Don’t groan, but today we’re going to do a little math.
I said, “Don’t groan!”
Fine. Groan a little, but this may help you play a video game so pay attention, or just skip to the bottom of the article where I give you my conclusions and you can just trust that my math is infallible. (Which it must be, right?)
Math (ignore if you are lazy or really trusting)
We’re going to look at the concept of Effective Health.
Everybody has health, it’s a little green bar at the bottom of your screen. When you run out of it, you die. Effective Health is the idea that resistances (armor or magic) amplify the potency of your health.
A simple example:
You have 500 health, 30 armor, and 30 magic resist. That person has 650 effective physical and magical health.
Every geek just screamed out in agony, “What’s the formula?!”
It is rather simple:
health x (1+ (resistance type/100)) = effective health against that type of damage
In my sneaky example, the champion had the same amount of magic resist and armor, but now that you know the math, you quickly realize that in real life you will likely have more armor or magic resist, so your effective health varies depending on the type of damage you are taking. What is more, True Damage ignores resistances completely.
If you reach 100 points in armor, you just doubled your health against physical damage. The same is true of magic resist against magic damage.
If you could have as many items as you’d like and money didn’t matter to you, you could reach a high effective health any way that you wanted. Unfortunately, that’s not the case.
We need to spend our money effectively to achieve our desired level of durability, using as few equipment slots as possible.
If we assume that your opponents do roughly an equal amount of magic damage and physical damage, let’s do some math with tier 1 items:
- A Giant’s Belt is 380 health for 1,000 gold.
- A Chain Vest is 40 armor for 720 gold.
- A Negatron Cloak is 40 magic resist for 720 gold.
If we have 3 item slots and 1035 base health there are many possibilities, but I’m going to cover a few big ones:
- 3 Giant’s Belts give us 2,175 Effective health for 3,000 gold (0.73 cost efficiency)
- One of each gives us 1,829 Effective Health for 2440 gold (0.75 cost efficiency)
- Three Chain Vests gives us 2,277 Effective Health against Physical damage and 1,035 Effective Health against Magic damage with a 1,656 average Effective Health for 2,160 gold (0.77 cost efficiency)
Stacking just armor or just magic resist has a great cost efficiency — you get the most effective health per gold you spend — but also has the lowest average effective health for using three slots.
Stacking all health gives the most effective health that three slots can use with tier 1 items, but is the least cost effective.
Balancing health, armor, and magic resist gave us a moderate amount of average effective health at a moderate cost effectiveness.
In real life, it is highly unlikely that a team will do perfectly 50% magic damage or 50% physical damage. It is also unlikely that the magic doing spell caster is going to ignore the fact that you built all armor and not hit you more often than other targets, as much as it is unlikely that the champions doing physical damage will prefer you over squishier targets.
Let’s quick look at a champion with 2,000 health and four tier three defensive items (let’s assume that they have boots and one offensive item.)
Example item options might be:
- Warmogs is 1,000 health
- Thornmail is 100 armor
- Randuin’s is 500 health and 70 armor
- Sunfire Cape is 450 health and 45 armor
- Spirit Visage is 400 health and 55 magic resist
- Banshee’s Veil is 450 health and 55 magic resist
I’m glossing over cost effectiveness for these items because these items do more than just give resistances and health, but other important effects that would require calculations beyond the scope of this article.
Let’s look at two obvious options:
- Randuin’s, Sunfire, Spirit Visage, and Banshee’s Veil is 1800 health, 115 armor and 110 magic resist and an effective health of 8,075.
- Four Warmogs is 4,000 health for an effective health of 6,000 (remember that we had 2,000 base health in this example.)
I think that it would be unwise to stack only magic resist or only armor, but against teams that only did physical damage and no thought toward how you are ignoring the unique passives of these items (read: don’t do any of these things in real life):
- Four Thornmail is 400 armor for an effective health of 10,000 health against physical damage (base health was 2,000.)
- 2x Thornmail, Randuin, and Sunfire for 950 health and 315 armor for an effective health of 12,242 against physical damage
- 2 Thornmail and 2 Warmogs is 2,000 health and 200 armor for 12,000 effective health against physical damage
You can see that the items that give both health and armor actually help considerably more than just stacking armor or just stacking health.
Side Note: Having less actual health while having a high effective health actually increases the effectiveness of healing.
If you have 500 health, but through armor and magic resistances have 650 effective health, you can be fully healed from 1 health to full health for 499 points of healing. However, if you have no resistances and have 650 points of actual and effective health, you need 649 points of healing to get to full from 1 health.
There are certain champions that heal based on the amount of health that they have and certain items (like Warmogs) that heal on a percentage bases. However most items do not heal a percentage amount.
What you need to know (skip to here if you trust my math)
A safe bet against a balanced team is to spend roughly half of your money on health and then divide the rest of your budget between armor and magic resist.
If an enemy team does more of one type of damage (physical or magic) then get more of the appropriate resistance (armor or magic), but it is still important to have bonus health so that your resistances have something to multiply.
Early game, if the enemy jungler and the person you are laning against do primarily the same type of damage, you might consider buying the appropriate resistance before health. Otherwise, you might consider buying health before resistances.
For the math indifferent: Always get a mixture of health and resistances to maximize your potential durability.
For the math conscious: Roughly 30 points on your health bar for every 2 points resistances seems like a good rule-of-thumb ratio to be cost effective and utilize your limited slots effectively.