38*(1.05)*(1.35)*(1.45)*(1.5)*(1.5)*(1.25) = 2227.78%

Orchid Pops (Decrepify off cooldown):
2227.78*(1.05)*(1.35)*(1.45)*(1.25)*(1.3) = 7440.75%

Second Tick of Soul Catcher:
7440.75*(1.05)*(1.35)*(1.45)*(1.25)*(1.5) = 28675.37%

Twenty... twenty eight... WHAT THE HELL?

Yup. Our Nether Blast from Pugna that dealt twenty thousand damage now deals a whopping 93,195 damage. Have fun, everybody!