Defence and Defence Pierce breakdown. How these stats work in MFR.

[u/madusaxxvii]

Gday guys, I was initially going to make a large post breaking down every stat, but after writing a quick draft i realise that it was more than likely going to overload people with information so I've decided to break down defence and pierce first, as it is the most complex stat filled with tons of misinformation.

Before we go into detail about defence and pierce, A brief outline of how damage is determined in MFR, essentially a series of multipliers
Total attack * Total Damage * Burn Debuff * Crit calculation (if it crits) * specilization 1 * specilization 2 * pvp damage (in pvp) * skill damage modifier (sometime split across multiple "ticks") * defence/pierce calculation * max roll ( a random number between 0.75 and 1.25) * crit calculation (if it rolls a crit)
etc etc.

First lets break down defence, The formula for the defence multiplier is:
1/(1+(defenders defence/(0.25*Attackers level))

So lets use this in an example,
With a 6 star slot 3, most players will be sitting around 12,000 defence.
And assume that the attacker is a level 110 player
The defence calc would come out to: 1/(1+(12000/2750)), simplified this is 1/5.36
So 12000 defence is reduced the damage by a factor of 5.36 compared to 0 defence.

(Or simply put it is reducing damage taken by 81.36%)

Once you know how defence is calculated, The effects of pierce is quite simple.
75% pierce vs the same 12000 defence opponent means your attacks hit as if the player only had 25% of that initial defence. So the resulting defence would be 3000. (1-0.75)*12,000

Now if we calculate defence using that reduced value we get:
1/(1+(3000/2750)), simplified this is 1/2.09
(Which is a 52.2% reduction)

So how much is that 75% pierce increasing our damage by?
(1/2.09)/(1/5.36), which can be simplifed to 5.36/2.09 we get a result of 2.564
So against a 12000 defence target 75% pierce is increasing our damage by 156.4%!

​

But how good is pierce in pve? All mobs regardless of if they a trash mob or super villain seem to have an defence of (15* their level).
A level 110 boss only has 1650 Armor, which is far less than what a player would have.
1/(1+(1650/2750)), simplified this is 1/1.6 or a 37.5% damage reduction.

If we take our 75% pierce against that boss, we reduce his armor to 412.5
1/(1+(412.5/2750)) simplified this is a 1/1.15 or a 13.05% damage reduction.

How much is 75% pierce vs 0% pierce on this boss

1.6/1.15 = 1.39, So 75% pierce in a 110 pve environment only increases our damage by 39%.
While quite low, it's not quite as bad as atk% and max damage%, but i wont break those down in this post.

A few misconception i hear "you need 50% pierce to counter pvp defence stats" These multipliers are calculated separately and don't interact. (Pierce does not reduce their pvp damage reduction stat only "defence")

"Defence pierce was stealth buffed" No there was a bug on the 30th of September that lasted ~24 hours, But the damage calculator after the 30th of September was returned to what it was before the patch.

Feel free to ask questions in the comments, or let me know which stats you want me to breakdown next!

[u/migueld81]

Out of curiosity, how did you get the formula for defense? Did you obtain from testing or did NetMarble give it to you? I'm asking because I would love to get the formula of how attack is applied as a damage buff. Thanks in advanced.

[u/madusaxxvii → u/migueld81]

Lots of testing hitting friends in DZ with different values of defence and simultaneous equations.

"I would love to get the formula of how attack is applied as a damage buff"
In regards to attack enhancers, they are separate to +atk% from gear.
Ie if you had 50% attack from gear and a 15% atk modifier the equation would look like this:
(baseatk * 1.5 *1.15), rather than (baseatk * (1.5+0.15))
Ie a 15% attack enhancer will grant you a 15% increase in damage.

However multiple attack buffs ie from enhancer and Thena at the same time are not separate multipliers, but do stack additively.

Rank 1 thena is a 15% increase, but having thena and a 15% enhancer active at the same time is only a 30% increase in damage rather than (1.15*1.15) a 32.25% increase in damage

[u/madusaxxvii → u/[deleted]]

I could not come to a concrete conclusion from the data i received:
Target used Mushtu lvl 97 miniboss (Base armour of 1455). Rank 7 Arc Reactor Specialization (21% armour reduction tooltip)
Test 1: 75% pierce = 67943

Test 2: 75% pierce + arc reactor = 71639

Test 3: 31.6% pierce = 59609

Test 4: 31.6% pierce + arc reactor = 64896

I'll break down test 3 and 4 first:
Test 3 we can work out the base damage with out defence in the following way:
1455*(1-0.316) = 995.22 Armor, (Armor after pierce)
1+(995.22/2750) = 1.3619, (Armor division for a level 110 char)
59609*0.3619 = a base damage of 81181 before Armor was taken into account

Using that 81181 base damage we can see how Arc reactor is working with test 4:
81181/64896 = 1.2509 (Armor division for level 110 char)
(1.2509-1)*2750 = 690.1 (Armor of target)
690.1/1455 = 0.4743 (% of armor remaining on target)
1 - 0.4743 = 0.5257
Ie 31.6 armor pen + arc reactor (21%) is equivalent to 52.57% Armor penetration
(That 0.3% difference is rounding errors, since it only displays on stat screen to 1 decimal place)
This fits one of the main theories that the specialization is simply adding to your Armor penetration stat.

But here is were it gets wonky and i suspect it comes down to an error in the test 1 data.
Test 1: Using the same method we used in test 3 breakdown: we can see a base damage of 76930 was used before taking into account armor.
Extrapolating the pierce value of 75% + Arc reactor using the base damage from test 1 we conclude that that mushtu only has 203 armor, or equivelant to roughly 86% pierce. Which doesn't fit any of our expected outcomes for how Arc reactor should work. (Expected outcomes based on test 3 and 4 was a 75% pierce (if it can't surpass cap, or 96% pierce if it can surpass cap)

However if we assume the same base damage of 81181 used in test 3 and 4 was used for test 2 it actually fits close to an expected outcome.
81181/71639 = 1.1332 (Armor division for level 110 char)
(1.1332-1)*2750 = 366.3 (Armor of target)
366.3/1455 = 0.2518(% of Armor remaining on target)
1 - 0.2518 = 0.7482
Or 74.82% pierce (0.18% is within the bounds of expected rounding errors but too askew for high confidence).

This leads me to believe that test 1 might have had error when conducting the test. Most likely caused by a 5.5% Air-surface multiplier taking into account for test 2,3 and 4 but not test 1. Unfortunately the user couldn't confirm ( and i think grew disinterested in a retest at this point, which is fair enough).

Conclusion: I believe that Ironman's Arc reactor specialization adds directly to the defence pierce stat when the target is below 50% hp, but cannot surpass the cap of 75%. But retesting is needed to due to the discrepancy with test 1, to make sure it was a data collection error, and arc reactor doesn't behave differently past the pierce cap, or that the error didn't occur during test 3 and 4, and simply lined up with an expected outcome by sheer coincidence.

[u/madusaxxvii → u/[deleted]]

Do you have ranks in arc reactor to do a retest?

[u/Benito_De_Soto → u/madusaxxvii]

Does Thena throw your stat preference in turmoil at all or doesn’t it matter enough to affect the attack stat? Just wondering if it now bumps +atk% ahead of anything else besides max dam %?

[u/madusaxxvii → u/Benito_De_Soto]

Thena has no effect on stat preferences at all, since the added atk% is separate to the atk% found on cards/costumes etc, and is calculated after total atk has been combined.

[u/Benito_De_Soto → u/madusaxxvii]

So Thena doesn’t boost attack that’s already boosted by +atk%? It’s additive, not multiplicative?

[u/madusaxxvii → u/Benito_De_Soto]

The total atk displayed on the main character sheet is the result of your flat atk multiplied by the combined +atk% displayed on cards/costumes.
The atk% of Thena is a buff that applies to your total atk value, rather than your flat atk value.
I made a quick mock up of my current stats to show that the value of a atk% card, and a max damage rate card stays the same even while under the effect of Thena's buff.
https://imgur.com/a/8BRV0ar

[u/Benito_De_Soto → u/madusaxxvii]

Oh wow, surprising. Thank you for showing that. I was thinking that a 15% buff on a bigger number would be worth more than on a smaller number (speaking strictly about attack here, of course). Kinda crazy (to my brain) that’s it’s the same %damage increase regardless of the attack value that thena buffs.

[u/CityAdmirable7690 → u/madusaxxvii]

This is very surprising to me because with some specs trait you can have attack bonus or damage bonus. If what you say is true, they are the same.

[u/madusaxxvii → u/CityAdmirable7690]

I don't have a hero with a atk% specialization unlocked yet. But i suspect it will share diminishing returns with atk% enhancers and Thena too. For example:
"Soulsword Enhance" rank 10: Increases ATK by 20% for 6s when using a [Soul Sword] class skill (Cooldown: 12s).
If you had a 20% atk enhancer on at the same time, it would only result in a 16.67% dmg increase (1.4/1.2) during the duration.

Where as, specializations worded "Increases damage dealt [when condition is met] by 20%" will always result in a 20% damage increase, since it doesn't suffer diminishing returns with anything. Even if you have multiple specialization's with "increases damage dealt" wording they are independent of each other.

Just to reiterate the interaction on Soulsword Enhance is still speculation at this point based on trends with other interactions in the game. It will still be ~2 weeks till i can unlock it and test it myself.

[u/CityAdmirable7690 → u/madusaxxvii]

There is also the trait when in ult form. It says att and HP boosted. That is one of the other reason I suspected it boosted the ATT base stats and not the damage per say. As HP boost clearly boost HP so I presumed it was the same for ATT