Views: 2065 Armor/MR vs Health items
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In the league of legends, you will found out that you take damage every once in a while.
Of course, we want to prevent that, but there are so many items for defence, including:
* Magic Resistance (MR)
* Armor (Ar)
* Health (HP)
* Health regen (HP/5)
MR and Ar have the same system, which reduces damage in percentage.
While HP basically "blocks" the damage as a number.
And HP/5 grants HP back every 5 seconds.
Let's ignore Health regen, we just want to see how much damage we can take in a row.
Data
If we want to make sure which one is better than the other one, we must use certain data.
Defense
Each point of Ar/MR (or DF) will grant an amount of reduced damage done in a certain catagory (physical damage or magical damage).
The more DF you have, the less damage you take. So how much is that?
We multiply the damage by = 100 / (100 + DF) * damage
So we can basically say this: 100 * damage / (100 + DF)
This means, that the more DF you will build, each point extra will give less % in damage reduction. For this reason, you shouldn't build DF only.
Health
Now what is the deal with Health?
Health literally allows you to survive more damage, in an absolute number.
Easy as that.
Eureka
So what we really are going to calculate, is at what amount of DF you should start buying HP.
In order to survive, we need certain items.
What do we need to know for that?
Each point of DF costs 20g each.
Each point of HP costs 2,64g each.
Let's say we have a budget of 15000 gold.
When does HP become more worth than DF?
Calculations
Full DF
If we would only buy DF from those 15000g, we would get a total of: 15000/20 = 750 DF
750 DF will let us only take this % of the damage: 100 / (100 + 750) * damage = 11,8%
Full HP
If we would only buy HP from the 15000g, we would get a total of: 15000/2,64 = 5682 HP
5682 HP will allow us to take 5682 of the damage.
Full conclusion
The amount of damage we must take to make 11,8% just as worthy as 5682:
11,8% = 5682
100% = ?
5682 * 100%/11,8% = 48152 damage.
This is a rediculous high amount, for that reason, DF is by far less worth than HP.
Because you need to take at least 48162 damage to make DF as worthy as HP when investing all your gold in it.
Starting the balancing: at 50% reduced damage taken
So, to create balance, we must look at our facts again:
Reduced damage taken (%) = 100 / (100 + DF) * damage
Reduced damage taken (flat) = HP
Budget = 15000g
Each DF = 20g
Each HP = 2,64g
Amount of DF or HP cannot be bigger than:
DF <= 750
HP <= 5682
Amount of DF or HP cannot be smaller than:
HP > 0
DF > 0
When DF = 100 (costs 2000g), the damage taken is 50%
If DF = 100, HP = 4925
So now, we calculate the amount of damage we are allowed to take when we have both the HP as the DF.
"formula: source lol wiki"
4925 * (1+0,50) = 7387,5 allowed damage taken
The amount of "health" gain from DF = 7387,5 - 4925 = 2462,5 hp
We payed 2000g on the DF, but the health we gained is: 2462,5 * 2,64 = 6501g
For 2000g spend, you get 6501g worth of survival.
So when is it really balanced?
Balancing: splitting the money fair
DF is this time the half of the maximum, so is the health.
We will get the following:
DF = 375 (costs 7500g), the damage taken is 21%
If DF = 375, HP = 2841
Let's calculate the amount of possible damage taken again:
2841 * (1+0,79) = 5085 allowed damage taken
The amount of "health" gain from DF = 5085 - 2841 = 2244 hp
2244 * 2,64 = 5924g, which is more than 1000g less than you spend on DF
So splitting is definately not our option.
What do we have to do Meiyjhe?
Balancing
Well it is clear now that the amount of gold spend on DF must equal the amount of gold gain from DF.
So: Amount of gold gain from DF = A - B = C*2,64
Where A = HP * (1+%DF)
B = HP
And C = the Flat Damage Reduction (FDR) aka DF "health"
So we can create this formula:
((HP * (1+%DF)) - HP) * 2,64= FDR * 2,64 = Gold gain from DF
DF * 20 = Gold spend on DF
Gold spend must equal gold gain. So we conclude this:
((HP * (1+%DF)) - HP) * 2,64 = DF * 20
Now some formula magic:
((HP * (1+%DF)) - HP) * 2,64 / 20 = DF
0,132((HP * (1+%DF)) - HP) = DF
0,132(HP * (1+%DF)) - 0,132HP = DF
(0,132HP(1+%DF)) - 0,132HP = DF
0,132HP + 0,132HP*%DF - 0,132HP = DF
0,132HP * %DF = DF
Some more magic:
0,132HP * (1-(100/(100+DF))) = DF
0,132HP - 0,132HP(100/(100+DF)) = DF
0,132HP - 13,2HP/(100+DF) = DF
0,132HP(100+DF) - 13,2HP = DF(100+DF)
13,2HP + 0,132HP * DF - 13,2HP = 100DF + DF^2
0,132HP * DF = DF^2 + 100DF
0,132HP = DF + 100
0,132HP - 100 = DF
Voilá, we got our main formula, now the calculation will be easier (for me :D)
Now let's finish it.
The finishing touch
Now we have the final formula:
0,132HP - 100 = DF
But keep in mind: We also need to spend all 15000g.
To make sure that happends, we use:
750 "The maximum DF" - ((2,64HP "The cost per HP")/20 "The cost per DF")
Basically this: 750 - 2,64HP/20 = DF
Now the final touch:
750 - 2,64HP/20 = 0,132HP - 100
850 - 2,64HP/20 = 0,132HP
17000 - 2,64HP = 2,64HP
17000 - 5,28HP = 0
5,28HP = 17000
HP = 17000 / 5,28 = 3220
3220 * 2,64 = 8500g for HP
15000 - 8500 = 6500g for DF
6500g = 325 DF
Let's check if it is correct:
325 DF = 1-(100/(100+325)) = 76% damage blocked.
Health = 3220
Amount of possible damage taken:
3220 * (1+0,76) = 5667,2
Amount of "Health" gain from DF =
5667,2 - 3220 = 2447,2
Amount of gold worth:
2447,2 * 2,64 = 6460g ~ 6500g!
Conclusion
When you have more than 325 Ar/MR, only then health is more worth than defense.
However, since there are so many ways to penetrate armor/MR and stuff, that health is more reliable.
Since this only applies when your budget is 15000g and you want to spend it all on defense and health, there is a chance that the 325 Ar/MR isn't as exact as I hoped :P
Anyway, this calculation was a real challenge for me, even though it might be very wrong, I feel very smart right now :D
Thank you all for reading!
-Meiyjhe
Of course, we want to prevent that, but there are so many items for defence, including:
* Magic Resistance (MR)
* Armor (Ar)
* Health (HP)
* Health regen (HP/5)
MR and Ar have the same system, which reduces damage in percentage.
While HP basically "blocks" the damage as a number.
And HP/5 grants HP back every 5 seconds.
Let's ignore Health regen, we just want to see how much damage we can take in a row.
Data
If we want to make sure which one is better than the other one, we must use certain data.
Defense
Each point of Ar/MR (or DF) will grant an amount of reduced damage done in a certain catagory (physical damage or magical damage).
The more DF you have, the less damage you take. So how much is that?
We multiply the damage by = 100 / (100 + DF) * damage
So we can basically say this: 100 * damage / (100 + DF)
This means, that the more DF you will build, each point extra will give less % in damage reduction. For this reason, you shouldn't build DF only.
Health
Now what is the deal with Health?
Health literally allows you to survive more damage, in an absolute number.
Easy as that.
Eureka
So what we really are going to calculate, is at what amount of DF you should start buying HP.
In order to survive, we need certain items.
What do we need to know for that?
Each point of DF costs 20g each.
Each point of HP costs 2,64g each.
Let's say we have a budget of 15000 gold.
When does HP become more worth than DF?
Calculations
Full DF
If we would only buy DF from those 15000g, we would get a total of: 15000/20 = 750 DF
750 DF will let us only take this % of the damage: 100 / (100 + 750) * damage = 11,8%
Full HP
If we would only buy HP from the 15000g, we would get a total of: 15000/2,64 = 5682 HP
5682 HP will allow us to take 5682 of the damage.
Full conclusion
The amount of damage we must take to make 11,8% just as worthy as 5682:
11,8% = 5682
100% = ?
5682 * 100%/11,8% = 48152 damage.
This is a rediculous high amount, for that reason, DF is by far less worth than HP.
Because you need to take at least 48162 damage to make DF as worthy as HP when investing all your gold in it.
Starting the balancing: at 50% reduced damage taken
So, to create balance, we must look at our facts again:
Reduced damage taken (%) = 100 / (100 + DF) * damage
Reduced damage taken (flat) = HP
Budget = 15000g
Each DF = 20g
Each HP = 2,64g
Amount of DF or HP cannot be bigger than:
DF <= 750
HP <= 5682
Amount of DF or HP cannot be smaller than:
HP > 0
DF > 0
When DF = 100 (costs 2000g), the damage taken is 50%
If DF = 100, HP = 4925
So now, we calculate the amount of damage we are allowed to take when we have both the HP as the DF.
"formula: source lol wiki"
4925 * (1+0,50) = 7387,5 allowed damage taken
The amount of "health" gain from DF = 7387,5 - 4925 = 2462,5 hp
We payed 2000g on the DF, but the health we gained is: 2462,5 * 2,64 = 6501g
For 2000g spend, you get 6501g worth of survival.
So when is it really balanced?
Balancing: splitting the money fair
DF is this time the half of the maximum, so is the health.
We will get the following:
DF = 375 (costs 7500g), the damage taken is 21%
If DF = 375, HP = 2841
Let's calculate the amount of possible damage taken again:
2841 * (1+0,79) = 5085 allowed damage taken
The amount of "health" gain from DF = 5085 - 2841 = 2244 hp
2244 * 2,64 = 5924g, which is more than 1000g less than you spend on DF
So splitting is definately not our option.
What do we have to do Meiyjhe?
Balancing
Well it is clear now that the amount of gold spend on DF must equal the amount of gold gain from DF.
So: Amount of gold gain from DF = A - B = C*2,64
Where A = HP * (1+%DF)
B = HP
And C = the Flat Damage Reduction (FDR) aka DF "health"
So we can create this formula:
((HP * (1+%DF)) - HP) * 2,64= FDR * 2,64 = Gold gain from DF
DF * 20 = Gold spend on DF
Gold spend must equal gold gain. So we conclude this:
((HP * (1+%DF)) - HP) * 2,64 = DF * 20
Now some formula magic:
((HP * (1+%DF)) - HP) * 2,64 / 20 = DF
0,132((HP * (1+%DF)) - HP) = DF
0,132(HP * (1+%DF)) - 0,132HP = DF
(0,132HP(1+%DF)) - 0,132HP = DF
0,132HP + 0,132HP*%DF - 0,132HP = DF
0,132HP * %DF = DF
Some more magic:
0,132HP * (1-(100/(100+DF))) = DF
0,132HP - 0,132HP(100/(100+DF)) = DF
0,132HP - 13,2HP/(100+DF) = DF
0,132HP(100+DF) - 13,2HP = DF(100+DF)
13,2HP + 0,132HP * DF - 13,2HP = 100DF + DF^2
0,132HP * DF = DF^2 + 100DF
0,132HP = DF + 100
0,132HP - 100 = DF
Voilá, we got our main formula, now the calculation will be easier (for me :D)
Now let's finish it.
The finishing touch
Now we have the final formula:
0,132HP - 100 = DF
But keep in mind: We also need to spend all 15000g.
To make sure that happends, we use:
750 "The maximum DF" - ((2,64HP "The cost per HP")/20 "The cost per DF")
Basically this: 750 - 2,64HP/20 = DF
Now the final touch:
750 - 2,64HP/20 = 0,132HP - 100
850 - 2,64HP/20 = 0,132HP
17000 - 2,64HP = 2,64HP
17000 - 5,28HP = 0
5,28HP = 17000
HP = 17000 / 5,28 = 3220
3220 * 2,64 = 8500g for HP
15000 - 8500 = 6500g for DF
6500g = 325 DF
Let's check if it is correct:
325 DF = 1-(100/(100+325)) = 76% damage blocked.
Health = 3220
Amount of possible damage taken:
3220 * (1+0,76) = 5667,2
Amount of "Health" gain from DF =
5667,2 - 3220 = 2447,2
Amount of gold worth:
2447,2 * 2,64 = 6460g ~ 6500g!
Conclusion
When you have more than 325 Ar/MR, only then health is more worth than defense.
However, since there are so many ways to penetrate armor/MR and stuff, that health is more reliable.
Since this only applies when your budget is 15000g and you want to spend it all on defense and health, there is a chance that the 325 Ar/MR isn't as exact as I hoped :P
Anyway, this calculation was a real challenge for me, even though it might be very wrong, I feel very smart right now :D
Thank you all for reading!
-Meiyjhe
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