Optimal health:armour ratio

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BeakOr

Member

11-27-2009


tl;dr: Having made some possibly questionable assumptions about the price of health and armour, I've done some mumbo-jumbo maths to decide when armour or health is better value in terms of effective hp. I've looked at two scenarios: first, when the opposition does all magic or all physical damage; second, when they do equal parts magic and physical. Obviously no game is going to match either case, but it gives the general picture. I'll put a few sample numbers in bold at the bottom.

1) The price of hp and armour.

To get a single price for each point of health and armour I've looked at pure hp and armour items; it's not really possible to decide what proportion of the cost of a recipe goes towards health and armour. I've looked at ~1000 gold worth of each:

2 ruby crystals = 950 gold = 400 hp for 0.42 hp/gold.
Cloth armour + spiky armour (what's it called?) = 1000 gold = 70 armour for 0.07 ar/gold.

Magic resist is marginally more expensive than armour (0.063mr/gold), but I've ignored that, meaning I only have to do one set of calculations.

2) Effective hp

Armour and magic resist work by adding 1% of your hp to your ehp for each point of armour. This means:

1 hp gives (1 + ar/100) ehp

1 ar gives 0.01hp ehp

3) Case 1: all magic or all physical

The simpler case, because you only buy 1 kind of armour. Bringing in the price per point of armour and hp:

1 gold of hp gives (0.42 + 0.0042ar) ehp

1 gold of ar gives 0.0007hp ehp

By equating these expressions we get a formula telling us when armour and health are of equal value for money.

0.0007hp = 0.42 + 0.0042ar

multiplying by 100 and dividing by 0.07:

hp = 600 + 6ar

So if hp is greater than 600 + 6ar, armour is better value. If it's less, hp is better value. Some examples:

At 1000 hp, the critical value is 65 armour
At 2000 hp, the critical value is 230 armour
At 3000 hp, the critical value is 400 armour

In short, against a highly specialised team, armour stacking is quite effective (duh...).

4) Case 2: Equal parts magic and physical

Given armour and magic resist are (nearly) the same price, in this scenario it's best to have equal armour and magic resist. This means that the price of each point of armour essentially doubles (think about it); it also means I can pretend that there's just one armour stat instead of two.

So as before:

1 gold of hp gives 0.42 + 0.0042ar ehp

1 gold of ar gives 0.00035hp ehp

Equating the expressions, and fiddling around a bit, we get our critical formula:

hp = 1200 + 12ar

Some numbers:

At 1000 hp, hp is better value even with 0 armour
At 2000 hp, the critical value is 65 armour
At 3000 hp, the critical value is 150 armour


To summarize:

Against an all-physical team, armour stacking is very effective. For example, with 2000 health, armour is the best buy up to 230 armour. With 3000 health, armour is the best buy up to 400 armour. Obviously the same applies against an all-magic team, but with magic resist.

Against a balanced team, hp stacking is much better value. For example, with 2000 health, more than 65 armour and mr is bad value. With 3000 health, more than 150 armour and mr is bad value. (Note: I mean 65 or 150 of each, not total).


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Tekman

Senior Member

11-27-2009

interesting!


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JohnCataldo

Senior Member

11-27-2009

Quote:
Originally Posted by BeakOr View Post
To summarize:

Against an all-physical or all-magic team, armour stacking is very effective. For example, with 2000 health, armour is the best buy up to 230 armour. With 3000 health, armour is the best buy up to 400 armour.
I actually read what you wrote, but you really need to make clear that you mean players should stack magic-resist against an all-magic team (which is not what you say here).

It's kind of dumb and obvious, but pretty important.


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BeakOr

Member

11-27-2009

Quote:
Originally Posted by JohnCataldo View Post
I actually read what you wrote, but you really need to make clear that you mean players should stack magic-resist against an all-magic team (which is not what you say here).

It's kind of dumb and obvious, but pretty important.
ty


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Nadeko Snake

Senior Member

11-27-2009

HP stacking always. I did not think it was a question.

You mass armor you lose out on potential HP and are still vulnerable to (most) skills and magic.

You mass m/r you neglect physical attacks.

You stack HP you have all bases covered.
It's pretty obvious to stack M/R against an all caster team and armor against an all physical team, maybe, but when has this every happened? If often then you need to play against people w/o brain tumors.


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BeakOr

Member

11-27-2009

Quote:
Originally Posted by Nadeko Snake View Post
HP stacking always. I did not think it was a question.

You mass armor you lose out on potential HP and are still vulnerable to (most) skills and magic.

You mass m/r you neglect physical attacks.

You stack HP you have all bases covered.
It's pretty obvious to stack M/R against an all caster team and armor against an all physical team, maybe, but when has this every happened? If often then you need to play against people w/o brain tumors.
I think you've missed what I'm saying. Against a balanced team, it's true that hp stacking is at its most efficient. But if you have, say, 2000 hp and only 30 each armour and magic resist, then buying armour and magic resist is much better value for money in terms of ehp.

The point is, against a balanced team you don't mass armour or magic resist - you buy a balanced amount of both, which, according to my numbers, is about 150 armour and 150 magic resist at 3000 hp.


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JohnCataldo

Senior Member

11-27-2009

Quote:
Originally Posted by Nadeko Snake View Post
HP stacking always. I did not think it was a question.

You mass armor you lose out on potential HP and are still vulnerable to (most) skills and magic.

You mass m/r you neglect physical attacks.

You stack HP you have all bases covered.
It's pretty obvious to stack M/R against an all caster team and armor against an all physical team, maybe, but when has this every happened? If often then you need to play against people w/o brain tumors.
Stacking HP isn't right, usually, for the money spent.

It also depends on the enemy team, and I don't just mean that you stack all armor vs. physical. If the enemy team solos a Yi who is destroying your team, you should get some armor to compensate. Soraca might be doing some magic damage to you but you have to fight the thing that threatens you.

And as stated, armor and MR are more effective than +health most of the time, especially if you already have a lot of health. It's almost never right to stack Warmogs. 3x Warmogs is almost always worst than Warmogs, Force of Nature, Frozen Heart, for three item slots, against a balanced team. The reduced damage you take from both physical and magical more than makes up for the fact that you have two fewer Warmogs (plus those items have other benefits, of course).

There's exceptions, of course. Mundo's passive makes +health excellent for him, and arguably Malphite's passive as well (except Malphite also benefits directly from bonus armor with Ground Slam).

It's not so simple to say that MR or armor don't apply to all enemies so you just shouldn't take them.


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falcoBoat

Member

11-27-2009

Also you need to take into account heals and Heal and Rally: Armour/MR are much more important in that sense as the health returned is static but improved by damage reduction effects. Not only that, but in mid-level play and below a low health hero is a great baiter as the team might not realise their effective health is much higher than their bar is showing.

xx


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Bait

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Senior Member

11-27-2009

at lower levels, hp is more important. at higher levels, mr/armor is more important.
(hero level, not skill level)


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Jothki

Senior Member

11-27-2009

Hmm, so it seems that for mixed teams, the base armor and MR can start out fairly close to the optimum, meaning that you're usually better off stacking tons of HP. If you're actually trying to counter a damage type, the optimum armor is much greater, meaning that you're better off stacking the appropriate resistance.

Which looking back at your post you said yourself, so this post is completely pointless.