BfA Tank Diminishing Returns

Diminishing returns shows up in many places in Battle for Azeroth: damage reduction from Armor, Stagger and blocking attacks, and chance to dodge, parry or block attacks are the most prominent. Calling it an “often misunderstood” topic isn’t quite right… most people get it. People tend to argue about it a lot more than they actually misunderstand it, because there are a lot of valid ways to look at it… it’s like the Necker cube of WoW.

We are going to talk specifically about Armor, but the same logic applies to block amount, dodge chance, etc. — they all use a fundamentally similar formula.

Armor Formula

Armor reduces physical damage taken by a percentage. The formula that the game uses is the following:

Reduction = Armor / (Armor + K)

K is a constant that depends on who is doing the damage. Check out our tank formulas article for the full details. We will use level 120 characters getting hit by other level 120 units with a K value of 6300 in this article.

For example, say I’m a level 120 Warrior with 5000 Armor getting hit by another level 120 enemy (this is what your character sheet shows in the tooltip):

Reduction = 5000 / (5000 + 6300) = 0.4425 = 44.25%

As another example, say this same Warrior only has 2500 Armor:

Reduction = 2500 / (2500 + 6300) = 0.2841 = 28.41%

Reduction Percent Diminishes

So looking at our two examples, doubling my Armor from 2500 to 5000 does not double my reduction: adding 2500 more Armor only added 15.84% reduction, not another 28.41%. This is why people say that Armor has diminishing returns: the percent damage reduction gained per point of Armor goes steadily down as you get more Armor.

Let’s stop right there for a minute and reiterate this statement as an Important Sentence:

The percent damage reduction gained per additional point of Armor diminishes as you get more Armor.

This is a fact! It’s easy to see it by inspecting your character sheet with different Armor values in-game. It is mathematically, semantically, objectively, truthfully true! So then… why do people say that Armor doesn’t actually diminish?

Time to Live

So cool, Armor makes hits against me smaller. I know intuitively that will make me live longer, and that is ultimately what I care about. But how much longer can I survive if I add a specific amount of Armor?

For easy math, we will use the following example: you have 100,000 health, and an enemy is attacking you for 10,000 damage per hit, every 2 second. You are not getting healed and have no Armor. How long will you live? Most people can do this in their heads: 20 seconds. Here’s a formula though:

T = H * F / D
  • T = Time to Live
  • H = Health (100,000 in this example)
  • F = Frequency with which you are getting hit (2, or every 2 seconds in this example)
  • D = Damage taken per hit (10,000 in this example)

Using the formula for this example instead of our super-smart brains:

T = 100,000 * 2 / 10,000 = 20 seconds

Time to Live Does Not Diminish

Now let’s bring Armor back into the picture. All that Armor does is reduce damage taken per hit, or D in our formula here. Let’s calculate what D would be with 2500 Armor and 5000 Armor:

Final D = D * (1 - R)
  • Final D = Final damage taken after being reduced by Armor
  • D = Raw damage taken (10,000 in all our examples)
  • R = Percent reduction from Armor, using the formula in the previous Armor Formula section

With 2500 Armor:

R = 2500 / (2500 + 6300) = 0.2841
Final D = 10,000 * (1 - 0.2841) = 7159

With 5000 Armor:

R = 5000 / (5000 + 6300) = 0.4425
Final D = 10,000 * (1 - 0.4425) = 5575

And now let’s calculate our Time to Live with 2500 and 5000 Armor, and align them all nice:

0    Armor: T = 100,000 * 2 / 10,000 = 20.00 seconds
2500 Armor: T = 100,000 * 2 / 7159   = 27.94 seconds
5000 Armor: T = 100,000 * 2 / 5575   = 35.87 seconds

So let’s see… when I had 0 Armor and added 2500 Armor, I lived for an extra 7.94 seconds. When I had 2500 Armor and added another 2500 Armor, I lived for… and extra 7.94 seconds! OMG they are the same! You could do this with any amount of Armor and raw damage, you will get the same result, which we will summarize in another Important Sentence:

Your Time to Live gained per point of Armor does not diminish as you get more Armor.

This is a fact! It is mathematically, semantically, objectively, truthfully true! You can say it to your friends and they have to believe you. Another way to say this same thing is that your Time to Live has a linear relationship with Armor. When people say that, they are expressing the same concept as our Important Sentence.

So… are there diminishing returns or not?

OK Yellowfive… nice math tricks. But which is it really. Does it diminish or not? Or in other words, should I be thinking about Armor as a diminishing percent reduction to damage taken, or a linear increase in time to live? Which is more useful or better?

There’s really no right answer here — it all depends on what you are doing.  But this is what I would recommend to people: even though the percent damage reduction diminishes as you get more Armor, from a practical standpoint, you want to think of the true value of Armor as linear. It doesn’t matter if you are a fresh max-level character or a totally geared-up raider, each point of Armor that you add is just as valuable as the last — your time to live against a constant damage source will increase by the same amount.

There are of course other nuances to the game that can make it a bit more complicated than that, but generally speaking you don’t want to actively avoid Armor or any other “diminishing” stat like Parry as you get more of it. Don’t let the fact that your in-game character sheet barely moves as you get more and more geared up fool you, you are in fact getting just as much value per point as you were before.

Important Note

There is a somewhat common misunderstanding that arises when talking about Time to Live. Some people look at the above and say the following:

  • With 0 Armor I lived for 20 seconds.
  • With 2500 Armor I lived for 7.94 extra seconds, and 7.94 / 20 = 39.7% longer than when I had 0 Armor
  • With 5000 Armor I lived for 7.94 seconds longer than when I had 2500 Armor, and 7.94 / 27.94 = 28.42% longer than when I had 2500 Armor

Then they say that Armor still diminishes because going from 2500 to 5000 Armor gave me a smaller percent increase in Time to Live than going from 0 to 2500. It isn’t really a “mistake” to look at it like this… but you have to realize that you aren’t actually talking about “Time to Live” anymore. You’re talking about “Percent Increase to my Current Time to Live.” You are not talking about absolute Time to Live.

An easy way to understand the difference is to look at the “units” of the quantity being measured. The unit for Time to Live is seconds. Seconds corresponds to a real, physical quantity in the world: time. In contrast, “Percent Increase to my Current Time to Live” has no units. It does not correspond to an intuitive physical quantity. It is a purely relative quantity that is relative to your current amount of Armor. Only from this relative perspective does it seem to “diminish”. When you transform it to a physical quantity (number of extra actual seconds that I will live) it becomes linear.

So you can see how easy it is for people to argue in circles about this. Both perspectives are “correct”, you simply need to agree on which perspective to use when having a conversation. Our preference is to use the perspective of the real number of seconds that a point of Armor will increase your Time to Live. It is more concrete and intuitive, and from that perspective, Armor does not diminish.

Proof

This section is a footnote for the math nerds of the universe. The ultimate goal is to prove that Time to Live is a linear function of your Armor. In other words, we should be able to come up with a formula of the form Ax + B for Time to Live, where x is how much Armor we have, and A and B are constants. Let’s do that!

Recall our Time to Live formula:

T = H * F / Dreduced

And our formula for the value of Dreduced after Armor reduces a raw hit D:

Dreduced = D * (1 - R)

And then our formula for R, the reduction from Armor (we will use “x” for Armor in this proof):

R = x / (x+ K)

So let’s substitute that all into our Time to Live formula to get T as a function of x:

T = H * F / (D * (1 - (x / (x + K))))

Now let’s algebra the shit out of this to see if we can get something that looks like T = Ax + B. Note that H, F, D, and K are all constants in this formula.

T = HF / (D - Dx / (x + K))   distribute D
T(D - Dx / (x + K)) = HF      multiply by rhs denominator
DT - DTx / (x + K) = HF       distribute T
DT(x + K) - DTx = HF(x + K)   multiply by (x + K)
DTx + DKT - DTx = HFx + HFK   distribute DT and HF
DKT = HFx + HFK               combine like terms
T = HFx / DK + HFK / DK       divide by DK
T = (HF / DK)x + HF / D       cancel K and regroup
T = Ax + B
  where A = HF / DK
        B = HF / D

And there we have it — Time to Live can be written as a linear function of Armor. Just to ensure that we didn’t mess up our algebra, let’s redo the Time to Live examples using the new formula:

A = HF / DK = 100,000 * 2 / (10,000 * 6300) = 0.0031746
B = HF / D = 20
0 Armor:    T = 0.0031746 * 0    + 20 = 20.00 seconds 
2500 Armor: T = 0.0031746 * 2500 + 20 = 27.94 seconds 
5000 Armor: T = 0.0031746 * 5000 + 20 = 35.87 seconds

And there we have it, we didn’t mess up our algebra, we get the exact same results as expected.

 

Diminishing Returns & Other BfA Tank Formulas

In Battle for Azeroth, how does diminishing returns affect Armor, Block Amount, Stagger, Dodge, Parry, and Block Chance?

Some things haven’t changed and you’ll be familiar with them. Other things are a little different with Battle for Azeroth. We’ve figured out everything you need to know through data mining and a dizzying amount of in-game testing. Continue reading

Master Loot Removal: A robot’s study on human feelings

With some math, some simulations, and one infographic, Mr. Robot showed how losing Master Loot has almost no impact on your personal or team’s progress (outside of split raids, of course).

But what he didn’t talk about, were our human feelings on the matter. Continue reading

Personal vs Master Loot for BfA – Infographic

Blizzard announced that guild raids will no longer have a Master loot option – all loot will be Personal loot.

As it stands right now – on Personal loot if you win an item that is a higher iLevel than any other item you own for that slot, the item cannot be traded. If the item is equal or lower iLevel, it can be traded.

In a recent dev Q&A, Ion Hazzikostas (Warcraft Game Director), explained some reasons for this change:

  • All other loot in game has been on the Personal loot system (dungeons, world bosses, etc)
  • Master loot puts your fate in someone else’s hands, and you no longer have any control over it
  • If you help kill a boss, you should have a chance to get loot
  • It was not to take away split runs, however, they mention that is a welcomed side effect. (A split run is where a team takes their roster of 20 and split them up into 4 farm teams, for example. Each team consists of 5 ‘real’ players and 15 alts. All items that drop are Master looted to the 5 ‘real’ players, allowing the team to gear up faster).

The dev Q&A video from April 26 is queued up to the Master loot / Personal loot question below:

Watch Live Developer Q&A with Ion Hazzikostas from Warcraft on www.twitch.tv

This change is pretty controversial. A lot of people really love it, or really hate it.

The Internet is full of debates on the merits and flaws of each system. Instead of adding to that, I’ve done what we do best: run the numbers and let the data do the talking. (Click for full size) Continue reading

Battle for Azeroth Developer Q&A – Off GCD Change

BfA GCD Change - Dev Q&A

The Warcraft developer Q&A on Thursday spent the first 15 minutes talking about the off-GCD change. It’s probably the most controversial change so far.

Let’s take a look at what this change is, why Blizzard made it, the possible downsides, and how it might impact gameplay.

What is the Off-GCD ability change?

If you haven’t had the chance to keep track of all the changes in the BfA alpha, the Global Cooldown (GCD) has been one of the biggest. In the alpha, some abilities that were not on the GCD were put back on the GCD. You might see this referred to as off-GCD or OGCD.

If you didn’t have a chance to watch the video yet, here are some resources that might interest you:

That seems like a simple change, but it definitely affects a lot of different aspects of the game. The latest developer Q&A addressed the reasoning behind this decision.

Why did Blizzard make this change?

This is the big question everyone has been asking. In the dev Q&A, Blizzard explained that one of the main reasons for this change was to bring back some more meaningful decision-making in-game. When things are off the GCD, then there is no choice between A or B, you simply use them both. Continue reading

Legendary gear suggestions – why are they sometimes unusual?

Best legendariesHas this happened to you:

You own some of the best legendaries. You are excited to equip them. Then Mr. Robot says, “Nope, I’m going to equip some other ones instead.”

You then start to wonder if Mr. Robot is drunk or just trolling… you have the best legendaries, why isn’t he recommending them?

It comes down to 2 things:

  1. Mr. Robot takes into account all of the gear you own, including the iLevels on all of your gear. If you have a really low iLevel slot, sometimes it is best to replace it.
  2. Margin of error.

Customized Gear Recommendations

Sometimes the best legendaries for you right now are not the same as a ranked list of legendaries, even if you own them all.

WHUT?! No way that is right…. or is it? Continue reading

Addressing Toxicity

Toxicity is a real problem in some of the class Discords. Earlier this week I posted an article that tried to shed some light on it. But since I posted some statistics in aggregate, lumping in the good Discords with the bad, many Discord moderators got really upset.

I understand why they were upset: they want to distance themselves as far as possible from these toxic people and it isn’t fair to be associated with this bad behavior.  Because of this, I took down the original article – iIt wasn’t fair to lump them together, implying that everyone was engaging in poor behavior, instead of just a small group.

That outrage is encouraging – most people don’t want this toxicity.

Regardless of the poor execution of my first article, the toxicity is there. The problem that prompted the article still exists and so I am going to continue to address it.

Why me? Why is AMR posting this?

I’m making this post as a commentary on the state of the Discord community right now. There is a small group of toxic people poisoning the perception of what otherwise is a great resource for WoW players. In fact, it extends well beyond this community – it is affecting people (and even game developers) across all games. This is hurting our gaming community and we wanted to add our voice to say, “We don’t like it either.”

To quote the director of Twitch.tv, who recently spoke out about this topic: “This is about the leaders of the industry setting a good example that we shouldn’t allow or tolerate this, and we should fight against it, and set proper examples.”

How bad are some of these channels – are people just overreacting?

In this article, you will see quotes with racial slurs and homophobic remarks. I have blocked out names and icons, replaced with their Discord rank (moderator or expert), as well as identified if someone is a “Regular.” A Regular is defined as one of the handful of people in the ‘in-crowd’ who account for 75% of daily messages in the spec channels (on average). Anyone labeled as a “user” either just dropped in or has very little participation.

I’m sharing some examples that focus on channel admins and moderators. If it looks like I am cherry picking examples from these people, it is because I am (full disclosure). Admins, moderators and special rank members need to stop doing these things, not engaging in it. Admins and Moderators are setting an example and others follow their lead to fit in. Continue reading

T20 vs T21 Gearing Strategies

I’m seeing a lot of questions about which gearing strategy to pick, so I wanted to give you a thorough explanation.

T20 vs T21 gearing strategies

First, let’s talk about which one is right for you, how to select it, and then we’ll cover ‘why.’

We have four default strategies for DPS to pick (tanks and healers, I’m getting to you).

  • Single Target: Based on Garothi (see boss script details), and good for single target fights with mostly T20 and T21 gear. Recommended for Garothi, Felhounds, Imonar, Kin’garoth, Varmathras, The Coven, Aggramar, and Argus.
  • Multi-Target: Based on Mythic+ with higher gear, and good for T20 and T21 gear. Recommended for Mythic+, Antoran High Command, Portal Keeper, and Eonar.
  • Pre-T21 Single Target: Based on Goroth and good for single target fights with mostly T19 or T20 gear.
  • Pre-T21 Multi-Target: Based on Mythic+, good for AoE fights with mostly T19 or T20 gear.

Tanks have a whole bunch of new ones (see, we love tanks!): Raid Boss Low Level, Raid Boss Heroic, Raid Boss Mythic, and Mythic+ for 16-20, and 20+.  As of writing this, all tanks are done except Blood DKs, which should finish by the end of the day, 12/15.

Healers are up next and we HOPE to have them all finished by Dec 19th.

What to choose (and how to choose it)

Most of you probably had Pre-T21 Single Target selected when Antorus came out, which was good because you had mostly T20 gear, maybe even some T19 bonuses carefully balanced in there with your T20 4pc.

If you are getting T21 pieces now, you will want to switch to the Single Target strategy.  The order I listed them above is the order they are on the Gearing Strategy drop down menu. So to select it, you will have to scroll UP (that has caused people to miss it, and I am sorry about that).

Gearing-strat-dropdown

Scroll-up-strats-i

 

Why two different strategies?

You might be wondering, if these auto-adapt as your gear changes, why have two different strategies? Wouldn’t it make sense to put them all in one?

Yes, but…

The number of combinations explooooodes. If you want to include all gear combos with T19 (and relevant iLevel gear), T20, and T21, it gets a bit insane.

It is also not necessary to look at those combos because it is very, very, veeeery unlikely someone has such a strange gear selection that they would want some T19 iLevel stuff, T20, AND T21. That means you won only 2 items for each slot, ever.

In reality, you will span two tiers. For example, right now you probably have a lot of T20 and some T21. If we limit the combinations to a cross over between two tiers, it is giant, but manageable. And since we run every relevant combo for those two tiers (and all of the talents and relic combos you might have as well), being a manageable size is important. It lets us finish up all of the gearing strategies in a week, instead of a month.

Wondering what adaptive gearing strategies are?

I explain what they are and why they are a necessary update to the old stat weight systems people have used in the past (us included).

 

 

Garothi Worldbreaker script overview

 The script scales with the custom fight duration you put in.

  • Phase 1 lasts until Garothi gets down to 65%
  • Phase 2 (Apocalypse Drive) lasts for 20 seconds, which is about the length it is taking in logs. * I will be collecting more data this week and adjust the average if needed
  • Phase 3 lasts until the boss is at 25% health.
  • Phase 4 (Apocalypse Drive) lasts for 20 seconds.
  • Phase 5 (Burn phase) is the last 25% of Garothi’s health

This article describes the default script. I also have variations that may interest you.

While the scripts are totally customizable, the user interface isn’t as friendly or self explanatory as we normally present. So if you have a request for a variation, let us know in Discord or our Forums.

To use a custom script, click the link and then click the ‘add to my list’ button at the top of the page. You can then select it in the boss menu on the sim setup page.

  • A version where Bloodlust happens at the end of the fight, “Garothi Bloodlust at End.”
  • For players who ignore Eradication: melee who use cooldowns to stay in range of the boss, and ranged players who don’t move toward the back of the room, “Garothi (H) – Ignore Eradication.”
  • For ranged players who aren’t good at the ‘run and gun’ while moving, you’ll find you lose DPS compared to the default script. Try this script instead, which assumes you lose some spell casts while moving, “Garothi (H) – Move it.” I actually like to sim myself using the default and this one to see how much DPS I can gain if I practice dps’ing while on the run.
  • For dual wielders: Garothi has a bug where you can’t miss. Normally for bosses you can’t get behind, your attacks can’t be parried or blocked, otherwise it would be unfair to you. However, your attacks should still miss. But on Garothi (just like Krosus), you can’t miss. Here’s a script for that: “Garothi (H) – No Miss Bug.”

Phase 1:

Bloodlust happens at the beginning of the fight by default.

Annihilation

These are little green puddles that 1-3 people have to stand in to soak damage.

  • The number of puddles spawned scales with your raid size, averaging about 1 zone per 4 players.
  • In the script, we assumed melee have a 20% chance to have to soak a puddle, based on placement or absent minded ranged.
  • We assumed 100% of ranged will soak, allowing melee to stay in range of boss when possible.
  • ~1.5 – 2.5 seconds of run time required (random run time selected within that range)
  • Repeats every 32 seconds.

Decimation

When players are targeted they have to run far away before the decimation is dropped, then continue to run to get out of it.

  • The number of targets scales with your raid size, where DPS and healers have a 28% chance to be targeted.
  • In the script, if melee get targeted, we assume they are out of range of the boss.
  • If ranged get targeted, we assume that 10% of the time they will be out of range of the boss, and 90% of the time they will maintain range on the boss while running.
  • Assume 2.7-3.3 seconds of running (for ranged) or losing range of the boss (for melee).
  • Repeats every 32 seconds.

Phase 2 – Kill a weapon during Apocalypse Drive

This script has you killing the annihilation weapon first, since that appears to be the heavily favored strategy.

Surging Fel

This is the green strip that appears during Apocalypse Drive.

  • Assume melee and ranged are always in range of the boss
  • Very small amount of movement, 0.8 – 1.2 seconds to move a few steps.
  • Repeats every 5 seconds

Eradication

This is a raidwide AoE that does less damage the further away you are. So people run to the back of the room.

  • Assume 4-5 seconds of movement time, and loss of range of the boss for melee (assume ranged can still target boss). Melee end up 40 yards away from the boss and the scripts will use gap closers when possible. The default script does not account for people who stay in range of the boss and use cooldowns to survive or mitigate the blast. But I have a variation that does, “Garothi (H) – Ignore Eradication.”

Phase 3 – Empowered Decimation

Empowered Decimation

  • More people are targeted during the empowered version of Decimation, such that you have a 42% chance to be targeted and required to run.
  • Assume 2.7 – 3.3 seconds of run time and loss of range of the boss for melee.
  • Repeats every 16 seconds.

Phase 4 and 5

Phase 4 repeats to mimic the previous Apocalypse Drive. And phase 5 is a burn to take the boss down as fast as possible.

Adaptive gearing strategies – good bye stat weights

That’s right – stat weights are so last-gen. They are actually more like the iPhone 4… they barely work anymore and definitely can’t play any of the new games.

I’m not really exaggerating. Let me explain 🙂

The problem with stat weights:

Stat weights only rank the stats on your items and don’t rank any procs. That means they don’t rank procs from your relics, legendaries, trinkets or set bonuses. Thats… uh, half your gear!

If a system can’t rank half your gear, it is time to retire it. Even though some of our Moms still have the iPhone 4 because change is scary, it doesn’t stop us from trying to show them why a newer model is better.

I talk more about this in the video below (stat weights, not iPhones) and I also explain the new system that solves the problem. (Look at my face, SO SERIOUS!) If you like videos… /highfive. If not, keep reading and you’ll still get the most important points.

Continue reading

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