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.
- MeatHeadMikhail
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Feb 24, 2016MeatHeadMikhail posted a message on T10 Vaults for New Players, Armor vs All Res AnalysisPosted in: News
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Feb 23, 2016MeatHeadMikhail posted a message on T10 Vaults for New Players, Armor vs All Res AnalysisPosted in: News
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.
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.
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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. -
Feb 10, 2016MeatHeadMikhail posted a message on Patch 2.5 Wishlist, LoN Bombardment Pony CrusaderPosted in: News
In-geom allows you to re-mount less than every 4 seconds, in addition to the other reductions of course. Without it it's annoying when you click on something and dismount, then have to wait before getting back on.
Actually, you need 65+% CDR to have permanent horse with swiftmount. This is the fastest T10 build so far I have tested, but I would omit in-geom, it is not important and it makes you hurry like crazy not picking up anything on the ground, once you start picking-up, you lose it quickly and mortal-drama kllls mobs faster and more. In my opinion there is no need to change anything running high GRs or T10, even the blind flash is more useful than consecration, with almost 70%CDR you can use it all the time and elites or rift guardians dont do anything, they just die before they cast anything. Once you hit around 14-15k strength, you kill almost everything just with the horse:)
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Feb 9, 2016MeatHeadMikhail posted a message on Patch 2.5 Wishlist, LoN Bombardment Pony CrusaderPosted in: News
For the record there has been some commentary on specific changes given ideal gear, including some skill changes like AC-Rally, Laws of Hope-WoA, Avarice Band/Boon of Hoarder, etc. I've addressed these as they are all preference. For example, AC-Prophet allows you fully negate multiple stacked Molten explosions and Arcane beams so you can pick up globes and move on without worry, etc. Once you meet certain gear thresholds (like all 13 ancient items) you can start dropping certain items in favor of more quality of life changes. Note that TOO much movement speed is bad, as you will miss the damage ticks from your Thorny Pony.
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Feb 5, 2016MeatHeadMikhail posted a message on Monstrous' Armor Rack, Quin's GR 100 Support MonkPosted in: News
Great idea, hopefully we can get something like this this year. A huge technical feat for sure (make sure nothing can be exploited - lost gear, duping, etc) and a large monetary concern (will probably triple/quadruple effective stash space per account).
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Jan 3, 2016MeatHeadMikhail posted a message on Which Class Will You Play on Season 5?, Quick Gem Leveling TipPosted in: News
That doesn't make sense. Arachyr + Manajuma's is used for normal rfit speed farming. Every other spec is superior to Manajuma's + X for high GR. Furthermore, Arachyr 6pc boosts chicken damage - nothing else does.Quote from ActionJunkie»
Quote from MeatHeadMikhail»
Guys - it's not a build video, it's specifically a general concept for (newer) players regarding fast upgrades. I just happen to have a geared DH and all I had to do was swap a couple pieces and passives and I'm ready to go. Furthermore, chicken doc can be fast at the very low tiers, but once you get the uppers (50+) it slows to a crawl since LS doesn't tic for enough damage to kill trash before you're too far away. DH scales into 70+ without much trouble with fire UE.
True. BUT so many peeps need to realize chicken doc isn't exclusively arachyr... all it requires is 2piece Manajuma's. You can run Helltooth or whatever your heart desires with insane movement and do GRifts 65+ easy.
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Jan 3, 2016MeatHeadMikhail posted a message on Which Class Will You Play on Season 5?, Quick Gem Leveling TipPosted in: News
Guys - it's not a build video, it's specifically a general concept for (newer) players regarding fast upgrades. I just happen to have a geared DH and all I had to do was swap a couple pieces and passives and I'm ready to go. Furthermore, chicken doc can be fast at the very low tiers, but once you get the uppers (50+) it slows to a crawl since LS doesn't tic for enough damage to kill trash before you're too far away. DH scales into 70+ without much trouble with fire UE.
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Dec 11, 2015MeatHeadMikhail posted a message on New PTR Patch datamined! - Patch 2.4 December 11thPosted in: News
I think some of the people here are missing the point - the update to sets is not meant to make them more powerful than what's currently in the game. Power creep is inevitable via paragon (and now Caldesann's Despair cube recipe) - making sets even stronger will only make the problem worse.
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Dec 8, 2015MeatHeadMikhail posted a message on Technical Patch 2.3.0b, Patch 2.4 Transmog ShowcasePosted in: News
Mentioned at BlizzCon that S4 ending 'late December' (date unknown) and that there'd be a 'slightly longer break' between seasons - 2 weeks is a likely time frame. There also has to be a 2 week official 'season ending' announcement, which has not come yet. Highly unlikely you'll see the patch before next year, as employees are on vacation and not there to troubleshoot any massive problems.
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Dec 4, 2015MeatHeadMikhail posted a message on Blue Post Round-Up, Anthony Evans' Toxic Hound WDPosted in: News
Yea this is pre-nerf. Dog still hits hard though, just not as obscenely hard.
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Nov 16, 2015MeatHeadMikhail posted a message on Maintenance Reminder, Invoker Set and Crit, Patch 2.4 New Zones and ImprovementsPosted in: News
^ This sounds right. So if you miss a season you don't just get a tab at the end for nothing, you will still need to complete 4 seasons (at some point) to unlock all 4 additional tabs. It's not that hard guys, like 30 hours of work solo, at most.
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Nov 6, 2015MeatHeadMikhail posted a message on BlizzCon 2015 - Day 1Posted in: News
Very nice QoL improvements, though I can't help but feel the general lack of excitement from EVERYONE (fans and devs alike) this year. As I predicted, they're still trying to 'get it right' with D3 base, and I have a feeling with the new Kanai's Cube recipe we'll be seeing yet ANOTHER major power spike in GR progression. Oh well, at least it'll keep people going to get those 80+ gem upgrades converted to gear. Pumped for 2.4 PTR next week though!
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Sep 30, 2015MeatHeadMikhail posted a message on Blizzard Games on Sale, New ATI Drivers for D3, How to Cow LevelPosted in: News
Yea hadn't thought of that, could even throw in Harrington's since you'll have full uptime. Might be worthwhile if you can stash up like 20+ bardiches ... if you have the stash space that is.
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Sep 29, 2015MeatHeadMikhail posted a message on Fan Made Necromancer, Quin's Ranking Clears, Double Generator Monk BuildsPosted in: News
Funny cause Asia always has the 'wierd' builds with the top clears. The 81 or 82 or whatever clear it was had 3 zdps in it.
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Sep 29, 2015MeatHeadMikhail posted a message on Fan Made Necromancer, Quin's Ranking Clears, Double Generator Monk BuildsPosted in: News
Would be funny to see Alk vs. Quin for Barb. Alk has been #1 barb since seasons started AFAIK. Sader, well no one plays sader this patch. Wiz EU is like 72 I think.
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1
Hey guys, in anticipation of the next PTR, today I give some tips on how you can get ready now to quickly and efficiently test whatever you want. I discuss certain mats/items to save and a fast strategy for acquiring gear every re-copy. The first minute is for newer players explaining how to get started so skip that if you already know. Enjoy & discuss!
https://youtu.be/ywnhvaJ5Hww
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G62 Raekor's
Hey guys, today I clear G62. Quite a few changes over the last tier. I crafted a Standoff and got rid of War Cry for Sprint/Marathon. I also dropped Relentless for Nerves of Steel. Now using all diamonds, Bane of the Stricken, and stacking physical resistance. As a result, this tier is total noob play as I try to adjust to the new rotations (keep missing Battle Rage and Sprint buffs). Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/Q0gJEJ06qcE
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G65 DMO
Hey guys, today I clear G65. I bit the bullet and switched to DMO, as Firebird's was starting to take too long. The build (which I may cover later) is the standard high GR setup seen on leaderboards. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/8cg1bB1SWUc
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Keep in mind that just because no major features are being introduced (that we know of), doesn't mean it's going to be bad. There are lots of items and sets being rebalanced/reworked, in addition to a brand new set of items.
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G61 Raekor's
Hey guys, today I clear G61. No changes over the last tier but a nasty boss fight against Saxtris. I think I'll need to switch to full diamonds. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/sptAzgR-I4c
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G64 Firebird's
Hey guys, today I clear G64. No changes from the last tier and this was a GG rift. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/D94PgKVi2-8
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Hey guys, today I go over some of the 2.4.1 datamined notes and give my (previously accurate) predictions on release dates for the PTR, the patch, and Season 6.
Based on previous history and some comments by Blizz, we can expect the following:
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PTR this coming week, before March 12th
Season 5 ending Friday, April 15th
2.4.1 on Tuesday, April 19th
Season 6 on Friday, April 22nd (if something goes wrong worst case is Friday April 29th)
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Here's the video if you want to watch:
https://youtu.be/fuyY3oue-EE
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G60 Raekor's
Hey guys, today I clear G60. From the last tier I swapped out a couple rubies for diamonds to help with the incoming damage. Clear time was almost 2 minutes faster, probably due to RNG and pylon placement. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/5h7AQ3Hhh-Y
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G59 Raekor's
Hey guys, today I clear G59. No changes over the last tier. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/EIwa70Cz7iI
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G63 Firebird's
Hey guys, today I clear G63. I dropped a lot of elite damage and switched to a crappy Endless Walk set, losing a lot of sheet damage but ultimately gaining more. Much faster trash killing, resulting in a faster clear. I forgot to show the skills at the end but they're unchanged from the last tier. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/qzbh8X25Q8A
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G58 Raekor's
Hey guys, today I clear G58. I managed to gamble cold-based Ancient Parthan Defenders so I swapped to those along with an Eye of Etlich, so those are the only changes. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/QnOjXa9YbBs
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G62 Firebird's
Hey guys, today I clear G62. This is the last tier before switching to Endless Walk, as I'm simply not doing enough damage to trash mobs. I discuss elite trailing and the corner Energy Twister strategy. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/sxdRLMfI740
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G57 Raekor's
Hey guys, today (about half a year later) I pick up where I left off with the Barb and clear G57. It's been over a year since I did anything with Raekor's and things have changed quite a bit. I don't have the ideal gear setup and I'm completely unfamiliar with the (newer) playstyle, so the next few tiers should be fun to say the least. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/uB5FAP0mLiE
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G61 Firebird's
Hey guys, today I clear G61. No changes over the last tier except a few paragon levels and some gem ranks. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/yEb0m_rS0Bs
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G75 LoN Bombardment
Hey guys, today I clear G75. No changes over the last tier and I may have to go back and get better gear for the next one. Enjoy, discuss, and be on the lookout for the next tier!
https://youtu.be/wkt3dpSK7fk