Agi Armour vs Str HP

This post is based on napkin math, so if it is not exact enough for you I apologize in advance. I also know that some one is sure to point out that armour is spelled incorrectly. I'm Canadian and that's how we spell it, so you'll have to deal with my spelling as it is my post. lol Anyways...


So I was watching a game recently with a Morphling in it, and in looking in his inventory he had a Black King Bar. I thought, well, that makes sense, Morphling is a squishy kind of hero so the hp and the magic negation makes sense. And then I went, oh hey! This is Morphling, he can always change the Str to Agi for more damage, attack speed and armour. That makes total sense!

So I sat down to figure out really at what point the armour from Agi really becomes better than just having pure hp from Str.

So to start with the basics.

1 point in Str gives you a flat 19 hp.

1 point in Agi gives you .14 armour (7 Agi gives you .98, or basically 1 armour).

1 full point of armour equals roughly 6% of your current hp in physical damage reduction (or .06)

So 1 point of Agi would give you .0084 (.14 armour per Agi * .06 damage reduction) of your current hp in damage reduction.

So using that calculation, I found that with Bkb's 10 Str you would get either 190 hp if you left the Str gain alone, or if you switched it over to Agi you would get 101 (100.8) "effective hp" if you were at 1200 current hp (.0084*10*1200).

So looking at it like that, I thought that really isn't a great trade-off, as the "effective hp" gained from the armour switch is only good against physical, or right click, damage, and not against magic damage.

Knowing that the "effective hp" calculation does go up as it is based on percentages I wanted to figure out at which point it actually gets better than just pure hp.

So I tried to figure it out like this. If 1 str = 19 hp then if you divide 19 by .0084 you will get how many current hp you will need for 1 agi to equal 1 str in effective health. That turned out to be 2262 hp = 18.9 effective health, which rounded up is 19. So that's what you would need to make it basically the same, but what about better?

So I divided 20 by .0084 and it turned out as 2380 hp = 20 effective health per agi. Ok, so now 1 point of Agi's armour is better than 1 point of Str's pure hp. How many Str is needed to get to that point though? (not counting starting hp or pure hp gain from items)

125 str = 2375 hp is the closest I could get. So I thought if you could have fairly balanced stats, what would it look like if you had 125 agi and 125 str? 125 agi * .14 = 17.5 armour * 2375 hp * .06 = 2494 effective hp. So if you had balanced stats at 125 each Str and Agi, you would have 2375 pure hp and 2494 "effective hp" from the armour which would total 4869 "effective hp" against physical/right click attacks.

Now I know that it's unlikely for a morphling to get 2375 hp to begin with, but if there's a baseline where one would want to leave his hp for effective use of the stat switch I think it would be around that point, with all the rest of the stats going directly into agi gain, as long as you have around 2375 hp.

Now, am I totally out to lunch in my calculations, and would one actually want to try and do this?

Also, this is my first post in Theory crafting for Dota 2. I read quite a bit when I was playing WoW before I found Dota 2.

Its kind of dependent on the game itself though. If your opponents have a lot of high-magic damage and has a snowballing hero, the armour might not help as much as the HP. However, when the enemy passively farms up a carry, the armour might be more effective. Especially on a Morphling I usually go glass cannon, Ethereal Blade, max Agi damage, meaning very squishy but fairly tanky against a carry's right-click damage.

Of course, the nice thing about Morphling is that if you're in trouble, you can swap to Str when in trouble, to defend yourself.

I would look more closely at your calculations, but I'm too tired. :X

This depends on the amount of armor you already have, your hero and the stage of the game, besides the enemy team composition.

If it's early game and you have 0 armor like some heroes such as Skywrath Mage, you should prioritize armor.

If it's mid game and you have 10 armor it should be enough, so build HP - but if you have 2 armor, you should look to build a cheap armor item like a flat Chainmail or, depending on your hero/role, a Mekansm.

Few things to bear in mind:

- Your spelling of armour is correct :) (I'm a Brit)

- Armour provides decreasing returns as it stacks, 2 points of armour taking you from 0 to +2 is worth 10.7% damage reduction. 2 points of armour taking you from 23 to 25 gives you 2% damage reduction.

- For agility heroes like Morphling, it's not just about armour, it's also about damage and attack speed. If you can kill the other guy faster, you're might be more likely to survive than doing less damage and having more HP.

- Like most agility related things, armour scales well late game, but isn't usually that helpful early on.

- As Sam has said, getting a bit of extra armour when you have very low base is important - all the big returns are between -6 and +6. Prioritise HP more when they have a lot of nukers.

*Reserved for lengthy Math Post*

EDIT, nvm, the Math hurts my head, so I'll post an in-depth guide to EHP here

http://www.playdota.com/guides/decoded-effective-hit-points

Ok. Thanks for all of the replies and info!

I wasn't sure if armour was set for diminishing returns or not. I kind of figured it would be, but I'm having a bit of an issue finding resources for that kind of information. Maybe one of you kind gentlemen could point me to a resource like that?

As a side note, I was playing a game using morphling the other day, and noticed that stat bonuses from items can't be switched, only base/natural stats, which to a point makes this post pretty pointless, as it's unlikely that morphling is going to get that many stats without items.

You mean the table here?

http://dota2.gamepedia.com/Armor

Well, not just for armour, but yeah. Thanks. :-)