Your math is right if you are looking at whole numbers. But with diminishing returns, it doesn’t really work that way if I understand it right. I am no DNA so excuse me if it’s wrong but compared to baseline(assuming he has zero armor rating) First armor-100% Second armor-50% Third armor-33.3% Fourth armor-25% Fifth armor-20% So adding fourth and fifth armor only gives you an additional 45% armor from what you already have at 3 armor ups. Which is less than 50%.
You're right about armor up. Each new ones has less of an impact. They all give the same armor rating but armor rating doesn't scale linearly.
However in the example above he was referring to furies. Diminishing returns does not apply to attack rating I believe. Only to resistance, armor (up and break).
The math should be the same for furies as well right? R1 HTD has attack rating of 4247. Fury increases attack rating by 389.8 Fury 1-fury 3 increases the base attack by 27.5% (5416.4) Fury 1- fury 5 increases the base attack by 45% (6196) 45-27.5 is 18.5 which is 41% increase. Which is still less than 50%
Your math is right if you are looking at whole numbers. But with diminishing returns, it doesn’t really work that way if I understand it right. I am no DNA so excuse me if it’s wrong but compared to baseline(assuming he has zero armor rating) First armor-100% Second armor-50% Third armor-33.3% Fourth armor-25% Fifth armor-20% So adding fourth and fifth armor only gives you an additional 45% armor from what you already have at 3 armor ups. Which is less than 50%.
You're right about armor up. Each new ones has less of an impact. They all give the same armor rating but armor rating doesn't scale linearly.
However in the example above he was referring to furies. Diminishing returns does not apply to attack rating I believe. Only to resistance, armor (up and break).
The math should be the same for furies as well right? R1 HTD has attack rating of 4247. Fury increases attack rating by 389.8 Fury 1-fury 3 increases the base attack by 27.5% (5416.4) Fury 1- fury 5 increases the base attack by 45% (6196) 45-27.5 is 18.5 which is 41% increase. Which is still less than 50%
Furies are attack rating increases and attack rating is not subject to diminishing returns. Armor buffs and armor break debuffs affect armor rating, and armor rating is affected by diminishing returns.
It isn't really the buffs and debuffs that are directly affected by diminishing returns, rather it is the stat itself. If I say Howard's attack rating is is 3898, that means he literally does that much damage when using an attack with a scale 1.0 attack. Light attacks do 0.25 scale damage, which means when a champion with 3898 attack rating uses a light attack they do 3898 x 0.25 = 974.5 damage. The attack rating is, in a sense, a direct measure of how much damage that champion does.
But when I say a champion's armor rating is 477, that doesn't directly mean anything. Armor rating is like the volume knob on a radio. Turn the knob to 7 or 8 and that doesn't mean the sound is now "7 loud." It doesn't mean the sound that comes out is 7 db or anything like that. Similarly, if you want to know how much "477 armor" reduces damage, you need to know how that knob works. And the way it works is via the Diminishing stat formula. The math looks like this:
Value = StatValue / (StatValue + 1500 + 5 x CR)
where CR is the challenge rating of the opponent (not your own CR).
When StatValue is zero Value is also zero. As StatValue gets higher, Value gets closer and closer to 1.0 (the numerator and denominator get closer and closer relatively speaking). But no matter how high StatValue gets, the net Value never exceeds 1.0. If you try to push StatValue higher and higher, Value will get higher and higher but at a slower and slower rate. Increases get "diminished" as you go higher.
It isn't that the second buff is weaker than the first. One +1000 buff has exactly the same effect as ten +100 buffs. The result is the same: the stat gets +1000 points higher. But however much +1000 pushes you higher, the *next* +1000 will push you less than the first.
[Note: the math changes when Stats go negative.]
As to the furies. It is important to be precise with language. If we are talking about the buffs specifically, then 5 buffs is 60% more than 3 buffs. In terms of the net buff benefit, 5 is 60% more than 3.
But in terms of relative damage boost, the difference between 3 buffs and 5 buffs is not the difference between 3 and 5, it is the difference between the base + 3 buffs vs base + 5 buffs. So if one fury buff is a 10% attack rating increase, then the difference between having three and having five is the difference between 1.3 and 1.5, which is a 15.4% increase in attack rating.
Two things can be true. If I get a $1,000 raise and you get a $10,000 raise, then you got a ten times higher raise than I did, period. But if we are both making $1,000,000 dollars a year, then in another sense you got almost no more money than me. I am now getting 1.001 million dollars a year and you are getting 1.01 million dollars a year, and so you're now making 1.01/1.001 = 0.9% more money than me. It is true your raise is 1000% higher than mine, and it is also true your net increase over me is 0.9% more money.
1000% and 0.9% are very different numbers, because they are measuring two completely different things. 1000% compares the two benefits against each other. 0.9% compares the net effect of those benefits upon each of us against each other.
Comments
R1 HTD has attack rating of 4247. Fury increases attack rating by 389.8
Fury 1-fury 3 increases the base attack by 27.5% (5416.4)
Fury 1- fury 5 increases the base attack by 45%
(6196)
45-27.5 is 18.5 which is 41% increase. Which is still less than 50%
It isn't really the buffs and debuffs that are directly affected by diminishing returns, rather it is the stat itself. If I say Howard's attack rating is is 3898, that means he literally does that much damage when using an attack with a scale 1.0 attack. Light attacks do 0.25 scale damage, which means when a champion with 3898 attack rating uses a light attack they do 3898 x 0.25 = 974.5 damage. The attack rating is, in a sense, a direct measure of how much damage that champion does.
But when I say a champion's armor rating is 477, that doesn't directly mean anything. Armor rating is like the volume knob on a radio. Turn the knob to 7 or 8 and that doesn't mean the sound is now "7 loud." It doesn't mean the sound that comes out is 7 db or anything like that. Similarly, if you want to know how much "477 armor" reduces damage, you need to know how that knob works. And the way it works is via the Diminishing stat formula. The math looks like this:
Value = StatValue / (StatValue + 1500 + 5 x CR)
where CR is the challenge rating of the opponent (not your own CR).
When StatValue is zero Value is also zero. As StatValue gets higher, Value gets closer and closer to 1.0 (the numerator and denominator get closer and closer relatively speaking). But no matter how high StatValue gets, the net Value never exceeds 1.0. If you try to push StatValue higher and higher, Value will get higher and higher but at a slower and slower rate. Increases get "diminished" as you go higher.
It isn't that the second buff is weaker than the first. One +1000 buff has exactly the same effect as ten +100 buffs. The result is the same: the stat gets +1000 points higher. But however much +1000 pushes you higher, the *next* +1000 will push you less than the first.
[Note: the math changes when Stats go negative.]
As to the furies. It is important to be precise with language. If we are talking about the buffs specifically, then 5 buffs is 60% more than 3 buffs. In terms of the net buff benefit, 5 is 60% more than 3.
But in terms of relative damage boost, the difference between 3 buffs and 5 buffs is not the difference between 3 and 5, it is the difference between the base + 3 buffs vs base + 5 buffs. So if one fury buff is a 10% attack rating increase, then the difference between having three and having five is the difference between 1.3 and 1.5, which is a 15.4% increase in attack rating.
Two things can be true. If I get a $1,000 raise and you get a $10,000 raise, then you got a ten times higher raise than I did, period. But if we are both making $1,000,000 dollars a year, then in another sense you got almost no more money than me. I am now getting 1.001 million dollars a year and you are getting 1.01 million dollars a year, and so you're now making 1.01/1.001 = 0.9% more money than me. It is true your raise is 1000% higher than mine, and it is also true your net increase over me is 0.9% more money.
1000% and 0.9% are very different numbers, because they are measuring two completely different things. 1000% compares the two benefits against each other. 0.9% compares the net effect of those benefits upon each of us against each other.