Tuesday, January 2, 2018

So you wanted to PvP Math, Huh?

PvP Mathing with Two Doors

by: Brian Randich
a/k/a Brian_R

I’ve already done an article about calculating DPS (damage per second), but that was made for PVE.  People have been asking for one about PVP, as the two systems function very differently.  They are so far separated that you can’t take conqueror hulls into PVE targets (except VXP weekend and very particular targets in TLC, remember to read the popup telling you what fleet to use in a TLC).  Even in those VXP targets, your conqueror fleets with 100,000+ armor will die in one shot.  There is a reason for this, and it follows in caps for emphasis:  ANY DAMAGE-TYPE-SPECIFIC DEFLECTION HAS NO EFFECT IN PVE.  STOP PUTTING RADIOACTIVE PLATES ON YOUR SIEGE HULLS, THEY ARE USELESS.  

So, I have 110,000 ballistic deflection on my King’s Writ.  What does that mean?  It means that any single instance of ballistic damage is reduced by 110,000.  This effect is applied last, after things such as splash damage reduction and turret defense.

Splash damage reduction applies first.  It reduces any splash damage.  Any weapon fired that has a splash statistic is considered splash damage.  We think of this as mortars or depth charges doing splash damage, but some cannons also do that, and missiles with a Proto-Nemesis.  This is important to consider when building to defeat a certain conqueror.  Sometimes, “smart-fire” weapons with no splash would do better than “dumb-fire” weapons with splash, even if the deflection is higher against the smart-fire weapon type.  This is pretty simple to figure out. 

Initial damage * (1-splash damage reduction %) = damage that carries through

In addition to this, splash damage decays the further the target is away from the center of the blast.  This is frequently seen in the FM, where turrets far away from the target survive an extra salvo.  It’s important to take into account the projectile speed of your splash-based turrets, as well as the turret’s splash and the attacker’s speed.  Too slow or too little splash and your shot may do far less damage than anticipated or miss entirely.

Turret defense applies next.  This is where you cackle manically if your attacker failed to put siege battery, resonance capacitor, etc. on their hull.  The attacker will almost always have 50% turret defense, further reducing your damage by half.  The omega weapons on an outpost are considered turrets, even though they are not buffed by fire support and the like that affect turrets. 

Then, deflection applies.  Whatever damage is left has the deflection amount on the hull subtracted from it.  If there’s 150,000 ballistic damage after splash damage reduction and turret defense, and the hull has 110,000 ballistic deflection, the hull takes 40,000 damage.

Adding all of that together, we get the following:

(Damage per salvo [note the type] * (1-splash damage reduction %) * 50% turret defense) – damage type’s deflection) = Damage to hull’s armor

The simple answer to people asking “how do I kill X hull” is usually to find whatever they’re weakest to using the above formula (although you usually won’t have to, their deflections make it clear) and make the strongest turret of that type that you can.  The attacker can have armor for nearly any damage-specific-type deflection and/or splash damage reduction, so keep that in mind if your super-awesome turret doesn’t melt the attacker like you thought it would.  People will try to put armor on to cover a hull’s weaknesses, and certain hulls can give boosts to certain deflections.  The Sloth is a prime example, giving concussive deflection to any other conqueror hull in the fleet, which is one reason why two King’s Writs and 3 Sloths (often one of these being the Sloth flagship) are popular:  the Sloth helps cover the Writ’s weakness of concussive deflection.

When attacking a conqueror hull, the most important number is damage per salvo.  Take the total damage number on the weapon and divide it by the salvo number to get damage per salvo.  For example, the new chaos chaingun has 150,000 damage of several types, but a salvo of 15, so each salvo only deals 150,000/15 = 10,000 damage before adding any bonuses.  You can figure out the damage per salvo and then add bonuses or do it the other way around.

Turrets, however, are very different.  They work like nothing else in the game does, and I had Renato explain it to me.  Bonuses to turret damage work in layers, even if they increase the same stat, as opposed to ships, who gather things from the same stat (ballistic damage, etc.) all together and have one bonus to apply.  First, turret damage is boosted by the specials.  Then, that total is boosted by transformers.  Then, that total is boosted by your faction.  Then, that total is boosted by fire support and other tactical mods.  Because I like equations, I’ll put a series of them below, with D0 being the starting damage, and D4 being the final damage that needs to be divided by salvos.

D0 * (1+% from specials) = D1
D1 * (1+% from transformers) = D2
D2 * (1+% from faction) = D3
D3 * (1+% from fire support) = D4

Now, let’s take all this and use it in an example.  How strong would an Epic Cataclysm Mortar (Epic Cat Mort) have to be in order to break the deflection of a King’s Writ?  We will assume there is no armor or additional splash damage reduction on the Writ (So 60% splash damage reduction, 50% turret defense, and 110,000 explosive deflection).  We will also assume an r15 Epic Cat Mort (37,146 damage and 3 salvos), 75% explosive damage from specials (Fuel Tank 01-X), a standard A-T Transformer (35% transformer), Draconian faction (20% from faction), with an unknown at the last equation being the fire support %, but we’ll be able to solve for that.

From the Writ’s point of view, a shot has to overcome 110,000 deflection after getting through 60% splash damage reduction followed by 50% turret defense.  “Breaking the deflection” will be defined as getting a damage high enough so that the end result after all the defenses is greater than 0. 

From earlier:

(Damage per salvo [note the type] * (1-splash damage reduction %) * 50% turret defense) – damage type’s deflection) = Damage to hull’s armor

Filling in what we know and putting in the favorite variable-representing-letter of X, we get:
(X * (1-60%) * (50%)) – 110,000 = 0

A bit of multiplication and algebra leads to needing 550,000 damage per salvo to break it.  That sounds like a lot, and it is.  Let’s set our D4 to 550,000, add in everything from the assumptions, and see what comes out.

D0 = 37,146/3 = 12,382
12,382 * (1+75%) = 21,669
21,669 * (1+35%) = 29,253
29,253 * (1+20%) = 35,104
35,104 * (1+X%) = 550,000

A bit more algebra gives us a fire support percent needed of 1,466%, which is clearly impossible.  There is a minimum damage that the turret will apply, so that’s good news, at least.  Even if you can’t stop a particular hull, maximizing damage is still a good idea, as the turret that fails against one hull could perform fantastically against another.  Even with the above numbers, people are claiming that King’s Writs will die to a well-placed Epic Cat Mort setup.  How is this possible?  IT IS RUMORED that critical hits ignore a target’s deflection.  At that point, your damage would merely be reduced by 80%, and considering you would deal at least 70,000 damage in the above scenario (remember, your crits deal double damage), you’d certainly hurt the attacker.  Also, critical hits could potentially have a higher minimum damage value than regular hits.  A while back, it was rumored that minimum damage was based on a percentage of the deflection of the ship being hit, so a higher deflection actually meant more minimum damage taken.  No one is really sure at this point, but with Bounty 5 going on now and some of the new hulls having over 400,000 explosive deflection, we might have a clearer picture of what’s going on, even if we don’t have all the numbers. 

While PVP math is simpler than PVE math due to taking it one step at a time and (mostly) clear numbers to work with, PVE math’s advantage is that the game gives you all the tools to solve it, as long as you look up some numbers.  I haven’t found anything on the game or in the forums that explains how the turret damage calculation works, and the equations above don’t make logical sense, but I trust Ren over Kixeye after mathematically proving how bad Kixeye are at their own math. 

Hopefully this helps when building certain turrets, but I don’t think this article changes much of the prevailing wisdom when it comes to turrets specifically designed and placed in the center to do damage, which is damage above all else.  But now that you have more knowledge, so go crush your enemies, see them driven before you, and hear the lamentations of their women.


  1. Thanks, I'm gonna read that a couple of times. Maybe I should have paid more attention in math class. LOL. Good work guys.

  2. Lol Mike Morfino. Ty George.

  3. wont be long and BP will be gone. Cutting their own throat

  4. Does not converge. According to your assumptions, the damage should be applied at any critical hit of any turret, which is clearly not observed. For example, blunderbuss does not cause any damage. Personal tests and tests of my friends have established that the epic cat begins to inflict damage to the king only from about 240% of the support. If the percentage of support is less, the king is not damaged at all.
    I agree with you - Kixeye has a very original mathematics (I suspect - very much depends on the substances that they smoke during the writing of the code), but in the case of PvP it works somehow differently, not the way you described.

  5. You math is a bit off, but it is close. Don't trust the in game info, you have to test everything.