General Guide by glizdka
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Indroduction
Hello everyone, I'm Glizdka and this is a part of my general guide to building a champion.
I decided to make it standalone guide, because general guide is very informative but very long at the same time, and some people might not want to read it entirely,
At the same time I made it a bit easier to follow
I find my statement very important to community, that believes in several myths, and can't open their eyes.
Statement of the myth
There is a common myth that you shouldn't buy more armor/magic resistance because each next portion doesn't give much more damage reduction,
They saw that:
when you buy 100 armor you get 50% damage reduction from 0%
when you buy 200 you get 67%, so ONLY 17% for the same cost.
when you buy 300 you get 75%, so only 8% more
when you buy 400 you get 80%, so only 5% more
50% is more than 17%
17% is more than 8%
8% is more than 5%
So it's not beneficial to buy more than, say, 250 armor
That's the statement of the myth.
Why is the myth a myth?
The myth is made by those ones that tried to apply working on fractions/percents for maths dedicated to total values
100 is two times more than 50
200 is two times more than 100
and so on, that's how maths work for total values
1/2 is two times more than 1/4
1/4 is two times more than 1/8
and so on, that's how maths work for fractions
what's the difference?
75% (3/4) is two times more damage reduction than 50%(1/2)
that's because damage taken is the rest, here it is:
25% (1/4) is two times less damage taken than 50% (1/2)
If you don't understand yet, keep on reading...
Effective Health (EHP)
Many people don't know the way armor and magic resistance works. Well, let me introduce term "effective health"  this is amount of damage required to be TAKEN to die.
It means basically that each point of defense (armor/magic resistance) increases effective health by 1% So if you have very high armor and low health it's like having high health and low armor. And if you have a lot of health it's better to buy more defense than health.
Damage reduction and Damage taken
100%  HP (without armor)/Effective HP (HP x armor)
100 armor is 200%EHP : 100%  (100%/200%) = 100%  50% = 50% damage reduction
200 armor is 300%EHP : 100%  (100%/300%) = 100%  33% = 67% damage reduction
300 armor is 400%EHP : 100%  (100%/400%) = 100%  25% = 75% damage reduction
At the same time:
50% damage reduction is 50% damage taken
67% damage reduction is 33% damage taken
75% damage reduction is 25% damage taken
Why do we want to operate on DAMAGE TAKEN not on DAMAGE REDUCED?
Because DAMAGE TAKEN is the thing that kills us, not DAMAGE REDUCED.
Now let's write it in fractions instead of percents to see it better:
1/2 damage reduction is 1/2 damage taken
2/3 damage reduction is 1/3 damage taken
3/4 damage reduction is 1/4 damage taken
More and more...
100%  HP (without armor)/Effective HP (HP x armor)
If we divide something we get fractures right, and fractures are a bit different than total values.
1/4 is TWO TIMES less than 1/2
so 25% is TWO TIMES less than 50%
so 1/4 damage taken is 3/4 damage reduction, and 1/2 damage taken is 1/2 damage reduction
so 3/4 damage reduction (75%) is TWO TIMES MORE than 1/2 damage reduction (50%)
So 75% damage reduction is TWO TIMES MORE than 50% damage reduction.
So from 0%>50% you gain 50% damage reduction
From 50% > 75% you gain 25% damage reduction
but previously gained 50% counts same as 25% gained further
let's have a look deeper:
Say you have 100 health, each armor point gives 1 effective HP
no matter if you have 100 armor and buy another 1 point, each one will give exactly the same
1 more effective HP
Let's say that someone can DPS you down in 1 second.
With 100 armor you get 50% (1/2) damage reduction
With 200 armor you get 67% (2/3) damage reduction
With 300 armor you get 75% (3/4) damage reduction
With 100 armor, he needs 2 seconds to kill you
With 200 armor, he needs 3 seconds to kill you
With 300 armor, he needs 4 seconds to kill you
Ofcourse each next armor point gives less points of %damage reduction. But at the same time each next % of damage reduction counts more.
Look at the percents in fractions now:
100 armor  1/2 damage reduction (50%)
200 armor  2/3 damage reduction (67%)
300 armor  3/4 damage reduction (75%)
400 armor  4/5 damage reduction (80%)
Now at damage TAKEN which is something that interests now, because it's DAMAGE TAKEN that kills.
100 armor  1/2 damage taken (50%)  you need to be attacked 2 times more
200 armor  1/3 damage taken (33%)  you need to be attacked 3 times more
300 armor  1/4 damage taken (25%)  you need to be attacked 4 times more
400 armor  1/5 damage taken (20%)  you need to be attacked 5 times more
If you want a mathematical proof, you can find it in next chapter.
Mathematical proof (not easy to follow part)
at 0 armor you got 0% reduction (that's obvious)
at 100 armor you got 50% reduction (+50%)
at 200 armor you got 67% reduction (+17%)
at 300 armor you got 75% reduction (+8%)
at 400 armor you got 80% reduction (+5%)
Ok, but we want to count our profit in percentage difference. I'll give you easy to follow example how to count profit in percentage difference
You have 100 AD and you buy 50  you get 50% more, as 50 is 50% of 100,
You have 200 AD and you buy 50  you get 25% more, as 50 is 25% of 200,
You have 400 AD and you buy 50  you get 12,5% more, as 50 is 12,5% of 400,
Now, let's count profit in percentage difference for damage reduction. To not get confused and to make it easier to follow I'll temporarly remove unit (%)
100 armor is 50 damage reduction (+50)
200 armor is 67 damage reduction (+17)
300 armor is 75 damage reduction (+8)
Now let's count profit in percentage difference like for example with AD:
0 to 50 is infinite difference as 50 is infinite perfcent of 0.
50 to 67 is 34% more, as 17 is 34% of 50
75 to 67 is 12% more, as 8 is 12% of 67
Well, you don't only get less and less points of reduction, but also percentage difference lowers, right?
But now, let's look at this other way, we don't care about damage reduced but about DAMAGE TAKEN as it is damage taken that kills us right? So let's transfor table above to DAMAGE TAKEN
at 0 armor you take 100 damage (that's obvious)
at 100 armor you take 50 damage (50)
at 200 armor you take 33 damage (17)
at 300 armor you take 25 damage (8)
What does it change? You will see after we count profit in percentage difference
100 to 50 is 50% less damage taken, as 50 is 50% of 100
50 to 33 is 33% less damage taken, as 17 is 33% of 50
33 to 25 is 25% less damage taken, as 8 is 25% of 33
But this refers only to previously taken damage, not to base damage taken. We want to know how much our profit gives in percentage comparison to BASE damage taken.
To count it fast we can multiply each gap's differences that are below and add it consequently to gap's difference itself.
Diffrences:
First gap is our base damage taken. There is nothing to compare, as it's our base 0 difference.
Second gap is 0>100 armor. Here we had 50% (1/2) difference to 1st gap.
Third gap is 100>200 armor. We had here 33% (1/3) difference to 2nd gap.
Fourth gap is 200>300 armor. We had here 25% (1/4) difference to 3rd gap.
Multipliers:
"1stto2nd" gap: 0 x 1/2 = 0
"2ndto3rd" gap: 1/2 x 1/3 = 1/6
"3rdto4th" gap: 1/3 x 1/4 = 1/12
Now let's add consequently to gap's differences all we have below
1st gap is base, nothing to compare here
2nd + "1stto2nd"  will give difference to base for 2nd gap
3rd + "2ndto3rd" + "1stto2nd"  will give difference to base for 3rd gap
4th + "3rdto4th" + "2ndto3rd" + "1stto2nd"gap  will give difference to 4th gap
Let's count this:
1/2 + 0 = 1/2
1/3 + 1/6 + 0 = 2/6 + 1/6 = 3/6 = 1/2
1/4 + 1/12 + 1/6 + 0 = 3/12 + 1/12 + 2/12 = 6/12 = 1/2
As you can (probably) see, for each gap, 0>100 armor, 100>200 armor, 200>300 armor, we have the same profit compared in percentage to other gaps up to base damage taken.
That "1/2" means that each next 100 of armor "doubles" base health portion
That "doubling" dosn't miltiplicate itself, it doubles only the base.
So if you have 1000 HP, first 100 armor doubles it to get 2000EHP (effective HP)
second 100 armor doubles base again so you get 3000EHP
and so on, and so on...
Conclusion
I hope tha now that you have read the article you won't believe in the myth anymore.
Thanks for reading and I hope I helped you, please don't forget to vote :)
A little credit:
jhoihjoi's guide how to create a...guide  that helped me a lot.

