# Health vs armor

When buying survivability items, one has a choice between armor+MR or health to determine which offers most survivability for your gold (there's also special effects like Zhonya's Hourglass).

If you do not care how this was calculated, scroll down to conclusions.

## Method

A fixed value is assigned to each stat based on tier 1 items (a practise you'll probably be familiar with).

- Ruby Crystal: 2,4 gold/health
- Cloth Armor: 16,7 gold/armor
- Null-Magic Mantle: 16,7 gold/MR

Survivability is expressed in how many hits a champion can survive. A hit does 1/(1+armor/100) percent of the original damage (the same applies to magic damage). This means a champion with 100 armor and 2000 HP would die after 4000 physical damage: 2000/(1/(1+armor/100)) = 2000*(1+armor/100) I've divided this number by 100 in my example (so that is the number of 100 dmg hits the champion can take).

We have a maesure of survivability as a function of health and resistance. And we have a health and resistance as a function of gold. What we want to do is find the optimum in survivability for a specific amount of gold (that means: which combination of HP and resistance that I can get for 3000 gold let's me take most hits?).

We could use Lagrange's equations for that, but an Excel graph will suffice.

## Assumptions

These assumptions are made:

- The price for each stat is roughly the same for tier 1 and higher. This is roughly correct; Ruby Crystal and Warmog's Armor cost 2.4 gold per armor (though obviously Warmog's takes farming but grants regeneration too).
- This focusses merely on armor/MR/HP stats, you will have to decide for yourself whether possible other effects are useful.
- I've assumed you face both physical and magical damage, so I've basically assumed made the price of one resistance point 2*16,7 gold (1 armor + 1 MR).
- In my calculations I have assumed 2000 HP and 30 armor/MR base (lvl 18); that's not a limitation of the method though and you could repeat it for different values.

## Results

Removed

In the images you see how much survivability you can get with 2k, 4k, 6k or 8k gold. The optimal result is the highest number listed (the highest number of hits the champion can take). Then see how much resistance (combined armor and MR) and how much HP you should get for this.

If you want to play around with this, you can find the Excel sheet here (for now).

## Conclusions

- It is best to spend almost 50% of your defensive budget on health, almost 25% on magic resistance and the rest on armor.
- If the enemy team has few (good) magic champions or physical champions, you can buy only armor or only magic resistance. This means that where you would have bought Cloth Armor and Null-Magic Mantle before, you can now buy Null-Magic Mantle twice and get double the survivability bonus! Therefore, it becomes advantageous to spend 65% of your money on either armor or magic resistance.
- Keep in mind that against true damage you should buy HP. Against scaling abilities like Madred's Bloodrazor, you should focus on MR. Vayne does true damage that scales with HP, so you best just sit down crying.