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Optimizing Effective Health Math with Spirit of the Ancient Golem Tanks

GundayMonday·7/16/2014, 8:31:45 PM·5 votes·888 views

UPDATE: Edited based on forum feedback. Now using the correct new health costs, and took a closer look at the optimal health/resistance ratios. Thanks for pointing that out Pushover!

Wrote a post walking through the math behind the new Spirit of the Ancient Golem and how to optimize a jungle tank build: http://graceunderfiero.blogspot.com/2014/07/league-of-legends-spirit-of-ancient.html

TLDR; Summary:

Spirit of the Ancient Golem 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. With Golem % health bonus and % hp runes, you want your ratio of health to resistance to be ~14 to optimize effective health as opposed to ~9.5 without the bonus.

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.

Riot did a great job balancing this item since Ancient Golem tanks can now focus more on buying health instead of resistances, which allows for better survivability against mixed damage team compositions.

18 Comments

Pushover7/17/2014, 7:50:21 AM3 votes

I would like to point out that % health regeneration doesn't favor health stacking over resistances. 1% of your health every second is 1% of your EHP every second, regardless of if you are a 4000 HP 100 armor tank (40 health is 80 EHP), or a 2000 HP, 300 armor tank (where 20 health is 80 EHP). Flat health regen favors resistances too, as each point of health is worth more if you have higher resistances.

You have a mistake in your math when determining the price of health. If 1 point of health costs 2.67 gold, after running your setup you get 2.67/1.4 = 1.9 gold per HP, not 0.5 gold/HP as you mention. And that skews your numbers severely, and changes your findings significantly.

EHP is a maximization problem of spending gold, something like maximize: (base HP + (gold spent on HP/gold per HP)) * (1 + (base resistance + (total gold spent - gold spent on hp)/100))

If you know calculus, you can find the maximum point (derive and find where the zero is), or you can simply graph it where gold spent on HP is X.

Still, aside from the big change in your numbers, a good post.

Pryotra7/17/2014, 7:38:42 AM2 votes

You look like you enjoy math. If you don't mind, I'd like to reference your post if someone were to ask me in the future about health and armor values.

Also, I'd like to invite you to math with me over in my math thread. I'll link it incase you are interested.

Mr Kryp7/16/2014, 8:43:54 PM1 votes

Very very nice.

logique7/22/2014, 2:39:34 PM1 votes

Hi, I got in touch with you in twitter.

So basically even % seals are outright better and scale more than hp/lvl.

(hp/lvl) Would be - 216 *1.25 = 270

vs

(% seals) 1.35 *200 = 270

I was wrong.

All right. I don't want to invest in %quints yet - please how would i reinterpret your table to determine new balance between hp / armour?

omg I can't believe how expensive they are.