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Balanced or Broken: Armor vs. HP

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Introduction

It's one thing to know that something works, it's another thing entirely to know how it works. -Jean Pierre Polnareff

In this series, we take a look at various DOTA Underlords in-game mechanics in order to not only determine what’s the smartest way to play but to understand why and by how much a thing is better than another. In today’s article, we will be reviewing the relationship between armor and HP so we can decide whether the two are balanced and if not, which is exploitable?

TLDR

At the current in-game values, items like Chainmail aren't just better 'most' of the time but by a much wider margin. However, there are scenarios where HP is better and they aren't insignificant so while in a vacuum you'd be hard-pressed not to choose armor there are some situations where HP might serve you best. Below are some general rules of thumb to help you get the most out of whatever build or goals you might have in a game:

HP is best when...

  • Your goal is to cast an ultimate on the equipped unit.
  • Trying to make low HP casters more likely to survive.
  • Taking magical or 'pure' damage.

Armor is best when...

  • Mitigating physical damage is your priority.
  • Using it on a unit whose prime role is to protect others.
  • A unit has a large base pool of HP. 
  • A unit has high base armor. 

Effective HP

In order to compare the two, we need to figure out a way to put both armor and HP on a level playing field and this is where ‘effective HP’ comes in. Effective HP, which we will call ‘EHP’ from now on, is the extra damage a unit can take due to its armor. This is not an in-game stat but is generated to help communicate the 'tankiness' of a unit. The easiest way to imagine it is that this number tells you how much HP you would need to stay alive exactly as long as an identical unit who instead has some armor. The formula for this is listed below:

3 Star Tiny's in-game stat sheet.

Effective HP = HP / ‘damage multiplier’

The damage multiplier is the way can take a value like, +5 armor, and understand how much damage that mitigates. The damage multiplier formula for DOTA Underlords is:

Damage Multiplier = 1- (( 0.052 x armor ) / ( 0.9 + 0.048 x | armor | ))

Note: EHP assumes that all damage is physical damage, magic damage is exclusively mitigated by ‘magic resistance’ and is not factored into this since armor does not protect you from it at all.

Case Study

When we use the above formulas we can make some practical comparisons that will not only tell us what is best but why, in what circumstances, and by how much. Specifically, we analyzed the following items:

  • Chainmail
  • Vitality Booster
  • Helmet of the Undying
  • Eye of Skadi

Chainmail IconVitality Booster Icon Helm of the Undying IconEye of Skadi Icon

Note: We are not considering the value of secondary effects such as Helm’s ‘undying’ mechanic and Skadi’s slowing mechanic. Additionally, there are a number of other considerations such as how armor items contribute to the slowing rate at which a unit gains mana when deciding the right item for your composition. However, those elements need to be assessed through different means entirely, here we are only using their armor and HP contributions as reference points to better understand damage mitigation. 

As can be seen below, in the vast majority of situations the +armor effects are not just better but scale into the end game better when HP pools increase. On average, a single point of armor represents an effective health increase of almost 6.3%. This means that with some reasonable assumptions we can say that Chainmail is roughly equal to +630 HP or 2.52 times MORE effective at mitigating physical damage than Vitality Booster which is +250 HP. We can see that this effective HP increase from Chainmail is almost 1.6 times more effective than Skadi is at mitigating physical damage.

Exceptions

The next question has to be, does the data allow for any exceptions? In some cases it does, in fact, when looking at the lowest HP units in the game such as Shadow Fiend or Enchantress the gap in mitigation is small enough that we can begin to consider the flaw in using EHP as the end all be all metric, and those are, “magic and pure damage.” Since all unit auto-attacks are physical they are best mitigated by armor increasing items like Chainmail but for some units, like casters, their ultimate spells are counted as ‘magic’ damage and with others, like Demons, they do 'pure' damage and regarding both types, armor adds no value. 

Enchantress Stat Sheet

So is it still worth it? That depends, there are actual in-game examples but they are limited and only affect the early game. So a general way to understand when Vitality Booster's effectiveness is close enough to Chainmail's that we should consider fringe benefits like this is when we have a hero whose base armor is 5 and also has less than 500 base health. This requirement limits the pool to 1-star caster types such as enchantress, however, the moment a unit becomes two stars it's HP will exceed this threshold and Chainmail begins to scale well enough that it becomes optimal for the rest of the game. 

Note: While as we previously mentioned the fact that Chainmail can slow the rate at which mana is gained, HP buffs create new opportunities to gain mana over the course of a unit's life which on occasion can result in a cast that wouldn't have otherwise occurred. 

So does that mean if we want to protect a fragile backline hero from a powerful enemy spell that Vitality Booster is the way to go?  Unfortunately, even in that situation, there is another 'common rarity' item that can be obtained around the same time that is far more effective at protecting against magic damage. Hood of Defiance provides players with a whopping 50% magic resistance and with that robs the last bit of value from Vitality Booster. 

Hood Icon

Conclusion

So is this relationship ‘balanced or broken?’ It depends. Vitality Booster is terribly underpowered in terms of pure mitigation when compared to Chainmail in almost any situation. However, +HP has its place in specific circumstances and against damage types that ignore armor all together. 

Items like Skadi or Helm aren’t any different when it comes to mitigation but their secondary effects enable these items to carve out an even more clear place in a team composition so using those as an example we think the best way to ‘balance’ the use of these items while allowing them to remain useful in their respective niche is not to tweak the values but to add a secondary effect that reinforces their value in specific scenarios on top of their current effects. 

And finally, what does this data mean for negative armor effects and their potential value to increasing DPS? Are we vastly underrating them or is there something in the math that makes them different? Check out this article, COMING SOON, where we compare negative armor effects to other DPS effects to find out. 

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