[WoW|A:HotS] Infinite Progress Bars: Gear, Artifact Power, Vertical Advancement

One of the earliest blog posts I wrote was on leveling and other advancement systems. And with it comes a fairly uncontroversial statement:

Leveling, among other advancement schemes, is at its most basic a reward for time. Play a little longer, grind a few mobs, finish a few quests, and ding! You get a level, and along with it things like new abilities, better stats, talent/skill points, or any number of other things. Developers of MMOs know intimately that if you want to keep players playing, you need to give them rewards.

RPGs definitely enjoy their progress bars. Progress bars are so good at player retention/engagement that pretty much every game genre has borrowed them. MMOs are arguably the royalty of progress bars--outside of clicker games of course. But what happens when your playerbase balks?


I've Got The (Artifact) Power

In the latest expansion, World of Warcraft has created an alternate advancement scheme of sorts with Artifact Weapons. Starting at level 100, and well past the level cap of 110, you gain Artifact Power to level up your Artifact Weapon and gain traits to increase your character's power. Once you've gotten 51 traits, every point after goes into an "infinite" trait with an exponential increase in Artifact Power required for each point. To offset that, over time players automatically get more Artifact Power from each quest/boss kill/other activity as real world time goes on.

"Concordance" is the infinite trait in the upper right. In this screen I have 7 levels of Concordance. It takes about 3.8 Billion points of Artifact Power to get an 8th level.

I'm glossing over the previous patches and focusing on the current implementation, as its more in line with their original vision based on their interviews. It's also important to note that WoW is far from the first game to have an alternate advancement system. Diablo III of course has Paragon levels, but much earlier there was the original Everquest with what they called "Alternate Advancement" (dun dun duuun! That's where the term was pretty well coined).

What this does is ensures that players who don't play for a while can catch up, while preventing players who play a lot from getting too far ahead of the rest of the player base. But it also ensures that even if you play casually, you're never really too far behind. I pretty much only log on for raids and the occasional quest run once every couple weeks, and I'm within ~5 levels of more hardcore players.

Which kind of almost feels like it defeats the purpose of the alternate advancement. We're basically just moving forward on Blizzard's very defined schedule. Not that's a bad thing necessarily, given most designers will make spreadsheets trying to figure out advancement timing and schedule. Nor is it that different from gear drops from a raid, given those fall within a specific power level. It just feels really naked now.

But by creating this alternate advancement, it makes it easy for the designers to parcel out Artifact Power as partial rewards. Instead of dropping a big piece of gear, or giving a bump to a reputation that has no impact on your character's power levels, they can give you something in smaller, bite-sized pieces that allows you to continue progressing your character regardless of the activity you're doing. Filling that bar, which is industry-proven.


The Gear Treadmill

While Artifact Power is new to WoW, the gear treadmill is not. Most MMOs with an endgame beyond leveling uses gear acquisition as a way to increase character power without bumping their levels. WoW extended this treadmill by allowing pieces of gear to roll higher stats (Titanforging) or different bonuses (Gem Sockets, bonus tertiary stats) randomly.

What this meant is that there's no perfect set of gear anymore. Or at least, it's not attainable within a human's lifetime, let alone a raid tier's lifetime. Previously raiders could make a list of gear they wanted (called "Best in Slot" or BiS), and aim to get that gear. What it does for players who're never going to get the best gear in game anyways (which is at least 95% of the player base) is occasionally you get a nice surprise. Like my Paladin's bracers that should've been 910, but rolled 940 the other day (yay!).


You're Never Finished

But interestingly, the more hardcore contingent really dislikes these alternate advancements. If you're running for World First, you need every advantage you can get, which means busting your butt to stay on the forefront of that Artifact Power wave in the previous tier. An impressive amount of work, really, given the minute advantages it brings, also given if they were to just wait a couple weeks, they'd be in the same place numerically as they busted ass to get now. And similarly for the gear, because the gear can proc better variants at random, there's no end to the gear farming if you're aiming for the perfect (or at least best-ish) loadouts.

Really, the issue is that there's no endpoint. No finish. A large part of it indeed has to do with wanting to have a life outside the game and still be on the forefront, I don't doubt that. Logically it follows. But I wonder if that's really the only reason, especially since that reason only applies to a very small minority of the playerbase, and the complaints seem to be coming from far more than that minority. Maybe there's another reason that isn't recognized by players or the devs?

I've been playing another game, Alliance: Heroes of the Spire, where the developers pulled a similar design decision. At some point, nearly every hardcore player had a good chunk of the good heroes, and people were pulling duplicate heroes that were a disappointment--they were a waste if you had already "finished" that hero. The hardcore players were effectively done, so to ensure further engagement and to make it feel like dupes were a good thing, the developers created a Rank II where you could power up an existing hero by merging them with a maxed duplicated hero.

Rank II heroes use a different advancement mechanism from 1 - 6 star heroes.

The hardcore portion of the player base reacted very negatively to it. Part of it was the timing of how it was rolled out and the communication around it, but a lot of it was ostensibly based on the fact that there's suddenly more vertical power creep that players had to jump through when they thought they were done. More work.

On the face of it, as a game dev myself, the extra vertical advancement complaint felt farcical in nature, given A:HotS is still relatively young, and every other game in its genre has a similar mechanic for vertical advancement. But the backlash felt similar to what I've seen in the hardcore WoW community.


Changing the Rules

What both WoW and A:HotS have in common is the devs changed the rules of advancement.

For a decade--literally a decade--WoW had a level cap, you got raid gear, then next expansion dropped, putting everyone on an even playing field, and the cycle repeated. Now with the gear changes and artifact power introduction, the rules of how to advance between patches has changed completely, and the playerbase hasn't yet figured out where the line sits between meaningful advancement for each individual player and cookie-clicker-esque busywork.

For A:HotS, the maximum a hero could be was 6*60 (6 star, level 60). That changed after people had already burned dupes, and had a stable of heroes at maximum. Similar to the Flying/Not Flying argument in WoW, many players in A:HotS felt those changes somehow invalidated their previous work and rewards. The system worked in a specific manner, and the system changed, and that can feel like a betrayal.

As I mentioned earlier, I wouldn't attribute a fear of change being the only issue. Each advancement system mentioned so far has cons (and I've explored those cons), and they may likely be a bigger reason for certain players than a fear of change.

The gear BiS problem in WoW, for example, is an issue that only affects Mythic raiders who can finish the current tier in a reasonable amount of time before the next tier drops. For the rest of the playerbase who'd never have gotten Best in Slot anyhow, it's not an issue that should ever crop up outside of theory. But what makes that scenario different from an Artifact Power bar that can never be completely filled? At an abstract level, they really aren't, but I've noticed Artifact Power affecting casual players whereas the gear proc thing doesn't even register, which is really interesting from a player psychology perspective. Again, maybe it's because the mechanics of Artifact Power are far more naked than gear, or is it because it's new so it's subject to more scrutiny?

And as I mentioned in my original post on advancement:

But WoW and other MMOs have the problem that they’re really two games rather than one: a leveling game, and an end-game. And what system is good for one of those games isn’t really good for the other, as Blizzard’s experiments have proven.

Except now I can identify a third game: the leveling game, end-game, and top 5% players who can actually finish the hardest content, and what's good for the end-game doesn't seem to be that good for the top 5%, and vice-versa. Can they be reconciled? And then there's the potentially blasphemous question: does it matter if they aren't?
#WoW, #AllianceHotS, #GameDesign

[Alliance:HotS] Gear Set Bonuses

One of the things that makes Alliance: Heroes of the Spire so deep is the serious amount of gear customization you can do. Six gear slots, with set bonuses for having matching pieces that can seriously change how you'd deploy that Hero, and then slotting in gems, as well.

Gear set bonuses come when you equip either 2 or 4 pieces of a given set. The 2 piece sets are generally raw stat bonuses, whereas the 4 piece sets are the interesting effects:

• 2P Bone; +20% HP
• 2P Wraithbone; +25% HP
• 2P Furyborn; +20% Power
• 2P Dragonfury; +25% Power
• 2P Coldsteel; +15% Armor
• 2P Icesteel; +20% Armor
• 2P Sharpthorn; +10% Crit
• 2P Elderthorn; +20% Crit
• 2P Brightshield; +15% Block, +5% Reflect on Block
• 2P Sunshield; +25% Block, +7% Reflect on Block
• 2P Nightleather; +20% Aim, +5% Armor Penetration
• 2P Voidleather; +25% Aim, +10% Armor Penetration
• 2P Bloodstone; 15% Lifesteal, +10% Healing Received
• 4P Ironclaw; 35% Counterattack Chance
• 4P Swiftsteel; 40% Chance of Bonus A1, +50% Crit (Damage Only)
• 4P Wartech; 50% of Crits will have +200% CritMult
• 4P Witchstone; Buffs/Debuffs can Crit
• 4P Lifesilk; +30% Healing Done, HoTs can Crit
• 4P Titanguard; 15% Less Direct damage taken, Redirects 30% of party damage to self

That is seriously a lot of options. Today's post is going to be looking mostly at the 4 piece sets, though I may talk a bit about the 2 piece sets in relation. How much does each set help? When might you use each 4 piece set? Let's start with some of the easier to discuss sets.


Lifesilk
+30% Healing Done, HoTs can Critical Strike

Lifesilk is pretty straight forward: you want this unit to do more healing. The details are the +30% is multiplicative (so if your Pyrus heals for 30% health, with Lifesilk he'd heal for 39% health), and critical HoTs heal for 15% of maximum health instead of 10% for the basic version.

Since critical HoTs require critical strike, you may want to pair this set with things that increase your critical strike, but if the unit doesn't have any HoTs, then it'll go well with literally any 2P stat increase. On the other hand, for high-level arena, you may end up using a more defensive 2P for your healers to survive. My Anat, for example, runs Lifesilk and Sunshield so she can have the extra block.

Witchstone
Buffs/Debuffs can Critical Strike

Witchstone is possibly the most complex of the sets, because what does a buff or debuff critting even mean? You can find an exhaustive list on the Alliance website here, but here's the rules of thumb to remember:

• If the buff/debuff has a number, crits increase it (ie: Armor Break goes from -50% armor to -75% armor)
• If the buff/debuff doesn't have a number, crits make them unpurgeable (Stuns, Sleep, Silence, Debuff Immunity, etc.)
• Bombs are the odd one out, on a crit they stun when they explode
• Bar drains and Bar fills are affected multiplicatively
• Witchstone cannot cause HoTs to crit

Witchstone makes a good choice if you have buffs or debuffs you want to supercharge. Unpurgeable silence or stuns can do wonders in Path of the Ancients or some Lost Dungeons where one unit constantly cleanses their team. If the unit you're bringing is less about damage and more about control or support, Witchstone may make for a good choice.

An example here is Sunslash, the Order Sabretooth. He doesn't do much damage, but making his AoE Mark a Critical Mark effectively increases your team's direct damage output by 15.4% (130% extra damage for basic Mark to 150% extra damage for critical Mark).


Titanguard
15% Less Direct Damage taken, redirects 30% of party damage to self

Titanguard is a fun one, and in high level arena you can often see it appear in what seems at first glance weird places. The first benefit of Titanguard is a straight-up 15% damage reduction on Direct Damage. The damage transfer effect is not direct damage, nor are DoTs or damage reflect, so they would not be affected by this damage reduction.

The other benefit is redirecting 30% of direct damage taken by other units to the Titanguard unit. Again, direct damage, so DoTs, damage reflect, or other Titanguard transfers do not count. This will often alow some of your squishier units to survive that much longer, even if you don't have a taunt up, or allow them to survive against AoEs.

This does create a weakness in Titanguard units: it's often easier to kill them indirectly by piling on damage on other units, especially if said other unit has a lot of HP but not a lot of armor--Petra comes to mind here. Titanguard units may also be susceptible to teams that have a lot of high-power AoE attacks for a similar reason: 3 units' worth of damage redirects at once can drain the Titanguard unit's HP bar very quickly.

Finally, multiple Titanguard teams work interestingly: the 30% damage redirect is calculated first, then split among all available Titanguard units. So if you have 2 Titanguard units in your team, each one will take half (15%) of the redirected damage. You also cannot redirect damage to yourself, so if a Titanguard unit is one that's hit, they're not considered an available Titanguard unit in the damage transfer calculation.

Often you'll want to ensure Titanguard is on a unit that has a lot of health to begin with, since the damage transfer cannot be mitigated. Shields will still absorb it, but nothing else reduces it. So units like Petra, Valorborn, or even the Mechanics are good choices for Titanguard.

Ironclaw
35% Chance of A1 Counterattack

Ironclaw and Swiftsteel are relatively similar in a mechanical sense. They both give you more (automatic) uses of your first ability. The difference largely lies in the trigger mechanism. Ironclaw requires you to be attacked in the first place. This makes Ironclaw a good fit for units that get attacked often: taunters, provokers, and guarders.

Ironclaw is effectively a DPS increase, but it can also be useful if the Hero has a debuff on their A1 you want to apply as often as possible. Gaius' A1 stuns, for example. Otto's A1 hits like a truck. Both good reasons to bring Ironclaw to the table. In the case where you want more debuffs, you'll likely want to pair it with a surplus of Aim. Especially for tanks, going mostly Aim instead of Block feels weird, but if the enemy team is mostly Stunned anyhow, it's not a big deal.

Ironclaw on farmer units that have self-healing (i.e.: Otto, Petra) is ridiculously effective since they're always getting attacked.

Note that you cannot Counter more than once per attack, so if your Hero already counters as part of their kit, Ironclaw is not likely a great choice.

It's a pretty straightforward ability, but look lower in the post for an analysis of Ironclaw vs. Swiftsteel, because that's where things start to get muddy.


Swiftsteel
40% Chance of a Bonus A1 followup, +50% Critical Strike for Damage

Swiftsteel is a bit more complex than Ironclaw. Every time you use an ability, any ability, you have a 40% chance of following up with a Free Attack, which is a usage of your A1 against the target. If your target is friendly, or the ability has no target, the Free Attack will choose a random enemy, ignoring Taunt or Provoke.

Rallies and Counters count as ability usage for Swiftsteel procs, so you can get bonus A1 attacks on those. However, the Free Attack cannot proc another Free Attack--but a Free Attack proccing a Counter on the opponent to proc a Counter on yourself and then Proccing a Free Attack off that Counter can occur. It's rare, but when it happens you basically just watch the two units hit each other over and over until one of them dies or someone doesn't proc a Free Attack. It behaves like a bug, but it's permissable under the rules of Counters/Free Attacks.

Swiftsteel also provides a +50% Critical Strike, but for damage only. Heals do not benefit from this. This means you'll often pair a Swiftsteel set with either a +Power or +CritMult weapon, rather than the typical +Crit weapon many go with.

The reasons for going Swiftsteel are pretty well the same as going for Ironclaw: it's a DPS increase, and if your A1 has a great effect, you may want more of those. Midorimaru (or any Samurai Cat) is a great case for Swiftsteel to spread more DoTs, for example.

Look below for an analysis of Swiftsteel vs. Ironclaw, and Swiftsteel vs. Wartech.


Wartech
Half Critical Strikes are Supercrits (+200% CritMult)

Supercrits. The name sounds awesome, but what is a Supercrit? It's a Critical Strike that has an extra 200% CritMult applied to it. So for example, if you normally have 50% CritMult, a Supercrit will actually do 250% extra damage instead of 50% extra.

Unless you're rocking a surplus of Crit gem slots, you'll almost always want to pair this with a +Crit weapon.

It's ridiculously straightforward, and basically, if you need burst damage, Wartech is pretty much the way to go. But you also can't rely on it. On average it's really only increasing your CritMult by 100%, since only half your Crits will have it applied. So big, bursty, swingy damage.

Often units with big AoEs will get Wartech applied. If you're not terribly enamored of your Hero's A1, Supercrit may be the way to go for a damage increase. But how does it compare versus just 2 Dragonfury sets (+50% Power)?

For the sake of simplicity, let's pretend everything else is the same: stat allocations, etc. 100% Crit, no extra CritMult.

If we do 100 base damage, at 100% Crit with a 50% our base damage is 150.
With +50% Power, our base damage changes to 150, which after a crit is 225.
With Supercrits, our base damage is still 100, but a Supercrit is +250% damage, which is 350. But the floor half the time is 150. So an average damage of 250 instead.

So you can see that Wartech increases the average damage dealt a bit, even over +50% Power, but it's swingy. Sometimes you'll do way less, sometimes you'll do way more. If you have less than 100% Crit, the benefits of Wartech also go down. In this particular instance, you need 75% Crit to make Wartech do the same damage on average as 2 Dragonfury sets. Now, even if the average damage is lower on Wartech, it will still have a higher maximum. The maximum damage would still be 350. You'll just see it less often.

The above only holds for units that scale 1x with Power. If they have abilities that scale better with Power, then that 75% Crit inflection raises further. If their abilities scale worse with Power, then the Crit threshold goes down.

Enemy teams that have healers--Magitek Bards and Unicorns especially--basically have a HP reset button every few rounds, so burst becomes very important when fighting those teams, making Wartech attractive.


Analysis
Ironclaw vs. Swiftsteel

Because they're so similar, Ironclaw and Swiftsteel may be an interesting question of which to use.

To ensure the same number of potential A1 procs a round, an Ironclaw unit would have to be attacked 1.14 times a round. However, Ironclaw is always against the attacking unit, whereas Swiftsteel is against the unit being attacked (usually), or a random unit if none is targeted.

Swiftsteel, if you get really lucky on buff procs, can wreck backline units as it ignores taunts. It's not an effect you can count on however, as you'd have to proc it at 40%, and then randomly select the backline unit (25% chance if nothing else is dead), so basically, if you use a buff with Swiftsteel, you have a 10% chance to hit a given enemy unit. It can be deadly to the opposing team, but not something you can build around.

Every unit in the game has an A1 that will end up having to target a Taunter, so if you have an Ironclaw Taunt up, eventually they'll attack your taunter, and you have a little bit better than a 1/3 chance to hit them back.

So basically, Swiftsteel is great for focus fire, and Ironclaw is great for wrecking backline units.

What makes this complicated is Swiftsteel's 50% Critical Strike for Damage bonus. What it means is you can effectively run a +Power or +CritMult weapon instead of a +Crit weapon, so an extra +51% Power or +67% CritMult for a maxed out 5* weapon (which, depending on what your scalars are for your abilites, and what your stats allocations are before that, could be a 50%+ damage increase, or even more, but more likely in the range of +25%ish).

What that means is that the actual "must be attacked this often" value for Ironclaw to match Swiftsteel is:

So the upper bound of Swiftsteel's extra damage output to equal the average damage output of Ironclaw means the Ironclaw unit needs to be attacked an average of 1.71 times a round, which for most tanks is easily hit, even if they aren't tanking (given the prevalence of AoEs). So even with the Swiftsteel +Crit, Ironclaw is actually still fairly powerful in the Tank niche. However, if you have a Counter already built in (ie: Valorborn, or given by Diana), or Rallies, you may be better off going Swiftsteel because you'll have more than one chance to proc Swiftsteel a round, and you'll quickly outstrip Ironclaw with that.


Swiftsteel vs. Wartech

Here's where comparisons get complicated. The two act so very differently, making direct comparisons don't quite work. I'll be making some assumptions/shortcuts to make them easier to compare as DPS increases, but what a Hero's A1 is, and what you're aiming for really dictate this decision.

For DPS purposes, though, Swiftsteel is effectively 40% of an A1 and 50% bonus crit, and Wartech is effectively +100% CritMult.

Let's make some other assumptions: 100% Crit regardless of set; frees up Swiftsteel for a +Power or +CritMult weapon. That assumption means that you'd be getting 2/3rds the CritMult that Wartech gives, which given the 40% extra A1 DPS on average means that if you're only using A1, you're going to do more damage with Swiftsteel. On average.

Average is a dangerous word here, however, because most arena fights are over in a couple rounds (or drag on forever). You might decide to go +Power for more consistent results instead, but similar to the calculations we did for Wartech alone, on both cases Wartech will still burst higher than Swiftsteel.

The other thing that makes "average" dangerous is that Wartech favours AoEs heavily. A single AoE can only proc Swiftsteel once, however, you get the potential benefit of Wartech for all the hits of your AoE.

So once again, if you want consistent output, Swiftsteel may be better, but Wartech will give you better burst capability. And of course, if your A1 is an attack you want going off a lot, Swiftsteel is probably the way to go. If most of your damage is AoE, you probably want to go Wartech still. Anything that gives you extra potential Swiftsteel procs will favour Swiftsteel as well (Counters, Rallies).


The Future of Swiftsteel

The Swiftsteel changes effectively made Wartech niche (where before Wartech was the "best" and Swiftsteel was niche). There's a rumour that Swiftsteel proc rate will be reduced, which will bring it more in line with Ironclaw and Wartech so it's not quite so overwhelmingly powerful, but honestly, it's not the proc rate so much as it's the +50% Crit bonus that allows it to be such a great DPS tool. +51% Power on your weapon is potentially a massive DPS bonus--+67% CritMult is potentially less of a huge bonus unless your Hero doesn't scale well with Power, or you've already got a lot of +Power as the two scale off each other.

As long as that Crit bonus exists, or exists at that level, Swiftsteel will likely be the go to 4P for DPS. To balance it, the Swiftsteel proc rate would have to be reduced to the point where you'd rarely see it proc, defeating the original purpose of the set. +30% Crit would've been more reasonable, as then you could have the question, do I Elderthorn for my 2P? Do I Weapon for +35% Crit? Do I do both? Can I get Jewel slots to make up the deficit of one or the other? Right now it's basically, Swiftsteel, 7 Crit Jewels, go. Or Swiftsteel, Elderthorn, 3 Crit Jewels, go. Swiftsteel makes it way too easy to hit the Crit cap.

With that in mind, I forsee a nerf to Swiftsteel's Crit bonus one day (after the designers try the proc reduction), or a buff to Ironclaw/Wartech, although in the right situation Ironclaw will crush Swiftsteel's output today so I'm not sure about buffing it too much. Similarly, Wartech's upper bound already hits so hard today that buffing it the wrong way could be dangerous to game balance--part of why just buffs only doesn't really work as a game balancing tool despite people constantly suggesting it. The math breaks down eventually. Sometimes you just have to nerf.
#Theorycraft, #AllianceHotS

[Alliance:HotS] Stats and Stat Relationships

Alliance: Heroes of the Spire--like many RPG-derived systems--has a number of statistic on each hero, and they're not really explained in-game. I've had the luck to chat with the developers (they're quite available, which is super cool), and have gotten a few formulas out of them instead of having to reverse-engineer everything on my own, which is fantastic. So here I'll talk about a couple of the major formulas, then talk about what those formulas mean for numeric relationships.

WARNING: SO MUCH MATH AHEAD


Aim vs. Block

Possibly the most asked about, and one of those more misunderstood. Aim and Block affect how often your debuffs land, or how often debuffs land on you. They're directly opposed. The formula is as follows:

Noting that Aim and Block are both percentages, so divide the value you see in the UI by 100.

So an example might be Caelia, who has a 50% base rate to proc a Heal Block debuff on her target with her A1. If she has 73% Aim, and the target has 25% block, the result is:

So the two are linearly opposed, but multiplicative to the base proc rate. If the base rate is low, it'll still likely be low even with oodles of Aim. i.e.: a base 20% would only be 40% with 100 Aim against 0 Block, which is twice as high but no where near a guaranteed proc, but that Aim will prevent a high Block enemy from dumping your proc rate into the toilet, as 100 Block but 0 Aim means multiplying your proc rate by 0.

Basically, if Aim and Block are close, it'll be about your base proc rate. The further apart they are, the greater the effect but the base proc rate is still the biggest factor.


Power vs. Armor

Okay, so let's do some damage. The things to remember about damage rolls is that the only "roll" that occurs is the crit roll. Aim has nothing to do with your "accuracy" in the traditional sense (only for debuffs), and the damage itself is a static number based on your stats; there's no random variation.

The damage formula is just a string of multipliers:

Each individual factor is a little more complex, but not by much.

Raw damage is simply your power multiplied by the scale factor of the ability. In cases where the ability does bonus damage, that bonus damage is generally the stat multiplied by a different scale factor. You can find scale factors on https://spirebarracks-dev.herokuapp.com/ for each hero ability, though I'm unsure how up to date it is.

For example, Akamin's A1, Magic Bolt, has a scale factor of 1, so it's simply just Power in base damage. His Spray of Flame, however, has a scale factor of 1.15, so it does more base damage.

In the case of "bonus damage" such as Otto's A1, Backhand, you have 0.2 * Power + 0.44 * Armor as the RawDamage factor.

The Armor Factor is based on your opponent's armor. All attacks are affected by this factor--unless they penetrate armor, but I'm not covering that today. The relationship ensures what is known as diminishing returns. Basically, after a certain point, each extra 1% mitigation becomes more expensive than the last.

Armor Value vs. Percentage Mitigation

For example, to get 20% mitigation, you need 260 armor. 60% mitigation, you need 1560 armor. 80% mitigation, 4160 armor. 90% mitigation, 9360 armor.

That sounds pretty excessive, but each interval I chose was half the damage taken of the previous interval. However, armor does start to lose a lot of luster after 4000ish unless you can easily net those armor points.

Finally CritFactor:

Pretty simple, don't affect the calc if you don't crit. Increase damage by your Crit Multiplier if you do crit. Edit: Picture should say 1 + CritMult%, not +Crit%. Thanks Packo!


Crit% vs. CritMult%

Critical Strike Rate increases your damage, as does Critical Multiple Factor. However, the two are symbiotic. The more Crit% you have, the more you benefit from CritMult%, and vice versa. The good thing is that since this relationship is static, we can math out the optimal numbers for best performance.

The graphs compare the two look like the following:

Crit% on bottom left X axis, CritMult% on right, Z axis. Ultimate average damage multiplier on the Y axis.

That's a little hard to read, so here's a contour graph instead:

X axis is Crit%; Y axis is CritMult%. Contours from left to right are +0.2 damage multiplier

The darkest blue section represents an average damage increase of 0% - 20% over time. Then we have 20% - 40% in the mid-blue, 40% - 60% damage increase average in the blue-orange, and so on.

From this graph we can easily see that Crit% has the bigger effect on our average overall damage until we start getting close to maximum Crit%. At the 60% Crit% to 80% Crit%, we may actually be better off starting in on CritMult% (assuming you're going for damage, and not say, Witchstone, which cares naught about CritMult%).

A level 25 Weapon gives 35% Crit% or 67% CritMult%, whereas jewels are 5% each making Crit% jewels far more powerful than CritMult% to a certain point. The Crit% weapon is still more powerful than CritMult% unless you're rocking enough Crit% jewels to hit ~60% Crit without the weapon (which is 9 5% Crit% jewels. Attainable, but good luck).


Crit%/CritMult% vs. Power

This is going to be the most complex relationship, and depends entirely on what scale factors your abilities have. However, if we assume a scale factor of 1x your power, life gets a little easier. Then the amount of extra damage you do depends entirely on your percent increase to Power.

If we look at the contour plot in the section above, with the base level of CritMult, we'd need 80% Crit% to maintain a +40% damage for an A1 with a scale factor of 1, whereas a level 20 Power weapon will give you +40% damage by itself. This benefit gets even better for abilities that have better than 1x scaling for Power. Basically, if you go all in on Power, it should be numerically comparable to going all in on Crit% and CritMult%, if not better.

9 5* Power jewels is +99% Power, and Weapon and Gloves at 5* would be another 102%, meaning you'd do triple base damage, versus 9 5* Crit% jewels for +45% Crit% (60% total) and +134% Crit Mult (for a total of 184%), which only sits around double average damage.

Crit% jewels seem to be far more abundant than Power% jewels, though. I'm swimming in 5* Crit% jewels and have...0 Power% 5* jewels. Not sure they even exist. 4* give 8%, which is +72% Power. Which is still better on average than the Crit% route.

But barring Supercrits or mechanics that play off Crit% or Crits, Power seems to be the mathematically superior option here, especially at lower ends of gear. At least for average damage over time. For PvP, especially with Magitek Bards than can reset the health bars of their party every 3 turns, burst is the name of the game and Crit%/CritMult% will give you far better burst than just Power will.

Basically, Crit%/CritMult% makes your DPS swingier but a higher upper bound at low gear levels, whereas Power is good for solid, dependable DPS but not as swingy. But enough Power gems, and even Power can reach the upper bounds of what Crit%/CritMult% can manage.

And again, this goes entirely out the door if your abilities scale poorly off Power. So most tanks or multiattack abilities, like Pistoleers or Free Blades' A1. Or if you have things that proc off Crits, or you're using Supercrit (which I'm not going to do the math on today).


HP vs. Armor

Often people consider something called "Effective Health", which is a combination of factors that basically say: you have effectively this much health. For example, if you have 1000 HP, and 50% mitigation, your "effective health" is 2000.

Think of it this way: if an attack does 500 damage a shot, and you have 50% mitigation, each actually only does 250 damage, and it'll take 4 shots to kill you. Or if you have 2000 health and no mitigation, it'll take you 4 shots to kill you at 500 damage a shot if you have 2000 health. Hence an effective health of 2000.

Armor and HP tend to be diametrically opposed on gear, you either have armor, or HP, and HP generally comes in percentages (I'm ignoring raw value jewels for this), so you can directly compare how much effective health  your armor gives you versus how much health your HP gear gives you. But note that Effective Health scales off both HP and armor, so it's not a strictly 1:1 relationship.

Add to that the fact that the majority of healing is done via percentage heals, there's literally no reason to have more actual HP. Effective health is king here. What complicates this is that armor isn't a linear value. Diminishing returns makes this a lot harder to determine the relationship, and the hero's base armor will play a huge role here.

+HP% on bottom left X axis, Mitigation% on right, Z axis. Effective Health multiplier on the Y axis.

+HP% on the X Axis, Mitigation% on the Y Axis, every contour is +1x Effective Health, starting at +2x

As you can see in the plot graph, mitigation as it approaches 80% increases effective health significantly. 90% even more so. I actually had to cut it off at 80% or the graphs would be barely legible. 90% mitigation is basically 10x effective health, for example, vs. 80% mitigation which is only 5x effective health.

Which is to say, armor has a much larger effect on effective health than raw HP does. And remember that 1560 armor total is enough for 60% mitigation. But since mitigation is static, let's sub in the Armor formula for y in our contour graph:

+HP% on the X Axis, Armor on the Y Axis, every contour is +2x Effective Health

There's no easy off the cuff answer here, unfortunately. Some combination of health and armor is likely to be the best. Here's a closeup of the bottom half of the graph with a higher contour fidelity:

+HP% on the X Axis, Armor on the Y Axis, every contour is +1x Effective Health, starting at +2x

So ~2100 armor but no health is about x3 Effective Health, which is about the same as +200% HP and 0 armor. But if you could manage ~2100 Armor and +50% HP, you're looking at nearly x4.5 Effective Health.

No easy answers, but unless Rumble decides to put in attacks that do static HP in damage instead of percentages, or start converting heals from percentage to amounts that are static, your actual HP doesn't matter. It's all about the Effective Health. The one exception currently is Armor Penetration. This fact makes stacking armor penetration potentially extremely powerful against Tanks, but I haven't run the numbers yet. That's just a hunch.

Edit: There is one other thing: Armor Break. Normal is 50% armor reduction, Witchstone is 75%. For a tank with the 4160 armor for 80% mitigation, that means 2080/1040 Armor after the debuff, which amounts to 66%/50% mitigation. So basically, 70%/150% more damage taken. So HP is a buffer in case of Armor Break.


Conclusion

I don't know how speed works precisely, so that's the one stat I'm missing, but otherwise this is a pretty comprehensive mathematical look at the stats in Alliance. Power in general seems to be undervalued by the community and Crit% overvalued. Armor vs. HP has a correct optimal answer, but depends on how much armor your character can get. Crit% vs. CritMult% also has a correct optimal answer, and Aim vs. Block is pretty straightforward.

The wrinkles that get thrown in these are basically individual ability power scalars, "bonus damage" scalars like armor for some tanks, or Aim/HP/Whatever, or abilities that proc off crits, including armor sets such as Witchstone and Wartech. A lot depends on the individual hero still. And none of this takes into account buffs/debuffs.
#Theorycraft, #AllianceHotS

[Alliance:HotS] Theorycrafting Critical DoTs

I've been playing a lot of Alliance: Heroes of the Spire the past couple of months. It's a nifty Summoners War clone made by a North American company, which has been pretty cool because we get to talk to the devs relatively often--as a dev myself, I'm pretty appreciative of that access.

So, you summon heroes, level them up, gear them up with up to 6 pieces of gear, and let them loose on other teams and dungeons. The thing about gear is you can wear x number of a type of gear to get a benefit. For example, Bone gear will increase your hero's Health by an extra 20% for every 2 pieces of Bone gear you have on. Some more powerful sets require 4 pieces, making them mutually exclusive with other 4 piece sets--such as Swiftsteel (25% chance of performing an extra ability 1 attack every time you attack), or Titanguard (Transfer 30% of damage done to your party to you, reduce incoming damage by 15%).

My Sunslash's Gear Screen, wear 4-Piece Witchstone and 2-Piece Sharpthorn

However, one of the more interesting mechanics I've found in the game is that using a specific item set--Witchstone--your buffs/debuffs can critical strike, making them either 40% ~ 66%ish more powerful depending on the buff/debuff, or undispellable if it's not a numeric buff.

A prime example of this are Damage Over Time debuffs, aka DoTs. The regular DoT always does 5% of the target's max health in damage each round, but a critical DoT does 7% per round (an increase of 40% total damage). DoTs are great at shredding most PvE bosses, as they tend to be a big target with lots of Armor (damage reduction), and DoTs ignore Armor.

Razormane, Flameclaw, and Icefang are plentiful and, against the right targets, powerful.

As such, lots of people like to use Razormane or Flameclaw to take out bosses. The benefit of these cats is that they're quite common--they're available from the worst pull you can make, and even drop from some dungeons, and their main attack has a 30% chance to apply a DoT (and can apply a second DoT if they were stealthed when they attacked).

Where this becomes really interesting is Swiftsteel (25% chance of an extra attack) vs. Witchstone (If your DoT crits, it'll be 7% DoT). Are the extra attacks better than the critical DoT? Let's do some math.

Making this all slightly more complex is the fact that debuffs may not always land. The to-hit of a debuff is Base Chance + (Aim - Enemy Block). Pretty close to everything has a base 15% to block (Bosses actually hit 25% at the highest floor you can fight them at).

So we have two possible stats for our DoT to scale from: Aim (Hit%), and Crit%. To make this easier, we'll ignore stealth for Flameclaw, and just assume spamming the first ability over and over.


Varying over Crit%

Let's assume we have a 100% chance to apply a DoT (125% Aim against a Floor 6 boss), and vary the critical strike percentage.

For Witchstone, we have an Crit%, aka x, chance to apply a 7% DoT, otherwise it's a 5% DoT:

For Swiftsteel, it never crits, so the amount of damage we can apply is based on the Swiftsteel proc rate:

Now, there's a small flaw in this math that I'm going to glaze over, which is that these expected health percentage damage values are an average over a lot of samples. In a single fight where you might get 5 - 10 turns, the variation is going to be much higher, so take this with a grain of salt. But over a lot of fights, we can work without dealing with that flaw.

In any case, since Witchstone's damage is varying over Crit%, but Swiftsteel doesn't, that suggests there should be a solid inflection point where Witchstone will generally outperform Swiftsteel for DoT damage:

So, assuming we'll always apply a DoT, Witchstone will usually outperform Swiftsteel once you reach 62.5% chance to critical strike your DoT.


Varying over Hit%

Let's assume we have a 100% chance to critical strike, and vary over Hit%, aka y. I'll ignore the Block/Aim/Base Chance portion, and work with the Hit% directly to make life a little easier.

For Witchstone, this is simply, since it always crits:

For Swiftsteel, this means we scaled both the regular attack and the 25% proc attack by Hit%:

Comparing the two, we actually find out that Witchstone simply scales faster than Swiftsteel with Hit%. The only value of y where an inflection point can exist is y = 0:

We'll see this fact crop up again when we try to vary over both Crit% and Hit%.


Varying over both Crit% and Hit%

Remember, x is Crit%, y is Hit%

Witchstone:

Swiftsteel:

Equating the two:

Almost immediately we notice we can divide the entire equation by y, removing the variable. Basically, Hit% is meaningless to how they scale relatively to each other. Which means that 62.5% Crit% is the magic number where the two become equivalent for a really basic scenario.


How Reality Completely Breaks My Model

Of course, Swiftsteel is more interesting than I've allowed for in my modeling. It can actually proc off any attack, meaning that if you use Prowl, you could end up making an extra attack, where the Witchstone build might not get anything except an undispellable Stealth buff. But on the other hand, if you're using Swiftsteel and it procs on a move that has no target, I believe it picks a target at random, so it might be a wash depending on who it targets (unless you only have one target).

This actually makes Swiftsteel significantly more valuable than that 62.5% Crit% inflection point would have you believe, as a fully skilled up cat on auto-battle will only use it's A1 ability every other round based on cooldown rotation, which if you squint kinda makes it like a 50%ish proc rate instead of 25% proc rate--if we count each A1 usage as a double chance to proc instead, which is a small fallacy but close enough for demonstrable purposes--which would actually make the inflection point 130% Crit%, which is absurd as anything above 100% is wasted (also, good luck hitting that much Crit%). It also doesn't take into account the extra initial damage that each Swiftsteel attack would grant as well, though in the case of the cats, it's usually small enough to be negligible.

But Witchstone has other benefits. For example, Sunslash, the Order cat, has an A3 that Marks all targets for 3 rounds, increasing the amount of damage anybody does to that target by 30%; 50% on a critical strike if you have Witchstone, which means a significant chunk of extra damage overall to potentially the entire enemy party, which makes Witchstone a better bet for Sunslash for overall DPS (assuming you can stick those debuffs). He'll likely have fewer DoTs, but critical DoTs will help make up that difference a little.

However, the 62.5% Crit% inflection is something to remember if we run into other DoT classes. Enough Crit%, and Witchstone will outstrip Swiftsteel's performance. But at the end of the day, it also comes down to what other abilities your hero is rocking, and what you need that hero for.

But if you're just using Flameclaw/Razormane for Boss Shredding DoT application, Swiftsteel is the way to go. #Theorycraft, #AllianceHotS