The Perfect Lich Ult, Part 1 (SCRs and Permastuns)

In my previous blog entry, I tried to figure out the maximum amount of units you could cram into a single team, in order to maximize the damage of Earthshaker's Echo Slam. It was a lot of fun! Dealing with numbers that don't technically have a cap and seeing what their actual limits are is cool to me, so when I saw a comment about Lich's ult, I immediately knew the next question I had to ask.

What's the maximum amount of damage you can force out of Chain Frost?

Um... is this a serious question? If you get an Aghanim's Scepter it bounces an infinite amount of times, so you get an infinite amount of damage. Boom. Blog post done. Thank goodness.

Not so fast, buddy. It's all well and good to say that an ability with an infinite damage cap does infinite damage, but that's just on paper. We're better than that here, man. We want to figure out how much damage you could ACTUALLY get from it, not just theoretically.

I don't follow.

Any team worth its salt is going to Delta Split at the first sign of a Lich ult. As a result, even with unlimited bounces, you're never going to get unlimited damage: at some point, the madness will end.

Unless you cast it on the Ancient camp.

Shush. Anyways, it follows that in order to get maximum damage from Chain Frost against a competent team, you need to keep them in the same place for an extended period of time. Permastunning, in other words. 5-man permastunning, at that. This changes our question slightly, at least for now, from 'How much damage can Lich's ult do?' to 'How long can you permastun an entire team?'

Sounds complicated.

Doesn't need to be. In order to help tackle this problem, I whipped up a little statistic I call an SCR, or Stun/Cooldown Ratio. By looking at the AOE stuns present in Dota 2 and seeing which 4 heroes have the highest SCRs, we known what our ideal team is for maxing out Lich's damage output. Below, then, is a listing of SCRs I found for a good number of the game's potential 5-man stuns. All stuns are considered at max levels, and with Aghanim's Scepter upgrade if applicable. The units for each number should be read as seconds stunned/cooldown length.

Echo Slam : .0136
Ravage : .0184
Black Hole : .0222
Ghost Ship .035
Stone Form (Visage Familiars) : .05
Chronosphere : .1
Fissure : .11
Storm Hammer : .1538
Hookshot : .1666
Burrowstrike : .1972
Earth Spike .21
Hoof Stomp : .2115
Impale : .213
Split Earth : .2222
Boulder Smash .225
Ice Path : .2444
Unstable Concoction : .25
Light Strike Array : .2714
Enchant Totem : .3
Slithereen Crush : .3125

Huh. So Slardar actually IS the best at something? Interesting.

Normally I'd say shush, but I don't really like Slardar either. In this scenario, though, he's our 'carry' if you will. Our dream team of stunners, then, is as follows!



Wait... why isn't Alchemist up there?

Even though his SCR is pretty high, concoction's 16 second cooldown is too long to be covered by any combination of lower cooldown stuns. Jakiro might technically be worse, but the nine second cooldown on Ice Path makes him more spammable.

Anyways, when added up together (excluding Earthshaker's Echo Slam, because that's had enough attention lately), we can see that our team's SCR is:

.3125 + .3 + .2444 + .2714 + .11 = 1.2379

Which... is interesting.

Oh? How so?

Well, think about the units we're using here. Seconds stunned over cooldown length. A number of 1 or higher means that you get at least a second of stun for every second it takes for your spell to come back online.

Oh... OH! OOOH! Holy... are you saying...

Jakiro, Lina, Earthshaker, and Slardar can keep an enemy team literally permastunned. It's not easy. It requires a very precise order of spells and perfect timing on the team's part, but... it's possible. Permastunning is REAL.

Explain. Now.

Well, interestingly enough, a total SCR of 1 or higher doesn't guarantee that you can keep a target literally permastunned. I had to try a lot of permutations to get it exactly right, and as far as I can tell, fissure, despite it's low SCR, is REQUIRED. The order of spells to achieve full permastunnage is as follows:

With close to pinpoint timing and an infinite supply of mana, an enemy team has literally no opportunity to escape this. Not even a .1 second gap exists. Not even a .01 second gap exists. An entire enemy team, trapped in place, allowing our friend Lich's ultimate to bounce as many times as it damn well wants to.

Wouldn't it be easier to just use Meepo?

Earthbind isn't a stun! Your enemies could cast spells to interrupt your chains, or activate items to help them escape. Plus, doesn't that seem like a cop out to you? Like, at all?

I suppose... also, why is Fissure required? Even if you take it out, the total SCR should still be over 1.

Without it, Ice Path won't be off cooldown when the pattern resets. The stuns that come before it add up to 8.1 seconds of crowd control, almost a full second short of what we'd need. Fissure provides that extra 1.75 seconds necessary to form a completely unbroken cycle.

This... seems really, really broken.

It's not, if you think about it. Your team has to be perfect, you know? You have to practice this. You need to always hit every single hero. Your Earthshaker needs to make sure his Fissures don't block your team from landing their abilities: Slithereen Crush comes to mind as one that could get easily screwed up if something goes wrong. In short, if a team can pull this off, they really, really deserve to win.

So... I was right then. The damage potential of the ability is infinite.

Nah. You're still wrong. Well, maybe.

WHAT? WHY? How on earth is it NOT infinite?

Because: Chain Frost can only bounce when there's heroes left to kill. And all heroes have to die eventually.

... wait. Are you actually going to...

We'll just have to see, won't we?