Calculating Battle Arena "Power"


#1

When I did my firsts steps on battle arena, I was wondering what “power” on arena was supposed to be. At first glance, I thought it was how much “power points” I had invested on my character, but facing players with higher power values against my fully invested power character made me to discard this hypothesis. After it, I just figured out it was a potential power measure, that I could compare against my opponent. Although, I have found it was not absolute: Facing and defeating players with higher power values and also losing for some with less power than me just encouraged to see battle arena power as a “magic number”. I’ve ignored it until recently, when I found the below post of @marwinberna on forum:

I thought it was such an absurd, cause I never saw a non-hacker player with this value. It made me to question how “power” is really calculated. So I did some empirical tests and I have found a formula that is pretty accurate (also that what Bekhor said is partial true).

1 Basics

If you're familiar with damage calculation, just jump for the next section.

1. 1 Full Weapon Damage (FWD) (Main Hand Values)

FWD = [ BWD * (1 + IQ) * (1 + WD%) + WD+ + 5 * 75 + floor(PP * 19 / 98) * 75 ] * (1 + ED%) + ED+

Where:

  • BWD is MH Weapon’s Base. Every weapon usually have a different BWD, but since it affects in a minimal way on PVP, you can use the 144 (average value for many weapons). For detailed info, look at my spreadsheet here.
  • IQ is MH item quality. It is a percentage, so 25% means 0,25.
  • WD% is sum of all WD% on MH.
  • WD+: Flat Weapon Damage on MH (only).
  • 5 * 75: Basic damage, you always have 5 power points.
  • PP: Hero PVE Power Points. “floor” means round down function.
  • ED%: Elemental Damage% across all gear. Percentage.
  • ED+: Flat Elemental Damage across all gear.

1.2 Level Conversion Formula

If you have an affix with value X on level 100, then Y is its value at level 20, which can be found using following formula: Y = Xmin + 0.2 * (X - Xmin)

Where:
Xmin is minimal affix value. When crafting items, you will notice that affixes come with ranges, e.g. [10-50] Glasscannon, [10-75] Luck, etc. Value on left bracket is minimal value of it. Items which can’t be crafted, such PTL, you can take similar affixes to deduce its value, e. g. PTL is similar to Glasscannon, so you can assume it has same affix range (it really has). Also, that formula only works for non-eternal item affixes. In order to use it, just divide its value by 2 e. g. 86% Eternal PTL becomes 43%.

Examples:
50% Glasscannon turns: 10% + 0.2 * (50% - 10%) = 18%
45% Push the Limit turns: 10% + 0.2 * (45% - 10%) = 17%
74% Total HP% turns: 5% + 0.2 * (74% - 5%) = 18,8%
etc.

2 Evaluating Power

2.1 Power Affixes

Unlike your real power (damage output), there are few affixes which affects your battle arena "power". Full Weapon Damage affixes and following affects your battle arena power: - Push the Limit - Glasscannon (and Empower Talent) - Barbarian - Equality - Momentum - Pathfinder - Epiphany Bonus - Haunting Bonus

Not a complete list, I didn’t test every affix in this game, but many to deduce some things as I comment below.

Someone:

  • “Wow, I won’t read it anymore, cause you miss Defiant, then you must be wrong.”
    It was a big surprise to me that Defiant doesn’t insta boost power, because its description say that there is a guaranteed 25% boost, but you guys will notice that most of “conditional boost affixes” didn’t enter in this list either.

By conditional boosts, I mean boosts that only apply under very specific conditions. Examples: Angelic only boost skills with CD less than 1 sec, Masochism only when your HP is below 75%, Identity only when skill isn’t of your class, Skilled only for primary weapons and others. Even if you satisfy it for one skill, it won’t increases your battle arena power, because it counts only what increases all skills. This is somewhat the case of Defiant: While it always increases 25% damage, it has a conditional parcel which comes from your current HP. This shows that battle arena power is very limited and can be far different from your real power, which comes from conditional boosts and also DPS.

You can also deduce that things such Multi Attack, Extra Attack Chance, Attack SpD, Elemental Crit Chance/DMG, Crit Chance/DMG, Procs and others don’t boost your arena power, since I didn’t mention on my list (LOL) and tested them all.

2.2 The Formula

Power = 0.05 * FWD * (1 + MOD1%) * (1 + MOD2%) * (...) * (1 + MODn%)

Where:
-FWD is Full Weapon Damage
-MOD% is a power affix from my list, e. g. you have 2 PTL, then they become 36% (section 1.2), so (1 + MODPTL%) becomes 1 + 0.36 = 1.36
-Product of them all, because different affixes are multiplicative.
-0.05 comes from 95% damage reduction on arena.

2.3 Examples

0 Stats build (Quartz Everything) with Gauntlet (BWD = 384) at 25% Quality, 0 PP FWD = (384 * (1 + 0.25) * (1 + 0) + 5 * 75 + floor(0 * 19 / 98) * 75) * (1 + 0) + 0 = 855 Power = 855 * 0.05 = 42.75

0 Stats build (Quartz Everything) with Gauntlet (BWD = 384) at 25% Quality, 98 PP
FWD = (384 * (1 + 0.25) * (1 + 0) + 5 * 75 + floor(98 * 19 / 98) * 75 ) * (1 + 0) + 0 = 2280
Power = 2280 * 0.05 = 114.0

0 Stats build (Quartz Everything) with Gauntlet (BWD = 384) at 25% Quality, 98 PP, 2 +2 All Sets and 1 Equality Set Affix [Since with no HP/MP Mods, thus HP = MP]
FWD = (384 * (1 + 0.25) * (1 + 0) + 5 * 75 + floor(98 * 19 / 98) * 75 ) * (1 + 0) + 0 = 2280
Power = 2280 * (1 + 3 * 0.075) * 0.05 = 139.65

Hypothetical Bekhor’s Build (Solved: True)

Wand has 162 BWD and 50% IQ (Eternal)
3 Eternal ED+ and 4 Epic ED+ = 3 * 2080 + 4 * 1040 = 10400
2x PTL legend + 1x Eternal PTL = 0.18 * 2 + 0.36 = 0.72, but it is capped at 0.4, then it is just 0.4
2x GC + 1x Eternal PTL = 0.18 * 2 + 0.36 = 0.72 (see this update)
4 Empower Talent = 0.025 * 4 = 0.1

FWD = (162 * (1 + 0.5) * (1 + 0) + 5 * 75 + floor(98 * 19 / 98) * 75 ) * (1 + 0) + 10400 = 12443
Power = 12443 * (1 + 0.4) * (1 + 0.72) * (1 + 0.1) * 0.05 = 1648

Not 1700, but very near. Just add one barbarian and you can have more than 1700:
Power = 12443 * (1 + 0.4) * (1 + 0.72) * (1 + 0.1) * (1 + 0.18) * 0.05 = 1945

Final Commentaries

As you guys could see, battle arena power isn't that great, as it only tells you about a portion of your real power, since it doesn't consider many affix on its own calculation and consider only your MH weapon stats. But if you're still interested on it, this guide can help you with your curiosity. Another use sure is checking classic offensive affixes on a build that you see on arena and "reverse" his damage affixes (homework).

I also recommend making an excel spreadsheet to automatize calculation process, if you are really interested in power, or even if you aren’t, almost everything I said here applies in real power calculation.

For BWD values for all weapons, check my spreadsheet: https://tinyurl.com/DQBWD30

Special Thanks: Bekhor for causing my doubts and Midlumer for his Damage Maximization Guide, from where I got an explained version of damage formula.

Sorry for my bad english wherever you have found it.

@update 06/09/2017: Glasscannon cap is 100%, not 40% like it is supposed to be. Same applies for Barbarian. Not sure about PTL yet, but it’s probably working properly.

@update 07/09/2017: Even WD+ on MH not affecting OH damage, it still has a contribution on Battle Arena Power.


Immortal headache
BARRAGE skill
#2

Good Job @luisfsk. Thank you for taking out the time to provide this level of detail and understanding of the PvP power number for all players. :sunglasses:


#3

I’m trying to rebuild the said build I told you before. I just need sometime to farm Eternal Pet (which is dream to me) :joy:


#4

Thank you for this well though out guide.


#5

Thank you, it is pleasure understanding this game mechanics, so no problem about spending some free time xD. After all info that I got here, It is a minimal favor I could give back.[quote=“CuzegSpiked, post:4, topic:17727, full:true”]
Thank you for this well though out guide.
[/quote]
Thank you, but I wish I could have a better english to fully clear ideas.

Just in your dreams :joy::joy::joy:


#6

Your English is good :smile: .


#8

did you find it? it was a multiplication by 0


#9

Sorry. I get it now.

Are you certain that defiant don’ boost your power in arena? Just my thought, it say that it boost your dmg though. The conditional dmg is when you’re HP becomes low.


#10

I think defiant Increase damage but I can’t tell that easily or if it gives DMG boost as you lose HP. It definitely works at damage Reduction though so no issues there. Lets test.


#11

It boosts damage on arena, I’m sure about it, but doesn’t boost shown battle arena’s power. I mean, there is a conditional part on defiant and no conditional bonus increases shown battle arena’s power.


#12

Thank you.


#13

@luisfsk is correct. Defiant does not show in power display but it’s damage boost works in your attacks.


#14

Absoloutely


#15

It seems like flat WD is not part of thr formula. Why is that?


#16

Just a minor oversight. Flat weapon damage is added after the weapon quality.


#17

Because I forgot. I tested and it also increases power, even it only affecting MH damage. I already did correction on guide, thank you.


#18

By any chance you know if AI in practise match have a fix affixes on them?


#19

Probably not, cause sometimes I notice they’re recovering, sometimes reflecting DMG, etc. so I doubt too much.


#20

Is “damage to elites” good to have, or is it pointless…?


#21

It seems pointless although it is free DMG, only to magic+ enemies. It’s only 25% though and only found on certain gar. Whether it’s worth it or not depends on you but I just seen better days to spend affix slots.

In PvP , it’s only 9% instead of 18%. Halved the value of Glasscannon and Barbarian but the difference is that no cost for 25% increased DMG, the only difference is reliance on elites. More powerful with things like Frozen though but not often used in general.

It’s not on you whether it’s worth it or not. I didn’t find it worth the affix slots and because of such conditions. I preferred Execute DMG 100% or Demonic for eg and other forms of DMG that were more easier to achieve without reliance on elites.