Wednesday, July 16, 2014

League of Legends: Spirit of the Ancient Golem and Effective Health

League of Legends is one of my favorite games. Never heard of it? Watch this or read this or sign up and play for free. All caught up? Cool. The game is ridiculously hard, and there's a lot of math behind decisions. This is the main reason I enjoy playing. I prefer tank champions, which means my job is to be a brick wall, soak up damage, keep my teammates safe, and cause utter mayhem for the other team.
Riot games recently released a new item that tank players can use called the spirit of the ancient golem. I'm going to walk through some of the math behind why this item is awesome, and how to use it effectively in the game. Feel free to stop reading if that's not interesting, and I have a TL DR; summary at the very end. Otherwise onward!

Effective Health And Why It Matters

So lets say you're playing the game and about to fight an enemy attack damage carry (ADC). You need to stay alive for as long as possible. When your health is gone, you die. You can choose to be one of the following two tanks:

Tank 1: 5000 health, 10 armor
Tank 2: 3000 health, 100 armor

So which one do you pick?

To decide, you'll have to look at how League calculates damage reduction from armor, and then think about how much extra health each point of armor gives you. This is called effective health, and can be calculated like so:

Effective Health = Health * (1+ (Armor/100))

If we run the numbers for tank 1 and tank 2, they look like this:

Tank 1: 5000 health * (1+ (10/100)  ) = 5500 effective health
Tank 2: 3000 health * (1+ (100/100)) = 6000 effective health

So Tank 2 would have 500 extra effective health thanks to their armor reducing the ADC's damage, and survive a little bit longer. Here's a look at different combinations of health and armor so you can see the pattern:
What's interesting about this effective health stuff, is that armor becomes more valuable (creates more effective health), the more health your character has. Notice as you go from left to right in the chart above how the armor gets stretched into MORE effective health. If you run the numbers and simplify a little, you can figure out how much extra health each point of armor will give you:

Extra effective health = (Health/10) * (Armor/10)

Still with me? The main takeaway is that you need to balance stacking health and resistances like armor on your tank to be the best tank you can be, and that there is an optimal combination of the two at any given time. You can figure out this optimal combo by looking at effective health.

Spirit of the Ancient Golem = Tank Steroids

So what's so special about this new tank item then? Take a look at what it does again. Specifically this:

Unique: 25% Bonus Health

What the heck does that mean? Every champion in League has base health. This is starter health and a little bit extra with each new level. You can also get Bonus health from your runes, masteries, and items that you buy in game. There are also some weird abilities that champions like Cho'gath, Nunu, and Sion have that give extra health when used. The Spirit of the Ancient Golem item, takes that extra bonus health, and multiplies it by 1.25 to give you extra. Take an item like Warmog's armor as an example:

If you didn't have any weird runes/masteries, buying Warmog's Armor would give you 1000 health + 250 extra health from the Spirit of the Ancient Golem passive. That's kind of a big deal, but you can optimize it further if you build a little smarter using runes and masteries. Specifically these:

If you max out your % health runes that means:
3 quintessences * 1.5% increased health + 9 seals * 0.5% Health = 9% Increased Health

Riot takes these into account separately, so you're multiplying your total health by 1.03x and then 1.09x respectively to get extra health. This counts as BONUS health, and also gets the 1.25x health multiplier from the Spirit of the Ancient Golem. If you run the numbers, this combo pretty much multiplies any extra health you buy by ~1.4x. This becomes huge since it changes around the optimal way to build a tank from an effective health per gold spent standpoint.

How Can We Use This?

Let's say we're running the above runes masteries setup, and have bought the Spirit of the Ancient Golem Item, but nothing else. You're level 6 and playing Sejuani, so you have ~1500 hp. You also have ~70 armor. You have 1000g which is enough to buy one of the following two items:

Here's your new effective health equation:

Buy Giant's Belt: (1500 health +(380 health*1.4))*(1+(70 armor / 100))  = 3454.4 Effective Health
Buy Chain Vest: (1500 health)*(1+((70 armor + 40 armor)/100))             = 3150.0 Effective Health

Giant's Belt wins out. Lets say you add in an extra cloth armor which costs 300g and gives 15 armor. That would be about the same amount of gold and looks like this:

Buy Chain Vest + Cloth Armor:
(1500 health)*(1+((70 armor + 40 armor + 15 armor)/100))                       = 3375.0 Effective Health

Stacking health still wins out in this situation (and most situations). This new item is strong because it changes the cost of health. Here's how much each stat normally is worth:

1 hp = 2.67 gold (ruby crystal cost / health given)
1 armor = 20 gold (cloth armor cost / armor given)

But now with this new build 1 hp = ~1.9 gold. That means every 20 gold I'm spending to get 1 armor, could be getting me ~10.5 health, when before that same amount of gold would be getting me ~7.5 health. This changes the break even point. Let's look and see the relationship between armor, health, and effective health:

The first chart on the left is the same as before and shows you a champion's total effective health at different armor/hp combinations. The second chart on the right shows how much gold each extra effective health point costs. Notice how the cost of effective health per armor bought changes based on the amount of health you have, and gets cheaper (more effective health per gold spent) as you gain more health. So how much health and armor should you buy in different situations? And how does the Spirit of the Ancient Golem change this?

Let's walk through the math to optimize effective health per gold spent. Here's what we know:

1 armor = 20 gold (cloth armor cost / armor given)
1 hp = 2.67 gold (ruby crystal cost / health given)
1 hp w/ Spirit of the Ancient Golem bonus = 1.9 gold (ruby crystal cost / health given with bonus)

We can rewrite our effective health equation from this:

Effective Health = Health * (1+ (Armor/100))

To this where we assume that we have H gold to spend on health and A gold to spend on armor.

Effective Health = 

(Current Health + H/Health Cost) * (1+ ((Current Armor+A/Armor Cost)/100))

This also assumes that A + H = Total Gold available.

Let's look at a level 6 Sejuani with 1500 health, 83.5 armor, Spirit of the Ancient Golem bought, and 3000 gold to spend as an example:

What we're looking at is the change in optimal gold spending with and without the Ancient Golem bonus to maximize effective health. With the bonus, you want to use ~600g extra buying health than you would without the bonus. That said, since your health and armor change as you buy more items and gain more levels, the optimal spending can also change. 

Let's look at the same Sejuani, but at level 11. 
Your items are Spirit of the Ancient Golem, Sunfire Cape, and Randuin's Omen.
Your health is at ~3375, and your armor is at ~230.
You have 3000 gold to spend again.

Here's what it looks like:

Notice that without the ancient golem bonus you would want to focus on armor (maybe a thornmail?). But now with the bonus, it's better to grab health and armor. Notice that the sweet spot numbers are larger with the golem bonus for the same amount of gold as well. Generally speaking, you want to have a ratio of health to resistances of ~14 (At least for tank mastery Sejuani). That means take your health, divide by armor, and get it as close to 14 as possible.

That means that tanks will perform better against mixed damage team compositions. Now if my bot lane feeds the enemy caitlyn, I have more effective health against AP damage if I choose to grab some extra armor. Before, the 0-5 enemy midlaner would still be able to chunk me down significantly more. Riot did a great job here, because now this means tanks should be grabbing more health and less resistances to get to that optimal effective health.

TLDR; Summary:

Running this setup essentially multiplies every additional point of health you add to your champ from items by 1.4x. This also decreases the cost of health from ~2.67 gold per 1 point in health to ~1.9 gold per 1 point in health! This allows you to get more effective health per gold spent building health than resistances compared to without the Ancient Golem passive.

Health Regeneration and Added Utility

Another thing to think about when stacking health is bonus health regeneration you can get from masteries and items. Check out this combo as an example:

Let's say you have 4,000 health with Warmog's Armor and Perseverance maxed. You are passively regenerating 1-2% of your maximum health every 5 seconds (that's at most 80 health per 5, or 16 health every second). Not to mention that you'll have your natural regeneration and regeneration from any items you bought as well. Imagine that on a Dr. Mundo with Spirit Visage passive, Mundo Passive, Second Wind Mastery, and Mundo Ultimate going. Late game, you're looking at a champ with 6k+ health regenerating more health than the enemy team can dish out. This means that you can facetank towers indefinitely during sieges, or safely tank baron with 1/3 of your health. Just something to think about since this mastery and passive become stronger the more health you have.

Now what about champs that benefit from stacking health? Let's use Sejuani as an example with her Flail of the Northern Winds ability.
The basics of this ability is that you're doing some flat amount of damage + a % of your ability power + a % of your bonus health in AOE damage every second around your champion. Using this build, a level 18 Sejuani running standard tank items is doing 240 base + ~400 from bonus health over 4 seconds to nearby enemies. Add in sunfire cape and you're looking at ~812 damage over 4 seconds to anyone standing near you (before resistances and stuff like that). Without the bonus health from Spirit of the Ancient Golem, you're only doing ~700 damage per second. That's ~110+ extra damage and a pretty big difference considering that you're not necessarily stacking health for offensive purposes. This means anyone going after your frail and fragile carries will have a ginormous wall of hurt to go through first.


Spirit of the Ancient Golem is a huge buff to tank junglers, and a lot of players don't know it yet.
  • The item decreases the cost of health from ~2.67g to ~1.9g, which changes when it's most effective to buy health versus resistances from an effective health per gold spent standpoint. More health over resistances early is generally better.
  • The item adds a lot of utility for additional health regeneration from tank items/masteries making champions like Dr. Mundo very scary during the lategame.
  • The item offers a considerable boost to abilities that scale with health like Sejuani's Flail of the Northern Winds.
I really like this change since it allows tanks to focus more on health than individual resistances, which allows you to be stronger against a mixed (AP and AD damage) enemy team comp!


  1. Wanted to thank Pushover from the NA League of Legends Forum for pointing out an error in my math. Fixed now!

  2. This comment has been removed by the author.

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