General DiscussionWhat does provide more tankiness. Raw HP vs Evasion.

abit weird question depends on what the other team have item / skill wise

You want to tank physical dmg. As much as possible. Btw, it's me.

idk man. evasion is always ezly countered by mkb/silver edge and then worthless. depends so much on the game and heroes. like if the opponent team doesnt have a proper mkb carry then butterfly could be the better choice. but butterfly is kinda bad on many str carries.. then u would go for solar crest instead, if u really need it. but like vs juggernaut e.g., i'd prob go skadi to be able to tank his ult (which is physical and cannot miss).
dunno man, vague question gives vague answers.

I dunno, I like BKB and Talisman of evasion before eagle song, makes me feel invincible, but sometimes if I notice that I already have like 2600 gold after ending as big kill steak and a team fight, I just for eagle song. o_O But evasion + BKB, especially on Shadow fiend is pretty sick. Of course if they already have MKB, that's another thing. This type of question is weird, depends on the situation, there's nothing else really to say.

Yeah, I guess I went a bit too far with this kind of question, I guess.

It all depends.

skadi sucks without some early game items , such as sang yasha ,manta and stats giving stuff , if u are thinking about tanking why you compare carry items? u want to initiate with those items or what? if u want tankiness on str hero go buy ac

You have to consider the sources of damage - physical or magical (composite or pure as well), if you want to determine what gives more Effective Health Points (EHP). Like - what the heroes of the enemy team are gonna do at different stages of the game.

Obviously, pure stats give EHP vs both phys and spell damage, while evasion is only useful for avoiding physical damage

You can calculate EHP here - http://devilesk.com/dota2/apps/hero-calculator/

You have to consider how relevant EHP is to the whole picture, like it's just one dimension/aspect of your item build. Imo you're really in a position to theorycraft (neither am I though).

Just see what good players (pros / high level players) build, use multiple replays to link the item builds to the context (playstyle, specific heroes, team / enemy comp etc.), and ask better players to confirm your 'theory'.

theorycraft 4head

Eye of Skadi gives you 725 HP and 3.5 armour. Since each point of armour increases your Effective HP by 6%, eye of skadi gives you an extra 877 Effective HP Plus 21% of your current HP.

Butterfly gives you 35% evasion and 4.2 armour. The armour will increase your effective HP by 25.2% while the evasion will increase it by 153.8%. This means your Effective HP will be 179% of your current HP.

Which one is better thus depends on the HP you have before you get the item. if your current HP is x then butterfly will increase your HP to 1.79x. Skadi will increase it to 877 +1.21x. If we equate the 2, we find the HP where they give the same survivability. This is 1512 HP. If your HP before buying one of those items is less than 1512 HP, then a skadi will offer more Effective HP. If you already have more then 1512 HP then a butterfly will give you more Effective HP.

This of course only applies to physical attacks. Spells that do physical damage are unaffected by evasion and Magic or Pure damage ignores both armour and evasion, so a Skadi will offer more tankiness against all of those. Also if the enemy gets MKB, then the damage reduction from the evasion is gone. If enemies have mkb, then buying Skadi will offer more Effective HP. The extra armour from butterfly will only offer more survivability if you already have 20881 HP.

Generally Skadi is better since it cant be countered and its effective against all types of damage, not just physical. Fairly certain my maths is right, let me know if you guys spot any mistakes

^Also everything i wrote only applies if your hero has 0 armour. Each point of armour your hero already has will increase the effectiveness of the 725 raw HP from Skadi, so Skadi will almost always offer more Effective HP then butterfly.

Considering thet pros will actually only build butterfly in their endgame push, when they know the opponents should not (in most cases) be able to get MKBs, let's say that evasion is not easily counterable. In that sense, you need to always consider the fact that a a first %evasion source will scale your EHP linearly (the same goes for armor but you never have 0 armor when you're actually building some armor or evasion items). What this means is that whether you have 10 or 100 armor, and whether you have 500 and 3500 HP, it will still give you the same % bonus, even according to armor. With armor calculations are trickier because you want to consider the armor you already have, and the same thing applies to raw HP.

With 35% evasion you're only being hit 65 times out of 100, which translates to 0.65 out of 1.00 which is 1.00/0.65 = 1.53 which is your EHP multiplier. With PA this gets even scarier since you have 1.00/0.50 which is literally = 2.00 so all her otherwise granted physical EHP is multiplied by 2.00. But let's consider the idea that we want to calculate the (evasion only) bonus to her EHP from 35% evasion by butterfly, so she'd have 50% and 35% evasion. First off, that's (1-0.5)*(1-0.65) since we are only calculating the times she's hit, and not when she evades attacks, that means it's 0.5*0.65 = 0.325 which means she's hit only 32.5% of the time, which is 67.5% evasion, and her EHP granted by evasion is now 1.00/0.325 = 3.07. So in reality, while butterfly does indeed not scale linearly with PA's evasion, it makes her evasion ehp gain multiplier jump from exactly 2.0 to around 3.0! This is actually pretty big, but you often have to ask yourself if more armor or raw HP would actually give her more sustain (and in fact, no EHP calculations actually take fights into the calculation, for lifesteal based heroes who build armor/evasion and don't have much raw HP, EHP actually lies in them not being disabled and actually hitting things so that they lifesteal, so a BKB might increase PA's effective HP in fights by a lot more than something like AC (big armor item) or butterfly (smaller armor item but big evasion item) would.

So the final formula that you should always use is the following:

Raw HP * (1 + 0.06 * Armor) * (1-evasion1) * (1-evasion2) * ... * (1-evasionN)

So, let's calculate how it goes for a lvl 25 shadowfiend:

Let's say your build is following:

Power Treads (+9 Agility)
BKB (+10 Strength)
Manta (+26 Agility)
Satanic (+25 Strength)
Silver Edge (+16 Strength)
Skadi (+25 Strength +25 Agility +250HP) OR Butterfly (+30 Agility + 35% Evasion)

So that'd boil down to:
1) LVL25 SF + 250HP + (10 + 25 + 16 + 25) Strength + (9 + 25 + 25) Agility =
(1757 + 250 + 76 * 19) HP * (13.34 + 59/7) Armor = 3451HP * (21.76 * 0.06) = 3451 * (1 + 1.3) = ~7937

So that's how much EHP you have with a Skadi, let's see with Butterfly:
2) LVL25 SF + 250HP + (10 + 25 + 16) Strength + (9 + 25 + 30) Agility + 35% Evasion =
(1757 + 250 + 51 * 19) HP * (13.34 + 59/7) Armor = 3451HP * (22.48 * 0.06) = 2976 * (1 + 1.35) * 1/0.65 = 2976 * 2.35 * 1.53 = ~10700

So the difference in physical EHP is pretty massive, and this does not account for lifesteal and attack damage that it leverages on, so it's essentially meaningless. I also forgot to add 1 agility for Manta (I wrote 25 instad of 26) and forgot to account for armor from satanic, but it does not matter much in this calculation since both builds include both items.

"^Also everything i wrote only applies if your hero has 0 armour. Each point of armour your hero already has will increase the effectiveness of the 725 raw HP from Skadi, so Skadi will almost always offer more Effective HP then butterfly."

Not really true, this completely depends on how much armor/evasion your hero already has, and evasion will scale BOTH your raw hp AND armor, so it's always better and in fact cheaper in the long run, IF you are only up against physical damage (or mostly at least) and the likeliness of the other team getting MKBs is low. The issues with evasion are obviously that it can be nullified by MKB, and that's why it's not OP.

Also another thing worth noting - Raw HP is not what you always want. Raw HP scales pretty badly with lifesteal since it does makes your hits count for less in terms of survivability. If you have 1800 HP lategame, but still have tons of armor and evasion, and manage not to be disabled through a greater part of the fight, you'll be lifestealing enough to regain all your lost health if you hit hard enough, since you take much less damage in general, however, if you have 3500 HP and lifesteal, obviously you're way tankier to start off with, but as the fight drags on, if you don't have much evasion and armor, your HP will count for less, and your lifesteal will do less work.

So all this is really meaningless and depends on very specific things.

I think you may have added, the 250 HP from Skadi to your Butterfly calculation, but otherwise everything is right. Looking at it now, i think I messed up the butterfly calculation on my post (i didn't consider that evasion also increases the effectiveness of armour), but the basic principle is the same: the more HP and armour you already have, the more effective the butterfly is. IF you don't have much HP then the Skadi will usually be better. Like FML said, evasion is usually best if you can end the game before the enemy gets MKBs. So for the scenario where you want to increase your survivability and all you have is a BKB, then Skadi is a better choice then butterfly.

^Shit, you're right, I forgot to remove the 250 HP from Skadi. Lots of unaccounted mistakes in that post, but still, the multiplier from Butterfly is pretty massive.

"So for the scenario where you want to increase your survivability and all you have is a BKB, then Skadi is a better choice then butterfly."

It's likely that at this stage (when you have a 10-8 sec BKB) something like AC is going to be much better, but it really depends on what you're up against, AC is kinda core on heroes like Shadow Fiend if they're up against something like Slardar. Skadi is a very safe item to go for though because it's good in 6 slotted context and its slow goes through BKB, but more importantly, if you get it early it actually increases your survivability by a ton, it's also good if you get it later but when you get a 750ish HP item when you have 1000 in total, it's obviously really good, and actually better than getting a full butterfly at that point (aside from damage).

Omg just use a hero calculator to figure it yourself, then remember armor and evasion don't do shit to magic. Use your judgement and this tool. Common sense will also help you decide and butterfly vs armor. If enemy team has like gyro or medusa those guys almost go mkb by default so keep that in mind. If enemy team has like a wraith king they can easily go mkb but have to notice you building butter first usually. If it's like a tiny or something building mkb is a huge inconvenience over aghs, ac, manta, moon shard.

http://devilesk.com/dota2/apps/hero-calculator/

holy shit these giant posts. just get butter if they arent getting mkb soon. if physical dmg is somehow your only concern, which it will only be in theory, then armor is the way to go. shivas guard is amazing btw between the -45 att speed and 15 armor will practically double your ehp vs. phys.

For physical damage Evasion is always better than Armor and Armor is always better than HP. Even on Terrorblade AC gives more EHP than Heart.