The Scientific Method of BP
By: Brian Randich
a/k/a Brian_R
PAC2:
We’re Running Out of Names for Weapons
So, there’s a new
ballistic weapon out on the market, a new siege hull, a new special,
and our first tier 7 hull. Most of these new items don’t stray
too far from the norm. The new hull weighs enough that you’ll need
the most recent dock upgrade, the new weapon is better than the old
ones, and the special. . . wait. We have a lot of good siege
specials, between siege battery, siege targeting, other building
damage things (high velocity rounds, etc.), and reload specials.
Once we get a few basic assumptions out of the way, things get. . .
interesting. I’ll be doing some math on the PAC2 with a couple of
simple layouts, then go deep on the math of the new special, the mass
augmentation nexus. By the end, I will tell you to get the special
and to NOT get the special. It’s Schrodinger’s special. (Hey, I
used its/it’s properly!) But what we go through along the way will
reveal quite a bit about how one can truly maximize damage in
practice.
PAC2:
PAC Harder
The new cannon
works similar to the first PAC. Good damage, good reload, everything
looks fine. The big change is the probability of secondary fire, the
big blue blast that destroys a bunch of buildings (which I will call
the hadouken). People tend to avoid questions about the dps and
instead ask “How long will it take to get a hadouken?” While
people will say to wait two minutes for a guaranteed blast, I’d
rather not do that, and no one is sure if that will work with this
current gun yet. Besides, we can figure out about how long it would
take to get a hadouken with binomals!
You might remember
from a previous article, but binomals are a way to tell the chance of
a certain number of successes (x) happening in a certain number of
trials (n) with a given probability of success (p). We’ll use
another neat trick of probability here, and say that 100%  chance of
failure = chance of success. Here, failure means we won’t get any
hadoukens in one salvo. First, we can assume 8 guns per ship and a
full fleet for 40 guns. So, 40 trials (40 shots), a 0.8% chance of
success, and no successes. Next, we’ll try 35 trials for 7 guns
per ship, and 21 trials for 7 guns and 3 ships, which seems like the
most practical amount for raid one of the new cycle in January.
1(binompdf(40,0.008,0))=0.275,
which means a 27.5% chance to get a hadouken in any salvo.
1(binompdf(35,0.008,0))=0.245
(24.5%)
1(binompdf(21,0.008,0))=0.155
(15.5%)
Now,
take 100% and divide that by 27.5% (or 24.5% or 15.5%) to determine
the number of salvos you would need to get a hadouken on average.
That ends up being about 4 salvos for 40 and 35 shots, and 6 salvos
for 21 shots. If you start the clock on your first shot (one salvo
is used), multiply your reload time by 3 or 5 as appropriate to get
the time needed for a hadouken.
I NEED ALL THE GUNS!!!
While
I certainly would not try to some specific build advice before we
have seen any targets (we don’t know about how much ballistic vs.
radioactive damage you need, for example), there is one question that
came up. Autoloader 3 is heavy, and it’s not likely to have all 8
PAC2 cannons on the ship with all the other best specials, so here’s
the math for 7 guns with Autoloader 3 vs 8 guns with Autoloader 4:

7 guns and AL3

8 guns and AL4

Avg damage/shot after crits 
97363

111272

Reload bonus 
110%

66%

Reload time 
0.32

0.39

DPS 
306030

285671

MAN, This Special is Lackluster
Now for the actual target of my wellcalculated ire: the mass
augmentation nexus. With 10% ballistic critical chance, 100%
ballstic critical damage, and 40% splash, this looks good, right?
Not quite, when compared to the other specials you already have
(remember to check your Forsaken research tech for the best
autoloader). Now, here’s a few assumptions that I will use for the
remainder of this article, which I think are reasonable if you can
get all the new stuff right now (maybe not for raid one, but probably
for raids two and beyond):

Your ship is skull rank, and the player has R+D 30 for 12% critical chance

Your special is at r15 (get on that, you can get two done in a month)

Four specials are already used for speed system whatever, a turret defense special, a defensive special (LA3, CL3, etc.), and a rangeenhancing special (Cannon System 4, Nuclear Accelerator,etc.)
This leaves two specials for offense, and I’m holding the other
four constant, so I don’t have to worry about them now. I’ll be
focusing on specials that increase building and/or ballistic damage,
specials that increase ballistic reload, and other specials (where
the nexus will go). I’ll be listing each special, what it does,
and its effect on dps.
DamageIncreasing
Specials
Name 
Bonus 
DPS effect 
Siege
Targeting 4 (r15) 
165% damage 
x2.65 
Siege
Targeting 3 (r15) 
93% damage 
x1.93 
High Velocity
Rounds 
80+55=135%
damage 
x2.35 
Normally,
we can assume 100% damage. With these specials, your damage becomes
(100+ bonus damage)%. Take that, divide it by 100, and you get the
boost it gives to dps. (100+165=265. Then, 265/100 = 2.65) So,
Siege Targeting 4 at r15 multiplies your dps by 2.65, and so on down
the line.
ReloadIncreasing
Specials
Name 
Bonus 
DPS effect 
Autoloader 4 
66% reload 
x1.66 
Autoloader 3
(r15) 
136% reload 
x2.36 
Autoloader 2
(r15) 
93% reload 
x1.93 
Here, it’s
important to note that the Buccaneer has no ballistic reload bonus.
From the BP Professor’s rank formula (Base weapon reload *
((1rank)/(1+total reload bonus) = Reload) and holding the rank
constant, each of these specials increases the denominator. 100%
reload would take the bottom from 1 to 2, halving your reload and
thereby doubling your dps. (.75/1)/(.75/2.36) = 2.36, so Autoloader
3 at r15 multiplies your dps by 2.36.
Now, for the other
things people might put onto their hulls:
Name 
Bonus 
DPS effect 
Mass
Augmentation Nexus 
10% crit
chance/100% crit damage 
x1.29 
Countermeasure
Loaders 4 
25% reload 
x1.25 
Siege
Reloader 
75% damage +
10% reload 
x1.85 
The mass
augmentation nexus probably needs some explaining, so here’s
another table, with a simple 10,000 damage shot for easy math:

Normal 
With
special 
Damge 
10000

10000

Crit chance 
12%

22%

Crit damage 
200%

300%

Damage per
shot (on average) 
11200

14400

Difference


1.29

With critical hits
in games, you deal increased damage when you land a critical hit, and
normal damage when you don’t. Normally, you crit 12% of the time,
and don’t the other 88% of the time. When you crit, your damage is
doubled. (12% of the time * double damage + 88% of the time * normal
damage = 12% * 2 + 88% * 1 = 112% damage on average * 10,000 = 11,200
damage per shot on average) Run that calculation on both sides,
divide 14,400 by 11,200, and you get dps multiplied by 1.29 for the
new special. Now that we have those three set up, let me order them
all, from best to worst, based on how much they increase dps, with
the new special in red.
Name 
Bonus 
DPS effect 
Siege
Targeting 4 (r15) 
165% damage 
x2.65 
Autoloader 3
(r15) 
136% reload 
x2.36 
High Velocity
Rounds 
80+55=135%
damage 
x2.35 
Siege
Targeting 3 (r15) 
93% damage 
x1.93 
Autoloader 2
(r15) 
93% reload 
x1.93 
Siege
Reloader 
75% damage +
10% reload 
x1.85 
Autoloader 4 
66% reload 
x1.66 
Mass
Augmentation Nexus 
10% crit
chance/100% crit damage 
x1.29 
Countermeasure
Loaders 4 
25% reload 
x1.25 
Second from the
bottom. For 15 million points! Your Forsaken researchable tech at
the start of the game is better than this! Even if you don’t have
a particular item or have weight issues, you can still do better than
the Mass Augmentation Nexus. Don’t get the new special, it’s
trash, end of story.
“But the new
special has splash! You can hit more turrets!”
Well done, and very
observant. Sadly, probably not enough. Let’s take this against
Autoloader 3 at r15, which you clearly all have, and can get it to
r15 in time even if you wait a week. Let’s assume you can hit one
more turret with this than normal, doubling your damage output. Two
birds, one stone. However, there is a decrease in damage out from
the center of the splash radius. It’s why there’s sometimes that
swearinducing turret in the back of a turret cluster in the FM
target that barely clings to life after you mortared the rest of them
to death. We don’t know how low that goes, but we can calculate
what it would need to be to matter. We will assume this is on the
edge of the splash range, as the 40%*6 = 2.4 extra splash radius
should matter. Take the 1.29x dps from the new special and assume a
direct it and an indirect hit for less damage and see how that
compares to the 2.36x dps from Autoloader 3. Since we don’t know
the percentage damage dropoff at the edge of the splash range, we’ll
call it Z. Add 1.29x dps for the direct hit and 1.29x dps times Z
and set it equal to 2.36x dps.
(1.29 + (1.29*Z)) =
2.36, Z = 0.83, so minimum splash damage would need to be 83% for
this to matter. We don’t know this number, but I don’t think
that’s the case. With two more hits, this number would have to be
at least 41%, which seems more likely.
As promised, I’m
going to tell you to get the new special. Why, when it was just
mathematically proven how bad it was? Kix tend to have a history of
increasing the power of certain things, especially new weapons and
specials, when they just aren’t as good as older tech. Remember
the Monolith? I do! If you want splash, think about what you’d
put on your mortars and go from there, those specials tend to have
much more splash.
So, if it’s so
bad, why does it exist? I’m going to go with laziness. This type
of special worked for torpedoes (Sealed Fire Charge) and depth
charges (PBX Payload) because there was only one offensive special
that was any good. The rest wouldn’t stack, and you’d be so much
better off with a defensive special rather than the small damage
increase from concussive upgrade that it wouldn’t be worth the
damage. The designers knew it worked in the past, but didn’t
understand why. One concussivedamage increasing special locked you
out of the rest, and there wasn’t any one that gave us extra ship
damage. Our builds often had a spare slot, but the only other option
we had was the PBX Payload or similar for more damage. Since our
specials for siege are very focused, very different (most only
increase one stat), and very powerful (they do their one job very
well), there’s enough room for all the best damageincreasing
specials to join in. You get to have speed, good defense, good
range, AND good damage, all at once! As shown above, nearly every
other special is better than this. I wonder what they’ll learn
from this.
Thanks for your hard work Brian
ReplyDeleteNice article but with 1 gaping flaw, when talking about Splash it only takes into account the 40% buff from the MAN (I assume) But the Bucc has a builtin buff of 150% as well, personally I'm looking at +225% so that tiny +2.4 splash radius becomes a healthy +13.5
ReplyDeleteAlso doesn't take into account the monster splash of 40 on overcharge. so +225% is now 90, what's that 4.5 tiles in all directions from the point of impact.
DeleteOP is wrong, because the 150% splash from the hull and any other special (Nuke Accel 2, etc.) stay there no matter what. Go mock up a build and put MAN on, then take it off, only 40% changes, only 40% matters. 6 * (225% with  185% without) = 2.4, which is the difference of the MAN.
DeleteNot sure how splash does/does not/should/should not work with secondary fire, but that 40% splash now becomes 16, but I don't like relying on secondary, as it's what a minority of the shots do.
You forgot to factor Drum Reloaders as an option
ReplyDeleteGood point! Went back, looked, saw r15 is 75% reload and 37% damage, add it up like siege reloader and you get x2.12. Not bad (fourth place), but there are better damage and reload options that are lighter (HVR), though it is a good option if you don't have the better stuff (but you should have HVR and autoloaders 3).
Delete