Tuesday, January 6, 2015

Plate Armor, Minimum Damage, and Half Damage


In the last article, I went after the "S" part of DPS (damage per second). In this article, I'm going to go after the D.

For the information in this thread, I'm going to mostly refer to Kixeye forum posts.  Organizing & reproducing the data here just gets a bit ugly.  I'll try to build up information so that it makes sense as I go through this article.

The key testing thread was put together by forum user Hwasung here:  https://www.kixeye.com/forum/discussion/519525/p1

Thankfully, the first entry has been kept up to date with answers.

HALF DAMAGE
I find this a weird topic.... apparently from the beginning of the game, weapons have done half of their listed damage.  Some years ago, Kixeye tried to fix this by cutting the listed damage on each weapon's blueprint in half.  Players lost their minds.  Kixeye put it back.  Weapons do half their listed damage.

I'm trying to find a solid reference of this whole story, but I can't.  Most long-time forum denizens just take this as fact.
One example is here: https://www.kixeye.com/forum/discussion/497633/
The Kixeye response in the testing thread I linked at the top of this article also makes reference to half damage.

Since we are used to seeing this, I have always done, and will continue to compute DPS based on the blueprint numbers.  But for those of you who have used the Survival Time Calculator & tried to translate it into reality... it was wrong... by at least that factor of 2.

ORDER OF REDUCTION/RESISTANCE FROM PLATE ARMORS
This was consistently a point of confusion among players, but I kept going back to a FAQ on the Kixeye forums:

Original Plate FAQ from forum post: https://www.kixeye.com/forum/discussion/417458
Which gets applied first: Resistance or Reduction?
Resistances are calculated first, then Reduction. So if you have 50% Resistance and 20 Reduction, you will reduce 250 incoming damage to 105 ((250 * 50%) – 20).

And then there was...

Newer Kixeye FAQ: https://helpcenter.kixeye.com/hc/en-us/articles/202084568-How-does-Forsaken-Plate-Armor-work-

Forsaken Plate Armor flatly reduces damage from the corresponding damage type per projectile. This damage reduction bonus occurs before any %-based damage reduction bonuses are applied. Each projectile in a salvo will be reduced by that amount. 

So that says reduction, then resistance... which is the opposite of what was originally published.  To re-run the case from the original forum FAQ, 250 incoming damage with 50% resistance and 20 reduction would not result in 105 damage, but instead would result in (250 - 20) * 50% = 115 damage.

The testing thread uses the information as originally posted in the forums - % Resistances then Plate Reduction.  With the modified plate reduction (as shown below & confirmed by Kix), all the data hangs together & makes sense.

AMOUNT OF PLATE REDUCTION
We have an actual post from Kixeye in the testing thread:
https://www.kixeye.com/forum/discussion/519525


From the post:
Here are the actual damage reductions being given by the Compound Plate armors:

Armor                            Ballistic Reduction    Penetrative Reduction    Explosive Reduction
Compound Plate II:               1.188234                      2.07                          2.667126
Compound Plate III:              1.675836                      2.92                          3.761604
Compound Plate IV:               2.163438                      3.77                          4.856082

x2 for the in game display value:

Armor                            Ballistic Reduction    Penetrative Reduction    Explosive Reduction
Compound Plate II:               2.376468                      4.14                          5.334252
Compound Plate III:              3.351672                      5.84                          7.523208
Compound Plate IV:               4.326876                      7.54                          9.712164

It looks as if the client is flooring the values before multiplying them by two to create the display values you see in the game right now. This has the potential in the case of these rather small values, where a difference of one has a large impact, to result in a fairly inaccurate displayed stat.

So to summarize for Compound Plate 4 (in units of weapon damage):
Displayed ReductionActual Reduction
CP4 Ballistic-4-4.33
CP4 Penetrative-6-7.54
CP4 Explosive-8-9.71

This also applies to the weapon specific plates, but those values were not made available.  Based on this information - those displayed values could also be off by 1 - 2 damage points per plate, which could add up even more as you stack plates.

MINIMUM DAMAGE:
The plate armor can never decrease the damage done to zero - Kixeye implemented a minimum damage per shot, which they chose not to share with us.  But bp-information pulled some data:  

http://bp-information.blogspot.com/2014/11/hailstorm-raid-prelim-info.html
(see the comments below the link)

Pass Through Ballistic: 5.89
Pass Through Penetrative: 7.31
Pass Through Explosive: 9:01


The kicker - those numbers apply AFTER half damage (described above) - so those numbers are related to armor points, not damage points.  The other weird thing... if there is no plate armor, then the minimum damage values do not apply.  This was all confirmed in the testing thread shown at the top of this article.

DESCRIPTION OF THE TESTING:

Testing was done by forum user Hwasung, and documented in this thread: https://www.kixeye.com/forum/discussion/519525

The following weapons were used:
- Cutlass 1: 92 damage
- Cutlass 4:  668 damage
- Hornet UAVs: 6 x 66 damage

The following defensive ships were used for various cases:
- 0% penetrative resistance
- 50% penetrative resistance 
- 54% penetrative resistance
- 94.4% penetrative resistance (Savage Kodiak was involved)
- 0% penetrative resistance, 1 x Compound Plate 4 (-6 penetrative reduction) 
- 0% penetrative resistance, 2 x Compound Plate 4 (-6 x 2 penetrative reduction) 
- 50% penetrative resistance, 2 x Compound Plate 4 (-6 x 2 penetrative reduction) 
- 45% penetrative resistance, -67 penetrative reduction

The following damage model was confirmed (by damage type):

With Plate:
Actual Damage per hit = 
MAX OF: [(Blueprint Damage*(1-% resist) - Blueprint Reduction)/2] OR [Minimum Damage]

No Plate:
Actual Damage per hit = 
Blueprint Damage*(1-% resist) / 2

Blueprint Damage: Weapon damage per hit, read from blueprint (divided by salvo if not 1)
% Resist: The total resistance of the target against the damage type.
Blueprint Reduction: Total plate protection against the damage type. Plate armor blueprint subject to errors as described above.
Minimum Damage: The minimum actual damage of the damage type that plate will allow to pass through, no matter how much reduction/resist is applied.

The weirdest effect of this damage model is that if you have a very high resistance, adding plate protection could result in higher damage taken because the minimum passthrough damage would kick in.

HORNET DEFENSE:

HORNETS! HORNETS!  (I don't know why that song is titled that... it's not about hornets.)

To wrap this up, I'm going to look at how to use resistance and plate to defend against Hornet UAV damage, to get a feel for how much plate is "enough".

Using displayed numbers - Hornets do 66 penetrative damage per strike, and the minimum penetrative plate passthrough is 14.62.  I also want to cover the cases where UAV damage is boosted, since many people use Atlas/Harlock Carriers and UAV Powercells to give up to 80% damage boost.


EDIT: I don't think I described this chart very well... this chart below shows how much plate reduction you can add and have it still be effective for varying damage amounts and for varying resistance amounts.  The bottom line shows the resistance percentage (for that damage amount and type) where any plate added will have the opposite effect on damage. 

No Damage Boost80% Damage boost
Hornet Damage per hit66.0118.8
Max reduction, 0% Resist-51.4-104.2
Max reduction, 20% Resist-38.2-80.4
Max reduction, 50% Resist-18.4-44.8
Max reduction, 80% Resist0.0-9.1
Resist % for no plate77.85%87.69%


With Compound 4 giving -7.5 (display) damage per plate, and Penetrative 3 giving -14 (or maybe up to -16), you can see that plate reductions may still have a place in your Hornet defense strategy until missile resistance gets near the point where it hits the min damage passthrough.  But if you go over the resistance threshold, then plate does no good at all, and may even hurt you.

EDIT: I don't think I described this chart very well... this chart below shows how much damage reduction you would get (when being hit by unboosted Hornets) from adding a piece of M armor (10% more missile resistance) versus adding a piece of Penetrative Plate 3.  Notice that you are always cutting the missile damage by another 10% when you add a piece of M armor.

Damage per Hit (DpH)DpH after adding another M ArmorDpH after adding another Pen Plate 3M armor BenefitPen Plate Benefit
0% Resist66.059.452.06.614.0
20% Resist52.847.538.85.314.0
50% Resist33.029.719.03.314.0
80% Resist13.211.914.61.3-1.4


CONCLUSION:
Damage calculation is a weird thing.  I used to dismiss "Kixeye Math" as "people just aren't good at math".  But this stuff is weird and non-intuitive to me.... and I'm good at math. 

Overall, the effect of truncating the decimal then doubling for display will make the plate armors MORE effective than the blueprint shows... unless you hit the minimum damage values, then plate isn't effective at all.  If deciding whether to add Plate or Defense armor, the plate helps more when your resistance is higher... until it doesn't.

Since it is ready, I'm going to release the update to the Survival Time Calculator.  It includes the changes to rank and reload damage, as well as the half damage incorporated into the survival time, and correct treatment of the pass-through minimums.  It also can be used to calculate DPS or DPS/hton of weapons against various defense types.  I think it's pretty cool, but it might be a little tricky to use.  I'm planning to put together a demonstration video... but it's going to have to wait.


Access the calculator at https://bpprofcalc.blogspot.com.  

If you've used it before, look for the new dropdown to select what it is calculating - DPS, DPS/hton, or Survival Time, and also look for the new spot to enter the rank bonus.  The cells needing protection are fairly well protected, but if you think you screw it up beyond help... just reload the page. 

I'm working on a new launcher comparison... all this stuff I'm learning has changed my evaluations of the launchers.