A sophisticated exercise in min-maxing that elevates theory-crafting to a rigorous optimization problem. It proves that even within the chaos of gameplay, there is an elegant numerical truth waiting to be calculated.
Deep Dive
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Deep Dive
Mathematically Correct Ekko/ZileanAdded:
Good morning, my lovely viewers. Today's script is going to be [ __ ] because I haven't gotten around to writing all of it. I was in the dumbs a Mayhem tournament and I had to be up at 2:00 a.m. for that one and then I had to play until the end cuz we didn't get eliminated. So, that left me pretty exhausted. But anyway, I'm here now.
Video is going to be out maybe a bit later than usual. Today's video is going to be a themed one because I thought of the idea and then decided to work the builds back from that. Anyway, you've seen the thumbnail. You know who we're playing today. Today's video is about Ekko and Zillian.
Ekko's ultimate is every assassin's best friend. If you mess up your combo, you can just reset and get all your health back. If someone's chasing you, you can teleport back and surprise burst them.
If someone pointing clicks you, no, they didn't. It destroys projectiles.
Chronobreak passively leaves an after image of Ekko when it's off cooldown, which shows where he was 4 seconds ago.
On activation, Ekko enters stasis and dashes unstoppably to the after image.
He also heals for a decent amount, scaling with AP and amplified by any damage he took recently. The damage scaling for this ability is ridiculous.
This could one-shot you even without the rest of his combo, which he can hit in even less time now thanks to Dusk and Dawn. Great item, Riot. Turn every three hit passive into a two hit passive. Well done. Anyway, I don't really care about the damage. That's boring. The good part is the healing. And I think it's very funny to heal to full after losing all your health. First, let's figure out how much AP and health we need. As you can see, our healing scales with AP and heal and shield power with an extra scaling based on your missing health. We're going to optimize for the most effective full health heal. Basically, a build where I can take as little damage as possible and still heal 100% of my max health. To do this, we look at the healing gain from R. We want to heal for 100% max health while minimizing health lost. So, we rearrange to get a formula for that. This goes into the build script after we change the parameters so it optimizes for the smallest value instead of the largest. I had it the wrong way round for an entire day and got really confused by all the builds it was spinning out cuz there's no way Warm monks is an optimal item here. Anyway, to LAR's Crazy Diamond on Ekko, you build donor, shadow flame, raidons, magis, staff of flowing water, and ardent sensor. Basically, we're just going for high AP numbers with some support items thrown in there for extra heal and shield power. With this build, we can get a max HP heal after losing about 65% of our health. That's about 1,650 damage when you have full build, converting to a 2512 health heal. If we take slightly less damage, the heal is still pretty good, but not 100% of your health. If you're a coward or want to mind control your enemies, you can swap out the magi for zas. For runes, take faith, arcane, comet, axium, archist, and revitalize for a little more soul on your healing. You could swap out your keystone for guardian and aftershock, but those runes are for babies who are afraid of taking damage.
We need a second champ to fill out our bot lane comp. And who else to fit the time theme than Zillian. If you want some actual synergies, you can use Zillian's EO to set up Ekko's W for an easy stun. And having Chronos shift on top of Chrona Break makes Ekko very difficult to kill. Ekko also loves the movement speed Zillian gives. And Zillian can attach his time bombs to him while he gap closes for another guaranteed stun. So overall, it's [ __ ] and playing against him is like waiting through tar. Every time there's too much ability haste in the game, off Meta Zillian builds start cropping up, like wrinkly locusts. This lets Riot know that they [ __ ] that [ __ ] up and need to make some emergency patches. The basic idea behind this build is to cycle between Zillian's three abilities. His Q is a time bomb that explodes after 3 seconds, which can attach to targets it touches. If two time bombs attach to the same target, it stuns for 1.5 seconds.
His Either speeds up an ally or slows an enemy by up to 99%. His W, which is the important part, reduces his other basic ability cool downs by 10 seconds. We want to chain stuns with slows and reset both abilities with W to keep our target still for as long as possible. This isn't quite an infinite CC chain, but it's close enough for our purposes. To use Zillian stand, the world build safer, shoen, and cryptoon. Actualizer is here for a specific purpose. There's a tech you can do using the 30% cool down reduction on the active where you can chain stun someone for about 8 seconds.
The rest of the items are just here to soup up your ability haste, which is why we're building Shojan despite having no AP. Her runes take airy, transcendence, gathering storm, and legend haste, as well as the haste shard. I don't have to explain the runes to you. Figure it out yourself.
Why didn't you use a hashmap? Why are we doing prime numbers?
Just use arrays at this point.
I hate every single one of you. I'm not a coder. I am not a compsai major. I came up with the idea to use prime numbers because I work more with maths than computers. There aren't limits on integer sizes and maths. I don't have to account for computation times and I was working from a more complicated concept, simplifying the idea used to suit my needs. Of course, a bunch of [ __ ] nerds in my comment section remembers what bit maps are. [ __ ] I have to implement them. Now, those of you who are normal and have no idea what computer science is, bit maps are a way of storing information inside integers.
You can convert any whole number to base 2 or binary, which gives you this string of ones and zeros. We can assign each of the digits in a binary number to a unique item group starting from the right. Since there are 22 groups, we need to use a 32-bit integer, but that's just nerd [ __ ] You don't have to pay attention to that. Just ignore these extra zeros. We interpret this number as a list of check boxes for each group.
For example, Moramana is in the group Manaflow, which is the 14th group. To store this, we change the 14th digit to a one and leave the rest as zero. If an item is in two groups, like Blood Song, we just do this for each group, changing the 12th and 19th digits to one. This fixes the issue of storing multiple groups in a very elegant way. If we want to get the groups a builders in, we just add the group numbers for each item. If you want to find out if a new item's groups overlap with a builds groups, we just use the bitwise and operation, which compares the bits in both and returns a one in that position. If both the build and the new item are in the same group, then we just check if the end result is larger than zero, which simplifies to this very neat shorthand in C. This code is much simpler and more performative than my old code with the primes. I mean, look at it. The logic's literally one line.
[ __ ] I can't believe I almost added the primes to my script. I hate showing you guys my code. You all make fun of me.
Now I know why Michael skips this part in the videos.
Since this video is about a bot lane duo, I can't really test it out on my own. I figured this would be a good time to use my clout as a small-time YouTuber and call in someone to help me out.
That's why I called in Osloo. We played the duo on my stream at twitch.tv/hilofir, where I stream at regularly scheduled times. You might have seen her videos before. They're pretty funny. Good builds to try out before everyone's MMR is reset.
>> What are we cooking? We're cooking for the next video. We're getting footage.
>> Let's record one big file. I'm sure this this has never caused me issues in the past.
>> I I think this is a pretty funny combo.
>> Yeah, honestly, it's not too bad. Just need to watch out for >> Oh, go in. Oh, >> that was the goat. The goat.
>> People will forget. Wait, I got the >> What the That's That's the thing that did that. That's the thing that did that. That's not me. That's not me. The thing did that.
>> Nice dodge.
>> I'm just taking because Yeah, fair enough. I >> It's so difficult to play on this ping.
I won't lie. We can just cut out all the bad bits, right? Um, >> yeah, we could do that.
>> We'll cut out all the bad bits, right?
>> Yeah.
>> Good job.
>> Well, I think I healed you. Oh, thank you for the heal. I am dead even. And this is my first time playing it, if you can believe that.
>> Oh, I I can I can believe it. You were you were trying to remember what the build was.
>> H I don't remember what the other items were.
>> I love this.
>> This isn't good. Whatever. I got four out of six. That's good enough.
>> Oh god.
>> This might be my first time playing Zillian ever, apart from practice tool >> as well. Yeah, I think it's plausible.
Yeah, >> I I >> if I can eat your >> She's ending the game.
>> Oh, [ __ ] >> Yeah. Yeah. I mean, yeah.
>> Get him, Trundle. Whack her. Oh my god.
Trundle wins those. The base the minions for >> Oh no. Where'd he go? Oh, he's dead.
>> Oh, he's dead.
>> We're losing to John.
Oh no.
>> If we can just like get through the leaning phase without Samira killing us, we're doing great.
>> Yeah.
>> Was tempted to do something.
>> Wait, >> she's slowed.
>> There we go. Just leave.
>> Oh my god, you almost died.
>> I never die. I've never died once in this game.
>> She's cheating, your honor.
Urono point and click >> slain.
>> Oh, she got collector. She got collector. Jesus. She got collector and crit me from like 400 health.
Okay, my bad.
Oh, wait.
What?
How much of this can I get >> before someone comes to stop me?
>> Oh.
>> Oh my god. Carthus would be a podcaster about death.
>> He would be.
>> That's so funny to me that that's literally his lore. He's like, "I love death so much. I want to go to Death Island." And Death Island [ __ ] kills him.
>> Cuz it's, you know, death island.
>> His whole character is, what if killing yourself was a superpower?
>> I'm a [ __ ] I'm a professional gamer.
>> I'm assuming you lost a cannon.
>> No.
>> No.
>> I wasn't watching.
>> What gave you that impression?
>> Listen, I make these videos, too, you know.
Guys, why are we here? Shouldn't we be taking the dragon?
>> You'd think so.
>> You know what? Let's go. Let's go here.
I can't ping it anymore.
Your team has destroyed.
>> Go in.
>> Oh my god, the full health.
>> We might be okay.
>> Thanks, G.
>> I don't speak fake words. Don't worry, he doesn't he doesn't speak Korean either. There's no way he's really a Korean speaker.
>> Yeah, I know. He's just typing gibberish on his Korean keyboard.
>> Korean people aren't real.
>> It makes him He thinks he makes him look sophisticated.
>> Oh, he's having fun. He loves it here.
>> He's still going.
What the [ __ ] Okay, we are all going to get killed by Samir if she gets in and manages to like alult. So, >> no, she >> don't let that happen.
>> Uh, >> they might end this time. That is the second enemy quadrakill. I'm bomb I'm bombed bomber bombering.
Yeah, let's let's go for the baron.
>> An enemy has been slain.
>> She's ignited.
>> Nice.
>> Easy.
>> I have no idea why she walked into that mo the world's most obvious W, but we'll take it. I still have a health potion.
>> I use both of mine because I was thirsty.
>> Of course, a British person would be drinking this early in the evening.
>> Early in the morning rather than playing on a laptop. I'm playing on a laptop in Spoons right now.
>> Is that a pub?
>> Yeah, it's a pub franchise across the UK. Known being the cheapest place to drink, but they're open.
>> [ __ ] makes a franchise for pubs. That's so evil.
>> Yep.
>> Pubs should be owned by guys, not companies.
I mean, they they're like you can like the people who own each individual ones are guys, but >> that's how franchising works. Yeah.
>> Yeah.
>> But like that's still evil. Like there's going to be a guy. It's going to be a [ __ ] pub.
>> That's spoons. But that's Spoons for you.
>> Like if you want a good pub, you go to a pub. But Spoons is open at 10:00 a.m.
>> Wait.
Oh my god. That That is That is the tickler combo. I might be able to flash either.
>> Wait, get this.
>> An enemy has been slain.
>> [ __ ] >> I think I think Jinx Jinx is probably worth more than cannon.
>> Yeah, that's true.
>> I can't hit it. Not a clue.
>> I don't actually watch League content at all anymore than yours.
>> Holy [ __ ] How did that [ __ ] work? play.
>> It's basically just chess, right?
>> I mean, uh yeah, except for the fact that they're two different games, but basically >> Yeah, like it's the same. It's the same thing.
>> Well, you've got all an enemy.
>> You don't even need to use it.
Wait. An >> enemy has been slain.
>> Let him die.
>> You almost died for that.
>> No, no, no. Cuz he was healing. He was healing. I have >> No, he wouldn't. He wouldn't have healed past it. There's no way.
>> I don't I don't trust it.
>> I don't I never trust a Mundo to die.
>> [ __ ] She's going to alult me.
I can smell it. I can smell it on the horizon. She's going to alult me. I can I can see it. I can Why did I say I can smell it on the horizon?
>> Uh, >> that's not quite right.
>> Dramatic effect.
>> No, but you can't smell things on the horizon.
>> Not even close.
>> Boots locked. I can't buy boots for some reason.
>> Did you take magical footwear? Wait, no.
Your your boots are >> They're in the 80 carry slot. I'm so stupid.
>> I'm good. I land those. An enemy has been slain >> again. An enemy has been slain.
>> Thank you.
>> Nice. Somehow this bot lane's actually good. I'm I'm >> Oh [ __ ] [ __ ] Nice.
>> Hey, we win.
>> It's pretty pretty big deal. Didn't mind yet.
>> That's one for two.
Thanks for making it to the end. I'm not going to apologize for this video coming out late. I was busy with actually important things. I don't have unlimited free time or the ability to make every video you guys want. And trust me, I get a lot of video suggestions. Some of them are actually good though, just not things I want to make, which is why I'm starting the bounty board. In the description, there will be a link to a website where I'll put a list of video ideas that I and some other content creators think are good ideas, but don't want to make ourselves. The idea is that you guys take those ideas and make your own YouTube videos about them. And as a small incentive, at the end of each of my videos, I will be gifting a legendary skin to the best video made from the bounty board since the last one. The winner will also get a shout out at the end of the video. Kind of like what Jax Films does with his video of the week thing. We need more small creators in the League space, and I need more videos to watch while eating breakfast. Thanks again for watching.
>> [ __ ] [ __ ] Ah, GG. Ah, GG. GG.
>> Zillian does no damage.
>> Yeah, he's he really is just a clear wave kind of guy.
>> This champ sucks. Why is it so good when we're playing it?
>> Uh cuz we're not like in lean all the time. And we're working together. We got the power of friendship.
>> That's true. It's the power of friendship. The power of friendship makes this wrinkly old man good.
>> Exactly.
>> All right. Well, uh cuz I lost. It's not good in the video. So, uh >> Oh, [ __ ] What?
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