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and to that i say, just aim for about 50 75% crit chance and dump the rest in damage, i mean comon people, 100% is just overdone, and the attacks you do are so rediculously fact already that u will most likely kill anything before you crit for a second time anyway, dont stick your finger in the honey jar if you dont want more honey then you have had :D,

enjoy the game, thats most importand,

trying to "help" new players with vaults is very noble but you also kill for them the best part of the game.

helping a paragon 600 guy is much better since they really enjoy the game for longer than only 2 hours and don't get bored immediately when they feel the progress is "done".

What your saying is partially right, partially wrong, and completely irrelevant.

It is mathematically the case that you want 10:1 armor:resist and 10:1 chd; that is to say, these ratios are the tipping point where one stat starts to gain value and the other starts to lose value relative to the other. These ratios are ways to describe the ratio of value between the stats, not to describe their current valuations on any given character, or the amount of stats on a given piece of gear. All of those things have to be assessed in context of aiming for an ideal ratio of 10:1.

This doesn't mean that it will ever be the case that you want to take 1000 armor over 1000 resist (although even then there would eventually come a time where you would); it just means that this ratio is where the stats are at parity (well, parity at 10x)

oops

Quote from horrax1»

trying to "help" new players with vaults is very noble but you also kill for them the best part of the game.

helping a paragon 600 guy is much better since they really enjoy the game for longer than only 2 hours and don't get bored immediately when they feel the progress is "done".

That logic is flawed. The 600 paragon guy might be getting burnt out and about to quit, where a new guy might be just getting into it and could outlast the guy who is already 600.

These "ratios" always make me laugh. Especially crit. You want to have as much as possible, there's no ratio. You never have "too much" of one or the other. When a hit isn't a crit, you might as well deal zero damage. Even if you have 60% crit chance and only have 350% crit damage, it still means that you will deal increased damage most of the time. If you had 50% crit chance and 500% crit damage (the ideal "ratio") you would deal more damage, less often. And the examples I've used are useless, just get 10% 100%, 6% 50%, etc... Stop worrying about pointless things.

Quote from Euphytose»

These "ratios" always make me laugh. Especially crit. You want to have as much as possible, there's no ratio. You never have "too much" of one or the other. When a hit isn't a crit, you might as well deal zero damage. Even if you have 60% crit chance and only have 350% crit damage, it still means that you will deal increased damage most of the time. If you had 50% crit chance and 500% crit damage (the ideal "ratio") you would deal more damage, less often. And the examples I've used are useless, just get 10% 100%, 6% 50%, etc... Stop worrying about pointless things.

And since we can't edit (but why?), for all res and armor you get all res on str and dex classes, and armor on int classes, it's not rocket science.

Quote from Euphytose»

These "ratios" always make me laugh. Especially crit. You want to have as much as possible, there's no ratio. You never have "too much" of one or the other. When a hit isn't a crit, you might as well deal zero damage. Even if you have 60% crit chance and only have 350% crit damage, it still means that you will deal increased damage most of the time. If you had 50% crit chance and 500% crit damage (the ideal "ratio") you would deal more damage, less often. And the examples I've used are useless, just get 10% 100%, 6% 50%, etc... Stop worrying about pointless things.

There is an optimal ratio, it's a proven mathematical fact. Keith (one of the ones who explained it to me) posted this comment on the video on YT. It's a bit much for a lot of people to follow, but it is in fact ... a fact.
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This "keith something or other" guy sounds like a gentleman and a scholar.

You don't really address the answer of "but why is it 10:1? Why not 9:1, or 11:1?"

Well, if you reeeeally want to know, here is way too much explanation.

Step 1: no calculus, where we derive this equation for toughness: T(A,R) = t * (3500+A)/3500 * (350+R)/350

To start with, you need the equations for how much damage reduction armor and magic resist give you.

For armor, you get damage reduction = (your armor) / (50*enemyLevel + your armor) . There's no "reason" for that - it is just how blizzard defined armor to work. Plugging in some numbers (assuming monsters hitting you are all level 70), 0 armor would give (0)/(50*70+0) = 0% damage reduction, 3500 armor would give (3500)/(50*70+3500) = 50% and 7000 armor would give (7000)/(50*70)+7000) = 66% damage reduction.

Resist is defined by Blizz to work very similar, the only difference is the number in the denominator goes from 50 to just being 5 (spoiler alert: 10:1 ratio detected!). Damage reduction from resist is (your resist)/(5*enemyLevel+your resist). So 350 resist for example would give 350/(5*70+350) = 50% damage reduction.

Now, we need an equation for toughness. How does 75% damage reduction translate into toughness? The answer is you find out how much damage enemies have to deal to you do "really" do 1 point of damage, and you multiply your toughness by whatever that is.

1 real damage = x incoming damage * (100%damage - y% your damage reduction)

1/(1-y) = x

As an example, if y (damage reduction) is 75%, then x (toughness multiplier from that reduction) is = 1/(1-.75) = 1/.25 = 4

So, toughness is equal to whatever your base toughness was times your multiple from damage reduction from armor times your multiplier from damage reduction from resist.

Toughness = baseToughess * 1/(1-DR from armor) * 1/(1-DR from resist)
(baseToughness is however much toughness you'd have with 0 armor and resist, which is influenced by things like your life)

Now take that and make it look uglier by substituting in the equations from what DR from armor and DR from resist actually are. Also I'm just going to drop monster level as a variable and set it to 70 to make life easier for people who like numbers instead of having letters float around.

Toughness = baseToughess * 1/(1-DR from armor) * 1/(1-DR from resist)
DR from armor = (your armor) / (50*enemyLevel + your armor) = A/(3500+A) [a = armor]
DR from resist = (your resist) / (5*enemyLevel + your resist) = R/(350+R) [R = resist]

becomes

Toughness = baseToughess * 1/(1-A/(3500+A)) * 1/(1-R/(350+R))

I'm going to clean this up a bit by calling Toughness T(A,R) and base toughness t

T(A,R) = t * 1/(1-A/(3500+A)) * 1/(1-R/(350+R))

Can you simplify algebra? I hope so!

make some common denominators
T(A,R) = t * 1/((3500+A)/(3500+A)-A/(3500+A)) * 1/((350+R)/(350+R)-R/(350+R))
subtract
T(A,R) = t * 1/((3500)/(3500+A)) * 1/((350)/(350+R))
pull the double division out into the numerator (aka multiply numerator and denominator by the denominator of the denominator)

T(A,R) = t * (3500+A)/3500 * (350+R)/350

Basically, resist functions the exact same way as armor, only it is 10x as effective.



step 2a: what is the constraint?

Obviously, to maximize that equation for toughness the answer is you want infinite armor and infinite resist. GG EZ who needs maths.

Coming up with a reasonable statement of constraint that accurately reflects the reality of the decisions you face in game is tricky.

The problem falls apart here because there is no smooth trade off of exchanging res for armor at such and such a rate. There's a tradeoff at one rate for amulet, pants, helm and chest, another rate for other item slots, another rate based on what you get from gemming and then there's paragon points.

Ideally, for this to be a nice clean problem we'd want to be able to say "okay, you have $X to spend on armor and resist, each point of resist costs $10, each point of armor costs $1 - that's the constraint" - but you really just can't do that here.

The "10:1" golden ratio answer actually is only true in that situation where resist is 10 bucks and armor is 1 buck. If you are getting an "exchange rate" shittier than than (for example, losing 100 resist on pants to gain 595 armor) moving closer to the 10:1 ratio might be a bad idea.

The 10:1 rule for crit and crit damage was arelevant because it reflected a very real in game situation, players face with the choice of 1% crit damage or 0.1% crit chance at that 10:1 price cost via paragon points. Also, although not quite right, there is often a tradeoff faced of 6% crit on rings or 50% critD, which is pretty close to the right tradeoff for the 10:1 ratio rule to be an effective guideline. Since these sorts of situations don't really exist for armor VS resist, the rule isn't...invalid... but it is just not really applicable.

Now... all that said, I'm going to just give up and use this unrealistic constraint to solve the problem

$10*each point of resist + $1*each point of armor = $budget
10R + A = C


step 2: calculus, where we maximize that equation


Alright, I'm going to make the equation look a bit different saying

tt = t / 350 / 3500

So now I'm hiding some stuff I don't care about inside tt

T(A,R) = tt * (3500+A) * (350+R)

Now I'll expand the terms out

T(A,R) = tt * (3500*350 + 3500*R + 350*A + A*R)

I don't really feel like explaining multivariable calculus, here is a good video that covers this problem:

https://www.youtube.com/watch?v=IHu4pJnYbYs

We basically just need to follow the same process but with our functions instead of the ones they used in the example.

Restating the constraint (10R + A = C) as a function:

C(A,R) = 10R + A

The derivative of T(A,R) based on A (holding R constant), aka the partial derivative with respect to A, aka d/dA

d/dA T(A,R) = tt * (0 + 0 + 350 + R)

Same thing, but for R

d/dR T(A,R) = tt * (0 + 3500 + 0 + A)

And also, the partial derivatives of our constraint function:

d/dA C(A,R) = 1

d/dR C(A,R) = 10

Now plus all of these partial derivatives into the system of equations derived in the linked youtube video to get 3 equations:

tt(350+R) - u = 0
tt(3500+A) - 10u = 0
10R+A-C = 0

Just gotta solve that system, you do like solving systems of equations, right?

combine first two equations to eliminate u
tt(3500+A) - 10tt(350+R) = 0
10R + A - C = 0

divide out the tt from first equation
(3500+A) - 10(350+R) = 0
10R + A - C = 0

simplify first equation
A - 10R = 0
10R + A - C = 0

equate the two equations
A - 10R = 10R + A - C

we now have R solved in terms of C
20R = C

R = C/20

A - 10R = 0

substitude in our solution for R in terms of C
A - 10/20C = 0

we now have A solved in terms of C
C = 2A

put C=C and C=2A and C=20R, the solutions we found for A and R in terms of C
2A = 20R

A = 10R

Your armor should be 10x your resist, there it is. It came out as a consequence of math following from how resist is 10x as effective (this comes from how blizzard defined armor and resist, culminating in a toughness function) but also "costs" 10x as much (from our constraint). With a different constraint (say 595R + 100A = C, which is based on the itemization budget on chests), the answer would have been different.

Umm .. the video is titled 'why 10:1 is ideal'. And the video explains why it's ideal. And the video also states multiple cases where it's not. So no, I'm not ignoring anything.

Quote from Frozenembers»

Quote from horrax1»

trying to "help" new players with vaults is very noble but you also kill for them the best part of the game.

helping a paragon 600 guy is much better since they really enjoy the game for longer than only 2 hours and don't get bored immediately when they feel the progress is "done".

That logic is flawed. The 600 paragon guy might be getting burnt out and about to quit, where a new guy might be just getting into it and could outlast the guy who is already 600.

no it's not flawed.
first of i have experienced that alot to back up my comment
the para 600 guy has all gear and just wants to play / grind the game. so there is no problem in giving him gold for greater rift empowerments and stuff...
some low guy just wants to experience the game until he got a full set or maybe too. test them out and then quit.
it's actually quite common that way. ALOT of people just run through a game for 1 week and get the next one.
in that case I feel it's a waste to help these people. they just play the game 3 days instead of 1 week. so you taking away gameplay for them
In that case it seems it's a big help but it's just...bad.