Treant Protector, Gold, and Natural Selection

Given up the MMR climb already, eh? I don't blame you, you're not cut out for competitive Dota.

I'll have you know I'm one hundred percent committed to finishing my calibration, THANK YOU. But I've been back for a bit and it's been a while since I've done something... mathy, you know? It feels wrong. So I'll be taking a brief interlude from dying to Sniper and Troll Warlord and spend some quality time in my old math corner, with one of my favorite heroes to boot: Treant Protector.

When Treant's Aghanim's Scepter upgrade was first announced, I didn't really understand how good it was. To my credit, I knew that it basically gave him free wards on a 20 second cooldown that could see into roshpit and that the enemy would need a Quelling Blade or Tango to get rid of (or Timbersaw. Friggin' Timbersaw), but I was a little confused by how Overgrowth interacted with it.

What, something about whether the damage goes through magic immunity or not? Because it doesn't, scrub.

No no, nothing understandable like that. For the longest time, since I'd never played a game with Treant since the update, I thought that the Aghanim's Overgrowth worked in sort of an expanding radius type thing. The initial cast still came from Treant Protector, and then any enchanted trees within THAT radius would ALSO trigger... etc, etc, causing a chain reaction as far along the map as you'd been able to set up.

But I know better now. I know that all of the trees cast Overgrowth independently, meaning that your Aghanim's Scepter makes Treant's ultimate a quasi-global skill, provided your team has the sense to fight within one of your trees' radius. It ALSO means that, since your trees provide vision into creep camps but don't block their spawns, you can farm the neutrals with it on cooldown if you so desire. This turns Overgrowth into one of the best, if not THE best flash farming skill in the game.

I decided to go into a Dota lobby and try and figure out just how much gold Treant Protector can farm with Overgrowth at any given time. I may have been in -wtf mode to set this up, but I was faithful to the mechanics of the game and only let myself cast the spell twice in succession (simulating a Refresher Orb). To give you an idea of my farming conditions, here's the mini-map:


You are REALLY enjoying that imgur account of yours, huh?

And HOW. Anyways, with repeated trials, spawning waiting for creep waves to get in position, and the double-casting Overgrowth, I was able to come up with a maximum gold gain of around 1500 gold, even hitting 1600 at once point. After repeated trials though, I found that my gold gain was gradually decreasing, and it only took me a few seconds to realize why:


After only a few trials of double-overgrowth, every single medium camp had wound up with mud golems. You may think I found this annoying, but I'm kind of pleased with this outcome. My college degree was in both math and biology, and I've always found virtual proofs of natural selection like this satisfying.

Virtual proofs of... it's a freaking video game, your science doesn't apply here.

Au contraire, mon frere, it applies in SPADES here. Natural selection, at its core, says that organisms that are better suited to handle their environment's pressures survive longer, living to pass their traits onto the next generation. If we think of every minute mark as a new 'generation' of neutrals (it is when they spawn, after all), it only makes sense that creeps with the 'magic immunity' gene would live through constant magical assaults and pass those traits on to their offspring. Thus: a jungle where all the medium camps are mud golems!

Interestingly enough, there's another place where natural selection could be seen while I was running this trial, this time having to do with towers. Since I put Eyes in the Forest trees on the lanes as well, the creep waves pushed and the top and bottom towers fell at just about the same time. The mid tower, however, lasted significantly longer. Any guesses why?

Eh? Oh! The same reason you never run Timbersaw mid, there aren't as many trees!

Gold Star. The tower's choice of habitat, as it were, gave it an overall better fitness. And as the fittest of the three towers, it survived. They call that something. It's on the tip of my tongue... ah well. But yes, much like a Magnoceros who doesn't live under an active volcano, the organism lives on to pass its traits to the next generation based solely on where it chooses to live. Pretty cool stuff!

Yeah ok, this is all fantastically interesting, I'm sure, but didn't you say you were going to do math in this blog? I don't see any math.

Ah, yeah... I kinda got sidetracked there. I did make a promise, didn't I?

Yup. Now what were you planning on calculating, exactly?

The maximum amount of gold you can get with a single refresher Overgrowth! Here are our baseline assumptions:

1) Each neutral camp in the game, including the ancients, are warded with Eyes in the Forest AND triple-stacked. You could argue that the maximum total gold you can farm is more than this, since you can sometimes get four or even five stacks of creeps in one camp, but I feel this is a reasonable assumption.

2) The lanes are also warded with Eyes in the Forest, and every enemy creep in each wave is caught by Overgrowth. They're also normal creeps, which makes sense, because there's no way a Treant Protector that gets an Aghanim's Scepter and has time to ward literally the entire map is on the losing team. Well... almost no way.

3) Each creep killed yields the maximum bounty.

With the baselines figured out, the calculations are actually rather simple. In order to get the maximum amount of gold out of our double Overgrowth we need to triple-stack the creep camps that are worth the most gold. By camp, these are as follows:

Small Camp: Harpies: 91 gold max bounty

Medium Camp: Ogres: 155 gold max bounty

Large Camp: Satyrs: 161 gold max bounty

Next, we have the ancient camps. Whlie most ancients are magic immune, the small black dragons (black drakes if we want to be technical) are not, meaning that they'll be cleared with Overgrowth as well! Each drake has a max bounty of 56 gold, making each ancient camp worth 112 gold as far as our calculations are concerned.

Lastly, the creep waves. Creep waves get gradually larger as the game progresses, and as far as I can tell the maximum number of creeps you can get in a wave is six melee and two ranged. With each melee creep being worth 48 gold and each ranged creep being worth 53, this gives each creep wave a value of 394 gold. Now all that's left to do is put it all together.

(91*2 small camps + 155*4 medium camps + 161*4 large camps + 112*2 ancient camps)*3 stacks per camp + 394*3 lanes = 6192 gold.

With passive gold gain set at 1 gold every .6 seconds at the time of this writing, Treant Protector gains an additional 15 gold passively over the nine second duration of his double ultimate. This means that, by double-tapping a single button, Treant has earned enough gold for a Divine Rapier. In NINE SECONDS.

Carry Treant new meta. CARRY TREANT NEW META.

Only time will tell, eh?

Hope you enjoyed, everyone! Safecyn, signing out.