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[EHP Guide] Easy ingame math

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Senior Member


Most people assume EHP is hard to calculate. It isnt, in addition to showing you why its easy I will show you how to do it.

Table of Contents

  1. Part 1 - Truly Understanding Armor
  2. Part 2 - Using Riots Formulas Against Them
  3. Part 3 - Finding Your EHP
  4. Part 4 - Weighing Item Choices
  5. Part 5 - Speedy Calculations
  6. Part 6 - Adjusting for Abilites and Items

Please do not skip part 1, but its up to you. All other parts, skip as you please.

Part 1 - truly understanding armor
When you hover your mouse over your armor or MR, it shows what percentage of damage you block. Now, this is swell for showing the value of your armor, but it lends itself very poorly to the math.

Lots of people say that armor falls off as you buy more. The damage blocked certainly does, but EHP gains do not.

Consider if every point of armor blocked 10% damage, and you could only get 10 points. Well at 9 points you only take 1/10th of their damage. At 10 points you are invincible - quite a difference.

10% reduction: 111% ehp
20% reduction: 122.5% ehp
30% reduction: 142.8% ehp
40% reduction: 166.6% ehp
50% reduction: 200% ehp
meaning % reduction gets better for each point you have.

So what does that mean? Well it means % blocked is a crappy way of measuring your EHP!

So how do we do it then? Well you can take the reciprical of the damage you dont block to find your true hp, but thats the hard way, dont bother.
Part 2 - Use riots formulas against them!
Instead lets do some algebra now to find a simpler way to do the math that we can count on our fingers.

(dont have to read unless interested)
The (simple) damage formula is:
D * 100 / (resistance + 100)

Essentially EHP is how large a nuke would bring you down to exactly zero health. If you have 2000HP and 3000EHP, 2999 damage will not kill you and 3000 will. Sooo lets make our unknown EHP the damage we take, and have the result be our literal health.

EHP * 100 / (resistance + 100) = HP

and solve for EHP by multiplying both sides by (resistance + 100)

EHP * 100 = HP * (resistance + 100)

divide each side by 100 and you've got your formula.

EHP = HP * (resistance + 100) / 100

EHP = HP * ResistanceRatio
ResistanceRatio = (resistance+100)/100
ResistanceRatio = 100% + resistance/100%

This is incredibly simple. A trained monkey could do this.

Part 3 - Finding your EHP
To find your effective magic/phys HP:
1. add 100 to your armor or MR to find your defense rating
2. add % to the end that to get your Resistance Ratio.
3. multiply by health.
example: 100 armor = 200% ratio, 3k * 200% = 6k EphsHP

To find your overall EHP:
1. add 200 + your armor + your MR
2. divide that by two
3. add % to that to get your Resistance Ratio
4. multiply by health
example: 50 armor and 150 MR = 400. 400/2 = 200%. 2.5k * 200% = 5k EHP

An important thing people dont talk about much is your phys/mag specialization. I mean, everyone says to build MR versus mages and stuff, but its important that you dont too build wide or too narrow a gap. Use the guide below to find your gap.

To find your phys/mag specialization
1. subtract your armor from your MR, or the other way around
2. add % to that
3. multiply by health
example: 200 armor - 80 MR = 120%. 3k * 120% = 3.6k health gap
(you could also subtract EphsHP by EmagHP, but this is easier)

This alone will hopefully help people in game go beyond "Dude I've got 4k hp and 120 armor!" Instead, 100+120 = 220% Resistance Ratio. So 4k * 220% = 8.8k EphysHP.

If you also have 80 MR, your Resistance Ratio is 180%, 4k * 180% = 7.2k EmagHP.

Making your overall Resistance Ratio 200+80+120=400, 400/2 = 200%. Meaning you have 8k EHP

If you keeps dieing to the many AD carries on the enemy team, dont just go WTF I have 50% more armor than MR! 120 - 80 = 40 extra armor. That 40% of your literal HP, only a 1600 health sway - not much. And thats if you ONLY take AD versus magic d

Part 4 - Weighing Item Choices
To start off, this is ALOT easier than you'd think! But its best to have a calculator, I'm guessing you're not great at dividing large, weird numbers. I use my phone.

If the item gives armor or MR (thornmail, FoN, FH):
1. take that armor amount and add % (45 armor = 45%)
2. multiply that by your health
3. that is your phys/mag EHP. Divide by 2 to get overall EHP
4. divide the value you wish to maximize by the cost of the item
example: thornmail is 100%, multiplied by 3k HP = 3k more EphsHP, 1.5kEHP. Divided by 2k gold is 1.5EphsHP per gold and .75EHP per gold

If the item gives armor and MR(aegis, guardian):
1. take the armor amount and add % (45 armor = 45%)
2. multiply that by health for your EphsHP
3. take the MR amount and add % (45 MR = 45%)
4. multiply that by health for your EmagHP
5. add your EphsHP and EmagHP and divide by two for overall EHP
6. divide your EHP by the cost of the item
7. OR if you dont care about phys/mag EHP, just add armor and MR together and use previous steps.
example: MadeUpItem gives 20MR and 45armor. at 3k health thats 45% of 3k = 1.35k EphsHP and 20% of 3k = 600 EmagHP. thats 975 EHP, for 1k gold is ~ 1EHP per gold.

If the item gives health (warmogs)
1. add 200 to your armor and MR.
2. divide by 2 and add percent (45+55 +200 = 150%)
3. Multiply health amount by that percentage (1k * 150% = 1.5k)
4. That is your overall EHP gain, divide by the cost of the item
example: kindlegem gives 200hp for 800g. At 55 armor + 35MR = 290, 290/2 = 145% thats 200*145% = 290 EHP; 0.36 EHP per gold (thank god for the CDR)

If the item gives health AND armor/MR (sunfire, BV, RO)
1. Ignore the health and find the EHP gain from the armor/MR/both
2. find the health gain using your would-be-total-armor/MR
3. you can also do health first and armor second, up to you.
4. divide by cost of the item.
example: sunfire cape at 3k hp and 60 armor and 50 MR. 155% of 450 health = 700EHP, plus 45 armor is 45% of 3450 hp is 1552 EphsHP, which totals 1476EHP, which is 0.56 EHP per gold.
Part 5 - Speedy Calculations
OK OK, so the reality of using this in game is that you cant.

Instead, I compare my resistance ratio to my health. With 100 armor my health items are doubly effective, and with 3000 health, 100 armor is worth 3000 EphsHP. Its pretty easy to compare Warmogs and Thornmail/FoN like this.

Similarly, you usually know your options (although people will usually exclude surprisingly viable ones such as Warmogs, stacking negatrons, and Spirit Visage). For instance, randuins or sunfire? Well its not hard to figure out the difference between 35 armor and 45 armor, and its not hard to figure out the difference between 350 and 450 health.
Part 6 - Adjusting for abilities and items
Remember to include any defensive sterioids. Remember that your shield as shen doesnt benefit from heath.

More complex ones, Mundo's ultimate does NOT scale off of HP! It scales off of EHP! If you regenerate 1400 HP, and have 10000 armor, thats more effective than a warmogs!!! Same goes to malphites and maokais passives.

Flat armor pen (such as black cleaver) doesnt decrease the effectiveness of buying armor, it decreases the effectiveness of buying health. If you have 200 armor, thats 300% health effectiveness. Warmogs is looking very cost effective right now. But if they have 150 armor pen, thats only 150% health effectiveness. Get thornmail! (maybe)

% armor pen (Last Whisper/void staff) essentially makes armor half as effective. at 3k health, 100 armor only gets you 60% of 3k, 1.8k EphsHP. with thornmail thats 2000 gold for 900 EHP! Bad deal!

% true damage is countered by EHP. 8% true damage is always 8% of your effective HP. Dont worry, though, you still get 92% effectiveness from your EHP maximizing.

Flat true damage makes it important to get health. I find I am repeatedly killed by ignite as a tank. Dont underestimate the value of health!

Madreds blood razer is NOT very good! at 0 magic resistance it would take 50 attacks to kill you! But still, bust out the MR and stop stacking health against a madreds.

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Senior Member


I, for one, believe this is worth a bump.

Heres a simple TL: DR;

Buying health has 100% effectiveness, plus 1% for each point of armor. So 100 armor = health is twice as effective. (remember to compare armor AND magic resist)

Every point of armor you buy is 1% of your HP in additional EphsHP. So 3k hp, 1 point of armor is worth 30 HP. 100 armor would be worth 3k EphsHP.

Bumps from other people aren't required but are appreciated.