Armor vs. Health Calculations

By Eunomiac on April 22, 2009 5:11:57 PM from

How does armor compare to health? Should I buy Scale Mail (+600 Armor) or should I wait to buy Banded Armor (+400 Health, +5 Health per Second) instead? Faced with these questions, I though to myself, "this is a chance to brush up on my grade 9 algebra!" Huzzah! (... yes, slow work day.)

Starting with my (... flawed?) assumptions:

1) I am assuming that armor works as advertised: namely, it reduces all incoming damage by the stated percentage.

2) To kill a Demigod, you have to deal damage equal to his health, plus additional damage equal to the amount soaked up by his armor.

3) The damage soaked up by armor equals 100*[1 - 2500/(2500 + Armor)] (as posted here)

If all of that is true, then the following formula will tell you the equivalent +Health bonus ('ΔH') for a given +Armor bonus ('ΔA'), depending on your Demigod's current health ('H') and current armor ('A'). If you want to mess around with it yourself, I tried to make it cut-and-pasteable into an Excel spreadsheet cell (but you'll have to plug in the variables yourself):

ΔH = H*(1-100*(1-2500/(2500+A)))/(1-100*(1-2500/(2500+A+ΔA)))-H

Now an example, answering the question above, for a Level 1 Erebus: How effective is Scale Mail (+600 Armor) compared to Banded Armor (+400 Health)?

Answer: After plugging in Erebus' Level 1 Health (H=1650), Armor (A=220) and the Scale Mail bonus (ΔA=600), the formula spits out ΔH = 364. So, all other things being equal, buying Scale Mail at Level 1 will protect you just as much as buying a +364 Health item would. This seems to correspond with what we'd expect, as Banded Armor provides +400 health and some regeneration for around 40% more gold. Should Erebus have 3000 Health and 500 Armor instead, then that bonus rises to an even +600 Health. So Armor has better staying power, improving over time, whereas increases to Health are static.

Of course, this doesn't take into account health regeneration, or potions, or any other subtleties that distinguish health from armor. But I think it's a good starting point, as it lets us compare armor to health directly. That is, as long as my math is right... anyone else care to verify?

0 Karma | 17 Replies

OK this is interesting, thanks for the informative post.

One thing you want to consider - armor does not mitigate damage from DG spells - so for example against a direct-damage build like a DPS UB armor can be very effective but against a nuke Fire TB it will be useless and the equivalent investment in HP items will be better

This is very interesting. I've always wanted to know - armor or HP? When shoudl I get armour, when should i get HP?

Also note the more armour you get, the less effecient it becomes. So 0-1k armour may reduce damage by 25%, but from 1k-2k it may only reduce it by 10%

Interesting article/graph about it here:
http://www.gamereplays.org/demigod/portals.php?show=page&name=demigod-tip-of-the-week-calculating-armor

So I guess once you have lots of HP - getting the scale mail (if you have a free slot) would be a really good idea, because its so cheap, and because it would so much more effecitve then at the start.

100*[1 - 2500/(2500 + Armor)] = % reduction of damage per second.

How effective it is depends on how much damage you are taking per second and should be compared to other items Health per second values.

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Let us say you are taking 100 dps

10% mitigation reduces that by 10dps which is equivalent to +10 health per second.

Let us say you are taking 200 dps

10% mitigation reduces that by 20dps which is equivalent to +20 health per second.

However, Armor only mitigates auto attacks. Special abilities bypass armor. In which case +health per second is infinately better.

Raw +hp helps versus spike damage by increasing your health buffer but is not useful if you have no way of replenishing that buffer.

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Early game Armor upgrade is better than +hp/+hp per second because there are fewer special attacks and the special attacks hit for less.

I focus on +hp/second mid to late game or when I have over 2k armor.

This is all well and good for autoattacking, but the vast majority of burst damage in this game comes from spells which are not mitigated by armor, therefore health and health regen are the clear winner.

I have a question...does armor mitigate damage you recieve from towers?

Quoting Abe07,

reply 5

I have a question...does armor mitigate damage you recieve from towers?

Yes.

Also, I did some math. Against normal attacks, UB gains 218ehp (ehp = hp with armour factored in) from the +600 armour item, and 464ehp for the +400hp armour item. Clearly the +400hp item is far better.

lets not neglect the inherent synergy between increasing armor and health. they feed into each other. armor makes each health point worth more so you'll almost certainly gain peak benefits from buying a mix of health and armor increasing items as opposed to focusing entirely on one type or the other.

Very helpful thread thank you. I believe what you should stack more of depends partial on how you want to play. For instance, if you want to play TB you should stack health and health per second over armor. since your long rage will prevent you from taking a good portion of auto atack damage, and armor is useless against long range abilites.

Armor scales quickly when you have low armor, so I recommend atleast one good piece of armor.

And another thing people seem to miss when comparing HP to armor is healing (ex. Sedna), heal rate, and life steal. Someone stacking HP and has no armor is much harder to heal and effectively gets worse regeneration. Basically you can assume a 1.xx modifier to healing/regen where xx is your armor reduction (vs autoattack). End game a lot of the damage you might take is autoattack. Just think what happens when UC pops rage + the bracelet of rage. Massive autoattack damage that completely outshines his spit, and it is all fully mitigatable by armor. Giants, towers, swarms of creeps and minions all do reducable damage.

Personally I like having 1500-2000 armor, depending on which items i feel i need.

500 armor is 16.67% reduction (below is what it would look like if this as a linear scale, for comparison)

1000 armor is 28.6% reduction (would be 33.3% based on the 500 armor reduction)

1500 armor is 37.5% reduction (would be 50%)

2000 armor is 44.4% reduction (would be 66.7%)

3000 armor is 54.5% reduction (would be damage immunity with 100% reduction)

its actually a common misconception that a linear scale is somehow the "normal" progression for armor and the the logarithmic scale has "diminishing returns". this isn't actually the case if the quantity you measure is time to live, as opposed to damage reduced. this is due to the fact that increasing levels of damage mitigation are compounded on top of existing mitigation. going from 80% to 90% mitigation doesn't increase time to live by just 10%, it increases by 2 times.

the armor progression in the game provides a linear rate of return on increased "time to live". diminishing returns is a myth.

Quoting transitive,

reply 10

Yeh, you're right heh. Just tested. 500 armour gives a static 200ehp bonus, no matter how much armour you had previously (even 10,000 armour to 10,500 armour) assuming your base hp is 1000.

This means that 25 armour gives a static 1% hp increase.

The following formula will tell you how much ehp you gain from that +600 (or any amount of) armour.

base_hp * armour / 2500

Percent Health Gained from X amount of armor can be calculated by:

(((x + 2500) / 2500) - 1) * 100

so 500 armor, will give you 20% bonus health against normal attacks. So 1000hp, would seem be 1200hp.

An example:

Is that 500 armor provides a 16.6666666666666% Damage Mitigation.

That means 100 damage will only do 83.3333333333 Damage, that means over 1000 HP, you can be hit 12 times before dying. 12 times, saving 16.666666666666 damage per hit, is 200 damage. Effectively giving you 200hp ontop of your 1000hp, which is a 20% Health bonus.

So basically 500 armor is a handy 20% Health Bonus. 1000 Armor is 40% Health Bonus. 1500 Armor is 60% Health Bonus.

This essentially means that armor has no diminishing returns in terms of how much health you have, just the actual damage mitigated has diminishing returns. It seems apparent from this that if you are against primarily melee heroes, it is best to go with Armor as it gives you a significant boost against melee damage.

If this math doesn't make sense to you:

The reason the Health Bonus is linear, despite the damage mitigation diminshing, is that not only are you reducing the weapon damage you take, you are also increasing the amount of times they have to hit you for you to die, this happens at the same rate giving a linear progression of health bonus.

Sorry if my examples/reasoning is a little vague its late, the math works though.

Quoting UhelligGudn,

reply 12

It seems apparent from this that if you are against primarily melee heroes, it is best to go with Armor as it gives you a significant boost against melee damage.
.

This isn't quite true.

e.g. (ehp = hp including armour reduction) There's 2 armours you can buy. One gives 500hp and 750 armour, the other gives 1050 armour. Lets say you have 4000hp and 1000 armour. The 1050a one will give you +1680ehp. Now, the 500hp/750a one will give you +2050ehp. This is because the 500hp is affected not only by the 750, but by your base 1000 armour, which brings that +500hp to +850ehp. You also gain 1200ehp from the 750 armour.

Of course armor depends on health, so health bonus' also help, also health bonus' work against abilities too, so it's more well rounded. However against those scary late game Rook's or UB's, Armor ontop of the large late game Health Pool may be more beneficial than a few extra base HP.

The Rook, Unbuffed, with no items has 4750HP at Level 20, with 658 Armor:

This by default gives him an extra 26.32% HP. Putting him at 6000 Modified HP raw.

An extra 500 HP will give him 5250HP, raising to 6631 Modified HP (+1881HP)

An extra 500 Armor will give him 1058 Armor, raising him to 6760.2 Modified HP (+2010.2HP)

Showing that Armor is more useful than health on a point to point basis. Of course if Armor is more expensive, it may not be more cost effective etc. Items with both health and armor of course have the benefit of both increasing Health Pool AND Armor so of course they provide more modified health.

At level 1 however you get 1900 HP and 240 Armor:

This gives you by default gives an extra 9.6% HP. giving 2082.4 Modified HP (+182.4HP).

An Extra 500 HP will give him 2400HP, raising him to 2630.4 Modified HP (+730.4HP)

An Extra 500 Armor will give him 740 armor, raising him to 2462.4 Modified HP (+562.4HP)

Showing that early on, with a small health pool, armor is less effective than health. Add to that the fact that it doesnt work against abbilities and its easy to see Health is better early game. However late game, especially against demigods with high DPS from their weapons, Armor can be more beneficial depending on your build. Combinational items of both Armor and Health give the best of both worlds.

Very interesting thread, answers a question I've been wondering about for a while...

Although health and armour have been proved to each have their strong and weak points, the choice you make on items has to reflect who you're fighting and who you're playing as, as was mentioned earlier.

Eg. Early game, if you're playing Rook and a DPS-focused Unclean strides into your lane and you haven't bought armour, he'll eat you for breakfast unless you can retreat to your towers. Either way, he drives you out of the lane, due to Rook's low-ish starting armour.

My other point - What about Sedna?

She has heals as well as absolutely crazy base Health/second in the late game... I'm wondering if, given the situation that you've stacked enough mana/regen items to hit heal on a continuous loop, whether it's better for her just to stack the health and not look so much at armour to take full advantage of her greatest strengths? Don't know if it's possible to factor in health regen per second into your equation (I'm no excel expert).

Just a thought.

Great read. Thanks!

AA %	Equiv.
20	18868
30	12579
40	9434
50	7547
60	6289
70	5391
80	4717
90	4193
100	3774

AA %	Equiv.
20	12579
30	8386
40	6289
50	5031
60	4193
70	3594
80	3145
90	2795
100	2516

AA% is the percentage of damage that you are taking that is affected by armor. Equiv. is the HP level where gaining a point of armor = gaining a point of health.

the second chart is where spending a point of gold on armor = spending a point of gold on health, assuming that you get 50% more armor for a point of gold than you do health.

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Armor vs. Health Calculations