A grenade by any other name...

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 well-calculated 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, CL-3, etc.), and a range-enhancing 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.

Damage-Increasing 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.

Reload-Increasing 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 * ((1-rank)/(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 swear-inducing 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 concussive-damage 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 damage-increasing 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.