Boring Introduction
This is everything I've found about the damage and damage reduction in Magic Rush so far. I might be missing something obvious, but my damage model passed everything I threw at it. I tested it as best as I could. The main points are below. If you want to read the story of how I came up with all of this, it's further down. I heard it's as good as The Girl with the Dragon Tattoo.
Too Long; Didn't Read:
There are two different damage formulas: one versus monsters (PvM) and the second versus other players (PvP).
In PvM, the damage reduction is purely proportional. The same amount of Armor and Magic Resist always reduces the same % of the damage.
In PvM, 100 Armor reduces the incoming damage by 20% and 400 Armor reduces it by 50%.
In PvM, one point of Armor increases the Effective Health by 0.25%
In PvP, Armor and Magic Resist also reduce the damage by a flat value.
In PvP, the effective reduction depends on how powerful the base damage is. 100 Armor reduces the base damage of 2000 by 24%. 400 Armor reduces the same damage by 60%. If we double the base damage to 4000, 100 Armor reduces it by 22% and 400 Armor by 55%.
Armor and Magic Resist matter more in PvP.
Damage reduction works the same for both physical and magic damage.
Armor and Magic Resist are lowered by attacker's Armor Penetration and Magic Penetration by a fixed amount and they cannot lower resists below 0. * Not all attributes affect the damage. Armor Penetration, Magic Penetration, and Critical Hit Damage Level from runes and item attributes don't increase the damage. Fixed in the 1.1.65 Update * On the other hand, Armor Penetration, Magic Penetration, Armor Reduction, Magic Resistance Reduction, and Critical Hit Damage Level from heroes skills and item passives work as intended.
Armor and Magic Resistance Reduction from heroes skills (including Awaken Passives) and item passives cannot lower the target's Armor or Magic Resist below 0.
Except for a few isolated cases, Critical Hits simply double the final damage.
Damage Formulas
Physical and magic damage use the same formulas. Obviously, Magic Resist only reduces magic damage and Armor reduces physical damage. The formulas use floating numbers which are then rounded to the nearest whole number and shown as such in combat. For example 1294.28 will be rounded down to 1294, but 2005.77 will be rounded up to 2006.
Monsters include the Campaign (all difficulties), the Abyss, Proving Grounds, the Dungeon, and (surprisingly) the Crusade.
Players include Alliance Duel and the Arena.
I'm not sure to which category Ladder Tourney and Alliance Wars belong; I couldn't reliably test them.
UPDATE: May 23, 2016
As of May 23, 2016 (version 1.1.69), the constant in damage formulas changed from 400 to 370, increasing resistance effectiveness between 0 to 5%.
Versus Monsters:
Final Damage = Base Damage * (370/ (370+ Resist After Reduction)) * Crit Multiplier
Versus Players:
Final Damage = (Base Damage - Resist After Reduction) * (370 / (370 + Resist After Reduction)) * Crit Multiplier
Base Damage
The formulas for calculating the Base Damage are:
Physical Base Damage = Total Attack Damage * Skill Multiplier + Skill Bonus Damage
Magic Base Damage = Total Ability Power * Skill Multiplier + Skill Bonus Damage
Attack Damage and Ability Power include offensive attributes gained from levels, stars, runes, quality, items, academy, item passives (for example Sapphire Scepter), and heroes skills (for example Saizo's passive).
Skill Multiplier is a hidden value which modifies Attack Damage and Ability Power. As far as I can tell it always stays the same. Basic Attacks generally have the multiplier of 1.0 (so against 0 resist they do the same damage as hero's Total Attack Damage or Ability Power), but there are couple of exceptions.
Skill Bonus Damage is the extra damage listed in-game under each skill's description. It is a flat damage increase and is not multiplied by Attack Damage or Ability Power. It increases with the skill level.
Damage done by summons (Emily's Bonas, Alma's Ghosts, but also Gerber's continuous damage) is calculated separately and is not increased by heroes' attributes. It increases only with the skill level. It is affected by opponent resist.
Click here for (an almost) complete list of Skill Multipliers.
Resist After Reduction
if (Base Resist - Lowered Resist - Resist Penetration) >= 0:
Resist After Reduction = (Base Resist - Lowered Resist - Resist Penetration) * (1 - (% Penetration / 100))
if (Base Resist - Lowered Resist - Resist Penetration) < 0:
Resist After Reduction = 0
Lowered Resist (shown in game simply as -Armor or -Magic Resist) can come from heroes skills (for example Coco's and Blaine's passives, Smoke's Venom, Jolie's Shooting Frenzy) or from item passives (for example Skeleton Scepter). It simply reduces the opponent resist by a flat value.
Resist reduction from two different heroes' passives (for example Alma and Blaine) stacks with each other. Resist reduction from the same items' passives (for example two Skeleton Scepters) doesn't stack.
-Armor or -Magic Resist alone cannot reduce resist below 0. Let's say your Alma and Blaine each reduce opponent's Magic Resist by 70. Your opponent Magic Resistance is 120. After applying those reductions, opponent Magic Resist will be 0, not -20.
Armor and Magic Resist is then further reduced by -Penetration and then % Penetration.
Penetration from Awakening passives (West, Crabbie) and item passives (Conjure Scepter) are the only form of penetration I could confirm to work. Flat or % Penetration from runes and item attributes doesn't work. Fixed in the 1.1.65 Update.
Crit Multiplier
if not Crit:
Crit Multiplier = 1
if Crit:
Crit Multiplier = (2 + (% Crit Strike Damage / 100))
As of now, Critical Hits double the final damage. The only way to increase the Crit Multiplier is to enable Killer Blade passive or (possibly - I didn't test it) use Mira.
How it all came together
CSV Logs
Here are the damage logs from my tests in a CSV format: Alliance Duels, Crabbie, Damage Multipliers (incomplete)
Beginning
Since Magic Rush blatantly steals respectfully draws tiny inspiration from League of Legends champions, I figured maybe they stole were inspired by their damage reduction formula too:
LoL Base Damage * (100 / (100 + LoL Armor))
I mean, why not? It's simple, it's tested, it follows a basic rule where each point of armor requires a champion to take 1% more of its maximum health in damage to be killed. But more importantly, it's consistent: 100 armor always reduce incoming damage by 50%.
I noticed that Magic Rush doesn't have that consistency:
| Damage versus 0 armor | Damage versus 12 armor | Difference | % reduction |
|---|
| 125 | 109 | 16 | 12.80% |
| 272 | 250 | 22 | 8.09% |
As you can see, it's neither a fixed reduction, nor a consistent percentage reduction. So Magic Rush has their own formula. Question is: what the hell is it?
First tests
/u/wiklr kindly suggested that the Alliance Duel would be an excellent way to test damage reduction. I tried that with my alliance, but the language barrier and sloppy reporting (for example omitting academy bonuses when reporting resists) didn't get me very far.
I've decided to do everything by myself. I made two F2P accounts on the same server, made an alliance (Squid Squad, the best name ever), and joined it on both of them. I didn't use my main account because it's easier to test things when there are less variables. Grey characters with no runes, no items, and no academy have simple stats: just health, attack damage and resistances. No critical hits, penetration, and passives to complicate things.
I needed some reference point. Earlier I figured out that Slimers in chapter 3 have 0 armor and magic resistance. They are great for testing damage because once you kill the big one, two extra smaller ones appear, also with 0 resists. I also quickly noticed the relationship between attack damage and skill bonuses, I discovered skill multipliers, and finally I devised formulas for Base Damage.
Base Damage (physical) = Total Attack Damage * Skill Multiplier + Skill Bonus Damage
Base Damage (magic) = Total Ability Power * Skill Multiplier + Skill Bonus Damage
I could've now accurately predicted the damage against no armor and with 0 penetration. Next, I started testing the role of armor by staging fights in the Alliance Duel between my accounts. I began with recording how much damage Lufia did versus different starter heroes. Then I slightly increased Lufia's attack damage and had her fight the same starter heroes with the same stats. I repeated the whole process a couple of times.
Immediately, I noticed that the same amount of armor reduces less % as Attack Damage increases:
| Lufia's AD | Actual Damage | Opponent Armor | % Reduction |
|---|
| 125.40 | 125.40 | 0 | 0% |
| 131.13 | 92 | 32 | 29.84% |
| 140.27 | 100 | 32 | 28.71% |
| 144.84 | 104 | 32 | 28.20% |
| 154.84 | 114 | 32 | 26.38% |
| 157.84 | 117 | 32 | 25.87% |
| 169.84 | 126 | 32 | 25.81% |
At the same time, more Armor reduces more damage against the same Attack Damage:
| Lufia's AD | Actual Damage | Opponent Armor | % Reduction |
|---|
| 125.40 | 125.40 | 0 | 0% |
| 125.40 | 120 | 4 | 4.31% |
| 125.40 | 119 | 5 | 5.1% |
| 125.40 | 116 | 7 | 7.5% |
| 125.40 | 109 | 12 | 13.08% |
| 125.40 | 106 | 15 | 15.47% |
| 125.40 | 104 | 17 | 17.07% |
UPDATE: May 23, 2016
As of May 23, 2016 (version 1.1.69), the constant in damage formulas changed from 400 to 370, increasing resistance effectiveness between 0 to 5%. The following section will still use the old constant for archival purposes.
A formula which would satisfy both criteria had to be similar to this one:
(Base Damage - Armor) * (100 / (100 + Armor))
I used this formula on data I collected and I plotted the final damage against the predicted damage. The red line should be as close to the blue one as possible.
I replaced the constant 100 in the above formula with numbers from 1 to 1000 and compared all the results with the recorded damage. 400 was the best fit. It's almost perfect except some insignificant rounding differences:
(Base Damage - Armor) * (400 / (400 + Armor))
I used the corrected formula and I was able to successfully predict damage for any value of Armor or Magic Resist and 0 penetration.
Penetration
UPDATE: May 09, 2016
As of May 09, 2016 (version 1.1.65), attribute Penetration gained from runes and item stats works correctly. The following section is left for archival purposes.
With high confidence I included Armor Penetration in my calculations. I naturally assumed that penetration reduces armor by a fixed amount:
Final Armor = Armor - Armor Penetration
and that Final Armor can't go lower than 0. The damage formula would be:
(Base Damage - Final Armor) * (400 / (400 + Final Armor))
Based on the above I made some predictions:
| Opponent Armor | Penetration | Predicted Damage | Actual Damage |
|---|
| 0 | 6 | 1327 | 1327 |
| 44.37 | 6 | 1165 | 1155 |
| 22 | 14 | 1054 | 1032 |
Something was wrong and I didn't know what. I went back one step and tested damage done by Mira with 0 armor penetration and 2 armor penetration. One of the gray runes gives exactly 1 penetration, so it was a good test to see what was going on.
| Opponent Armor | Penetration | Predicted Damage | Actual Damage |
|---|
| 0 | 0 | 279 | 279 |
| 21 | 0 | 245 | 245 |
| 21 | 2 | 244 | 245 |
| 61 | 0 | 189 | 189 |
| 61 | 2 | 188 | 189 |
Probably just a rounding error, but I wasn't sure. On a whim I used a previous formula without penetration:
| Opponent Armor | Penetration | Predicted Damage | Actual Damage |
|---|
| 0 | 6 | 1327 | 1327 |
| 44.37 | 6 | 1155 | 1155 |
| 22 | 14 | 1032 | 1032 |
That couldn't be right. But I confirmed it with more fights. Once again, I correctly predicted the final damage without accounting for penetration. Ok, so flat penetration doesn't work. What about % penetration? This one is easier to test. In fact, you can do it yourself. Pick a hero with Professor Boots: Crabbie, Karna, Muse, or Murphy. Professor Boots increase four attributes: Health, Dodge, Attack Speed, and % Penetration. No Ability Power, so your damage should only increase because of the additional penetration.
Fight solo with that hero and note the damage. Enhance Boots a little so their % Magic Penetration increases. They are a Green item so it won't cost much essence. Then fight the same enemy as before and note the damage again. It's the same as before enchanting. If penetration worked correctly, you would do more damage. But you don't. Something is definitely not right. Well, fuck me.
Everyone (including me) assumed that penetration from items and runes just works. But empirical evidence shows it doesn't. If we were wrong about this one, what else could we be wrong about?
Revisiting Assumptions
I had to be absolutely sure there were no other surprises and I couldn't assume anything. So I've decided to check what affected damage and what didn't. For example: does hero level have any direct effect on damage? Pm me a picture of an alpaca if you read this. We all know heroes become more powerful as they level up, but that's because their Attack Damage and Ability Power increases with level. But let's say we have two heroes with different levels but with the same Ability Power - is there any difference in damage they do to the same target?
Here's what affects the damage directly:
Ability Power and Attack Damage, including hero attributes, item attributes, and academy bonuses
Skill Level
-Armor and -Magic Resist from skills (for example Jolie's Shooting Frenzy)
-Armor and -Magic Resist from hero passives (for example Alma's, Coco's, Blaine's)
Bonus damage from passives (for example Saizo's and York's)
% Magic and Armor Penetration from item passives (for example Conjure Staff)
Armor and Magic Penetration from Awakened passives (for example Crabbie's and West's)
% Critical Hit Damage Level from item passives (for example Killer Blade)
Opponent Armor and Magic Resist
Game mode
Here's what doesn't affect the damage directly:
Hero level, stars, quality (assuming the same attributes) * Flat Armor and Magic Penetration from runes, item attributes, and bonus attributes gained from Purple+ quality Fixed in the 1.1.65 Update. * % Armor and Magic Penetration from runes, item attributes, and bonus attributes gained from Purple+ quality Fixed in the 1.1.65 Update.
Critical Hit Damage Level from runes, item attributes, and bonus attributes gained from Purple+ quality
Attack Speed (you will attack faster and your Damage Per Second will increase, but individual numbers won't)
Hit Level, Dodge, Health and Energy Regen, Life Steal Level.
VIP level, server, age of the account
Out of the usual suspects, only attribute Penetration and attribute Critical Hit Damage Level don't work as intended. Critical Hits will always do double damage unless you enable Killer Blade passive (I didn't test Mira's skills).
Damage After Critical Hit = Damage * (2 + (% Crit Strike Damage / 100))
Was is intentional or just a plain old bug? I'd say the latter. We already had a similar situation with Dodge gained from attributes: it didn't work until they fixed it in late 2015.
PvM and PvP differences
With the damage formula figured out, I switched my attention to the Campaign mode. Since the attributes of monsters are unknown, I couldn't predict the final damage. So I tried predicting something else: their Armor and Magic Resist. I knew the final damage and the attributes of my heroes. I just needed to put the numbers in the formula, right?
Wrong. Here's what happened. I used Crabbie, Blaine (both at Blue +2), and Thanos (Purple +4) against Wereboar Mages (Light MR) in the Campaign stage 3-5. So, if I filled my formula with attributes and final damage of all three heroes, I should've got the same MR each times.
| Hero | Damage vs 0 MR | Damage vs unknown MR | Predicted MR | % Reduction |
|---|
| Blaine | 1132 | 993 | 12.7 | 12.28 |
| Crabbie | 1536 | 1379 | 13.05 | 12.30 |
| Thanos | 15493 | 13590 | 13.9 | 12.28 |
I didn't. But I noticed that the % reduction is nearly constant. I remembered that the LoL formula I mentioned at the beginning also had the same consistency. So instead of this formula:
(Base Damage - Magic Resist) * (400 / (400 + Magic Resist))
I tried this one:
Base Damage * (400 / (400 + Magic Resist))
The results were more promising this time:
| Hero | Damage vs 0 MR | Damage vs unknown MR | Predicted MR | % Reduction |
|---|
| Blaine | 1132 | 993 | 14 | 12.28 |
| Crabbie | 1536 | 1379 | 14 | 12.30 |
| Thanos | 15493 | 13590 | 14 | 12.28 |
I tested other heroes and the Wereboar Magic Resist was indeed 14. Turns out, there are different formulas for PvM and PvP. Also, somebody really did steal was influenced by LoL. I'm laughing out loud.
...Wait a second. Remember how I said I couldn't assume anything? It should be obvious which fights are PvM and which are PvP. It should, but I've decided to test it anyway.
Turns out, the Crusade, where you fight other players, uses the same formula as PvM. I confirmed it when I fought the same member of my alliance in the Crusade and then later in the Alliance Duel (same heroes, same attack):
| Hero | Mode | Damage Taken |
|---|
| Jacob | Crusade | 3774 |
| Jacob | Arena | 3585 |
I didn't test the Ladder Tourney and Alliance War, because there's no reliable way to replay the same fight while slightly tweaking variables.
Passives
As I said before, lowered Armor and Magic Resist from skills (including hero and item passives) work as intended. So does % Penetration from item passives (for example Conjure Staff). You can't lower opponent's Armor and Magic Resist below 0:
if (Base Armor - Lowered Armor) >= 0:
Armor After Reduction = (Base Armor - Lowered Armor) * (1 - (% Penetration / 100))
if (Base Armor - Lowered Armor) < 0:
Armor After Reduction = 0
As you can see, Armor is first lowered by a flat reduction and then by % Penetration.
The damage formulas are now:
PvP Final Damage = (Base Damage - Armor After Reduction) * (400 / (400 + Armor After Reduction))
PvM Final Damage = Base Damage * (400 / (400 + Armor After Reduction))
I tested this formula with Blaine's passive, Skeleton Scepter's passive and Conjure Staff's passive in different configurations. Once again I correctly predicted damage. Everything was wonderful!
Until it wasn't.
Awakening Passives
UPDATE: February 21, 2016
As of February 21, 2016 (version 1.1.51), Awakening Passives no longer reduce resists below 0. The following section is left for archival purposes.
/u/chao009 posted a video review of Awakened Crabbie, complete with before and after stats and damage against the same target. That was a fantastic opportunity to further test my formula. There was one problem though - I didn't know Magic Resist of Bedivere and Pandarus shown in the video. Still, I noticed that something was off: Awakened Crabbie did more damage against Pandarus than a normal Crabbie with the same attributes should have done against Slimer with 0 resist:
| Hero | Opponent | MR | MR Penetration | Damage |
|---|
| Crabbie, regular | Slimer | 0 | 0 | 4646 |
| Crabbie, awakened | Pandarus | >0 | 89.3 | 5906 |
Clearly, Magic Penetration from Crabbie's Awakening passive can reduce the opponent's Magic Resist below 0. I wanted to know how exactly it worked, but I wasn't been able to contact /u/chao009 for more details. Luckily, the next week I got my own Awakened Crabbie and everything was clear once again.
if (Base MR - Lowered MR) >= 0:
MR After Reduction = (Base MR - Lowered MR - MR Penetration) * (1 - (% Penetration / 100))
if (Base MR - Lowered MR) < 0:
MR After Reduction = (0 - MR Penetration) * (1 - (% Penetration / 100))
PvP Final Damage = (Base Damage - MR After Reduction) * (400 / (400 + MR After Reduction))
PvM Final Damage = Base Damage * (400 / (400 + MR After Reduction))
As you can see, the opponent's Magic Resist is first lowered, but it cannot go below 0. Then, Magic Penetration from Awakening passive is applied and now it can go below 0. Finally, % Penetration is applied.
Here's my favorite part. Awakened Crabbie does more damage without Conjure Staff passive (% MR Penetration) than with it:
| Heroes | % MR Pen | Passive MR Pen | - MR | Damage vs Pandarus |
|---|
| Awakened Crabbie | 0 | 96.3 | 0 | 7166 |
| Awakened Crabbie + Conjure Staff | 6 | 96.3 | 0 | 7039 |
| Awakened Crabbie + Blaine | 0 | 96.3 | 96.2 | 7260 |
| Awakened Crabbie + Conjure Staff + Blaine | 6 | 96.3 | 96.2 | 7124 |
Take a close look at how MR After Reduction is calculated. The right part of the equation is always multiplied by the left side. This happens even if the right side is negative. Crabbie's Awakened passive lowers the enemy MR below 0. When he activates Conjure Staff's passive, negative MR is multiplied by 0.94 resulting in lower damage than normally.
Unreduced Damage, Dodge, Life Steal, and other curiosities.
Those are the only mysteries I didn't solve (yet). Unreduced Damage (for example West's and Zoe's passives) should in theory bypass all resistances and be added at the end, before calculating Critical Damage. From what I've seen, in PvM at least, it is simply added to the Base Damage and is still reduced by the second part of the formula. I need to do more testing.
The relationship between Hit Level and flat Dodge is also something I didn't explore. % Dodge (from Charon's ultimate) works as advertised.
Finally, Life Steal Level and actual life stolen in a fight is the last problem I didn't touch. I can tell it is somehow affected by resist and damage reduction. By the way, attribute Life Steal Level only works with basic attacks.
Also, several monsters in certain stages of the Campaign seem to be immune to -Magic Resist, for example from Blainie's passive. One of those monsters in a wolf from a second part of stage 11-5. I don't know how to explain it.
...So?
How does all of this apply to your day-to-day playing?
The first point is obvious: if you're serious about competing in the Arena, you can't ignore Armor or Magic Resist. At the same time, offense has a tremendous edge over defense, especially early on. The primary role of resist is to keep you alive long enough so you will deliver one more strike than your enemy.
It also limits the viability of all-defense stalling teams (if such meta will develop in the future). You can't rely just on Armor and Magic Resist alone - you have to look at skills that give you immunity (Gearz), revive (Sebastian), shields (Uther), mass silence (Smoke), and healing (you know who).
Or you can simply go the other way and just pack as much heat as you can.
The second one is less obvious, but just as important. Let's say your dominant team is magic and you invested a lot in Ability Power in your Academy, neglecting Attack Damage. Still, you want some backup physical heroes for a rainy day (and boy, does it rain a lot in the Dungeon when that blue furry mammoth shows up). Or you just want mix and match. The best candidates will be heroes who:
Physical heroes which fit the bill are Coco, Gearz, Jolie, West, York. Their magic vis-à-vis are Blaine, Medea, Merlynn, Muse. They will be great even if they are low on stars as long as they have well-leveled skills.
Eventually, we will be able to tell exactly which items offer the best offense and defense per essence spent. I haven't done it yet, partly because a) I'm too lazy and b) it's kinda pointless if certain attributes don't work.
Thoughts?
