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[xenoargh]

You can download a test of the rebalanced weapons resulting from the first efforts to understand / improve balance here.


I saw the discussion about using math to do some balancing work and analysis.  I think we need a thread for these tools.

Here's my first contribution; a Google Sheet with formulas that shows how efficient weapons are per OP, providing us with a tool for balancing weapons fairly accurately.

This Google Sheet (and the relevant formulae) might be of some interest.

Essentially, for weapons, it calculates hit percentages using the Circular Error of Probability, calculates DPS/Flux (with some assumptions), Time To Kill (ditto) and then uses that to create an analysis of balance.

This doesn't cover all possible squirrel cases and it certainly won't cover unusual balance due to scripting, etc., but at 1.0 balance most weapons feel pretty well-balanced vs. each other, and it covers the basic cases, including Beams, and it was very helpful to run this analysis to find the problem cases and fix them (once I was pretty sure it wasn't producing GIGO, heh).  

The weapons that aren't hovering around 1.0 are PD that have unusually-short ranges for their size class, just in case you're wondering.  If you really feel Vulcans should be fairly-balanced with everything else, feel free to copy the Sheet and work from there.

[EDIT]I've just realized that the formulas aren't visible in this export version.  I've corrected that, so that others can look at the math used.  Wait a few minutes and the GScript for that portion of the Sheet will be visible to copy-paste into your own work.*[/EDIT]

*Feel free to attempt to improve the formulas as well; I know I ignored a few things that I felt weren't terribly important, like how the CEP is influenced by turret speeds and bullet velocities; this matters somewhat when we get into slow projectiles or very slow turret speeds, but it's probably acceptable to simply add these things in via fudge-factors (i.e., if projectile speed <> range, then adjust accuracy via ratio, if turret rotations <> some default then adjust accuracy via ratio, etc.  I just felt these things rarely mattered in Vanilla, where these variables are largely kept in pretty narrow ranges.

[xenoargh]

Here's a second version that's set up so that people can mess with it.

[EDIT]Better now.[/EDIT]

[xenoargh]

After playtesting with my results, things were good, except for High Explosive weapon types; I under-valued its damage vs. Shields vs. its faster penetration of Armor.  I've corrected that and the results look pretty good; weapons feel roughly equal per OP, in terms of effectiveness.

A few things were pretty obvious from my playtesting of the stuff that's in this build:

1.  My thoughts about the weapons that have always been over-powered (Light Needlers, for example) or under-powered (Arbalest) were pretty well borne out by the math.  Light Needlers have have always been over-powered because of their sheer DPS/flux and range, Arbalest suffers from both issues.  Since I used exactly the same math to arrive at reasonable justification of the weapons that were fairly balanced, like Light Autocannons, this feels like a valid result.

2.  Beams were pretty universally under-powered, even taking into account that they don't miss.  The equation deals with projectile weapons that pretty much don't miss (short of user error) as well, so that's not a valid concern.

[Tartiflette]

You cannot compare beams to ballistic weapon because of soft flux. They are useless individually, but the instant you point enough of them to overcome the target's dissipation they are an automatic YOU DIE button. They just are the best stacking weapon available in the game.

[xenoargh]

Of course we can; they're doing damage just like anything else does.  There's nothing magic about DPS / time.  

What you're talking about is totally applicable to anything that concentrates enough fire, basically; it's the same principles behind Harpoon Swarms of Doom, what happens when you have 3 Enforcers with Light Needlers focus-firing on a Cruiser, etc., etc.

So, yes, it's the same thing in the end, and yes, Soft Flux is a big penalty, as is the Beam penalty vs. Armor.  That's just math; it doesn't care that it looks different because of the curving nature of "not doing enough to counteract Dissipation but is a Flux trade" and "is way more than Dissipation and will push into Overload shortly".  This is one of the many conceptual assumptions people are making that isn't justified mathematically.

There literally aren't differences between a perfect-accuracy weapon and a Beam, except that one of these does Soft Flux, which means that effective DPS against Shields is considerably worse, because it's not draining the total Flux pool through Hard Flux mechanics.

[Tartiflette]

I'm not saying you cannot compare them between themselves, but you can't really compare them to ballistic since those are opposed by armor and flux capacity x shield efficiency, while beam are opposed by armor and flux dissipation x shield efficiency (plus somewhat capacity against burst beams). They aren't balanced against the same mechanic.

[xenoargh]

No, you're really misunderstanding how this works.

A Beam does damage, per frame.  

So, at 75 DPS, a Tac Laser does:

75/60 damage, or 1.25 Energy damage / frame.

So, you're trading 1.25 Flux for 1.25 Flux, because Vanilla balance is 1:1.

But, it's Soft Flux.  So, every frame, that damage is being negated if the hit is on Shields, if Soft Flux expenditure is less than supply.  

So, for example, a ship with 300 Dissipation is dissipating 5 Flux / Second; one Tac Laser can shoot it forever and nothing changes, other than a Soft Flux "load" on the ship, preventing it from having the 50 no-Flux speed bonus (unless Captain bonus, but w/e).  To Overload this ship, ever, you need 4 Tac Lasers to hit it constantly, basically.

Shooting armor, the Beam's effected by dpsToHitStrengthMult, and therefore inflicts 0.625 damage / frame.

There's nothing magical about any of this.  It's just damage, but the Soft Flux effect, since it doesn't gradually build up Hard Flux, is pretty important, because that means that, until there are more Beams hitting a target than Dissipation can handle, the target is invulnerable and has its entire Soft Flux pool available for counter-attacks.

Now, compare this to, say, the IR Pulse, which is about perfect, in terms of comparisons, because it's also trading Flux at 1:1.

Every hit from the IR Pulse does 50 damage on that frame, however.  And it's Hard Flux, which means the ship that's hit just lost 50 Flux from its Soft Flux pool until it Vents, (except for ships with Captains that have the Flux Modulation 10 perk, but let's leave that aside).  This is a huge difference in TTK vs. Shields, because there is no possibility of recovery short of Venting.

Every hit does 50 base damage to Armor, as well, not half-damage, which is a huge difference, because that means that it's doing more than 15% against lighter Armor values, whereas the Tac Laser isn't, generally.

In Alex's current schema, after we pointed out that Beams were really meh, to make up for all these shortcomings and be at rough parity, doing it by the buff / nerf guesswork that has largely been how the weapons have gotten balanced up until now... the Tac Laser gets twice as much range... which is the strongest single stat.

Now, my number for Beams does not include a detailed TTK model for either Soft Flux's effects nor for the Armor penalty, to be sure; it instead uses a fudge-factor, where it divides the DPS/Flux by 1.5.  

When I have some time, we'll do the detailed TTK, as the math for both is pretty straightforward if we start with some baseline assumption, but I think you'll see that Beams come out even worse than the above as a result.

They're not balanced, in short.  To balance Tac Lasers at 1:1, they either need even more range or a reduction in their OP price (or significantly more efficiency, in terms of DPS / Flux).  I made them a bit more efficient in my rebalance, and it didn't fundamentally break Beams or make them massively OP; it mainly just meant that ships using them weren't trading at 1:1 any more... which is actually not a terrible thing, because trading 1:1 for Soft Flux is hugely worse than trading 1:1 for Hard Flux (and that's still terrible, vs. using Kinetics, which is why Ballistics > Energy right now).

Now, is my fudge-factor wrong?  Maybe; it was for HE for sure.  I'll review when I have time to do the TTK for Armor / Soft Flux; that should also give me a better factor for HE / Kinetic balance, where I'm still using a fudge-factor and it may still be wrong.  

I'm fairly confident Beams come out even weaker, though; playtesting appears to indicate they're still a little weak (but not terrible, like they were before their ranges went up... other than the ones whose ranges didn't go up, like the PD).

Long and short, though; the objective of this project is to arrive at a mathematical system that's sensible.  It can't be perfect, due to modded weapons having bizarre effects, but it can at least give us a starting place, like, "this has OP coded effect, so nerf efficiency to 0.5 plz", etc. 

Just try and be open-minded about this; I'm not here to inflict my personal tastes on folks with this and a playthrough with the current numbers feels pretty similar to Vanilla, except that there are fewer "junk" weapons.  The biggest noticeable change is that Energy weapons finally feel pretty good... and Large weapons no longer feel terribly inefficient.

I know it's not 100% comprehensive yet, but the objective is to finally have a decent measuring-stick for balance, not just a bunch of speculative nonsense that gets nowhere and buff-nerf cycles that are largely unproductive because it's poorly understood what XYZ changes actually do in relation to one another. 

But we can't do that if we're going to have Sacred Cows everywhere or presume things that have, in fact, changed multiple times, are somehow perfect right now.  They aren't; there's tons of junky balance in the weapons nobody uses because they're junk, for example, which has just robbed the game of diversity rather than adding anything.

[Thaago]

I find this interesting, but am unable to decipher the excel formula for the hit probability (based on circular error probability, as you mentioned). Would you mind writing it out in formula form and posting? Some of the values it has are... odd. Just looking at the kinetics, it gives Gauss and HVD's a 100% chance of hitting, Heavy autocannons 25%, and needlers 45%. Those number are not consistent with my experiences.

Hit probabilities are also heavily dependent on what target you are firing at and at what range: I would not be at all surprised to see the weapon Q factor being a complex function of target profile, speed, and range that changes based on shot speed and firing pattern/recoil. Guns like the HVD/Gauss would have a very steep dropoff in effectiveness as beyond a certain range the AI will dodge them a high % of the time, but below that range will be hit.

Re Beams:
Its all about hit probabilities. Beams are 100% effective out to their stated range, no matter the target. For the lovely Beamagon, that is going to be 2400. Muahahaha. But seriously, in small ship fights a beam will hit way farther away than a gun. Maybe when capitals slug it out hit probabilities are very high out to max range, but for destroyers/frigates, beams are the longest range guns.

Also, more than any other weapon the effectiveness of beams depends on what the target is doing. If the target is not firing, they must overcome its flux dissipation. If the target is firing at its own dissipation (a common way to build ships) then the beams increase the target's flux, effectively dealing damage. They make the perfect kiting weapon, but only if the target is engaging something else at the same time.

So... I'm with Tartiflette - it is rather disingenuous to compare beams straight up to other weapons. Yes, DPS/sec is easy to model, but everything else about them is not.

[Tartiflette]

That doesn't change my point: projectile weapons deals hard flux on shield, dissipation is inconsequential to them but capacity and shield efficiency are. A beam deals soft flux against shields, flux dissipation is the most important factor when defending against beams. You can compare every projectile weapons because they work the same way against every ship, but you cannot individually compare them to beams point for point with a single formula because the relevant stats they act upon are different for both weapons, and they have different balancing paradigm. In short: individual beams are weak by design because mass use of beams is unstoppable.

[xenoargh]

I think you massively over-rate the effects of Dissipation drain.  Let's do some math:

4 IR Pulses vs. a ship with 300 Dissipation and 3000 Capacity:  TTK for the Shields is 3000 / 50 * 4; it's 15 seconds.  Meanwhile, the ship's Soft Flux base shrinks 200 with every hit.

4 Tac Lasers, same stats:  TTK is 3000 seconds.  No drain in Soft Flux base (OK, it's 1 per second, but still... basically, zero).

This is why they needed 1000 range to be even roughly in the ballpark; it was the only practical way to get enough of them draining Soft Flux that they could justify their existence and be "support".

I can build a mod that demonstrates this pretty clearly, if that's what you need to really intuitively get what's going on here, but basically, this is just the mathematical truth behind the balance concepts here.  It's why Beams needed a buff, and are still underpowered for ships that cannot expect to use them from a distance enemies can't reply from (Eagles with ITU / Advanced Optics lurking behind a Frigate screen, for example, vs. Frigates) or can always expect to keep out of the enemy's range bands (the Wolf Pack phenomenon).

I find this interesting, but am unable to decipher the excel formula for the hit probability (based on circular error probability, as you mentioned). Would you mind writing it out in formula form and posting? Some of the values it has are... odd. Just looking at the kinetics, it gives Gauss and HVD's a 100% chance of hitting, Heavy autocannons 25%, and needlers 45%. Those number are not consistent with my experiences.

Well, there is certainly some fudging necessary here, because we cannot address every case.

So the hit probability is a perfect case, where it's an AI aiming perfectly at an object with a diameter of 32 pixels.  Why 32?  Because that's a little more than half of the average radius of Frigates, and Frigates are often able to maneuver about half their diameters in a new direction if they dodge.

To get a perfect CEP value, we'll need to factor in turret speeds and true time-to-target.  This explains some of the disparities (and in my examples, explains why I made range / shot-speed 1:1 pretty universally, so that it wouldn't be a major factor).  Turret speeds don't effect CEP directly, but they do effect the true time-to-aim variable, which (essentially) reduces the rate of fire (or can prevent the weapon from ever having a valid firing solution, if the target's moving fast enough- see aiming Hellbores at fast Frigates, for example).

On the Needlers, this is at the maximum range, where a surprising number of shots will actually miss, if we set up a 32-pixel-sized test target, etc., which we don't need to do, because Math.  

Experienced players often get a little closer than that when firing, and we do that sub-consciously.  Heavy ACs miss quite frequently at maximum ranges.  Gauss has perfect accuracy, but people firing it (unlike a perfect AI) tend to have problems with the brief pause between clicking "fire" and the actual firing event.  And don't forget that, unless you're playing modded SS, you don't have a leading-pip; you're doing that in your head.

[Thaago]

So is the calculation based entirely on the shot spread at maximum range? Because while that is important, it is far less important than projectile speed and target speed/profile. HVD's do not hit 100% of the time, despite their accuracy.

[Edit] Oh, I see, you are using a 32 pixel target as that is what you are assuming a frigate can't get out of the way. Eh? I would need to test. But I know that HVD's will miss most of the time at max range against most frigates.

Regarding beams... I honestly think you are heavily biased against them, Xenoargh. From what I've seen, your calculations ignore everything that beams are good at.

I think you massively over-rate the effects of Dissipation drain.  Let's do some math:

4 IR Pulses vs. a ship with 300 Dissipation and 3000 Capacity:  TTK for the Shields is 3000 / 50 * 4; it's 15 seconds.  Meanwhile, the ship's Soft Flux base shrinks 200 with every hit.

4 Tac Lasers, same stats:  TTK is 3000 seconds.  No drain in Soft Flux base.

...

This example isn't right. Consider two cases:
1) Target ship is not firing.
Time to overwhelm shields = infinite. The flux buildup from 4 tacs matches 300 dissipation.
Analysis: insufficient beams are not effective at kiting a disengaged ship.

2) Target ship is firing at its dissipation (the usual way ships are built, roughly).
Time to overwhelm shields = 10 seconds.
Analysis: against an engaged ship, beams quickly overwhelm the target at beyond retaliation range with perfect accuracy.


To reiterate what I said before: you cannot calculate the effectiveness of beams in vacuum, like you can other weapons. Their effectiveness depends on what the target is doing.

[xenoargh]

Anyhow, I'll set up a test mod tonight where we can just watch these things happen in real-time.  I know it's hard to believe some of what I'm saying here without seeing it in-game, because the game's huge number of fuzz-factors makes it hard to sort things out.  

On this basic stuff, though, I'm quite confident that, while my fudge-factors might need tweaking here and there, I'm basically on the right track

Oh, and Thaago... give IR Pulse Lasers 1000 range.  Get back to me about how great Tac Lasers are.  

Your entire case is built around their range and accuracy... which is completely accounted for in my math.  What you're not accounting for is the effect of Hard Flux; a ship that's under Beam attack which is able to leave that attack is unscathed, vs. a ship that took the same damage from IR Pulse Lasers, which has a permanent Hard Flux problem until it Vents.

As for HVD vs. Frigates, I don't know whether that reflects your errors, AI errors, or that Frigates can exceed that fudge-factor often (after all, this doesn't reflect an AI Wolf using Phase Skimmer to avoid shots, etc.); it has 1000 shot-speed for 1000 range, so, in theory, it should be accurate.  But we can lower the size of the "frigate" a bit or declare that accuracy cannot exceed 95% by fiat or something; that would help weapons with "perfect" accuracy a little bit (but make the HVD's balance in Vanilla even more suspect, unfortunately).

[Tartiflette]

Again, you cannot compare them that way! Are 4 IR pulse better than 4 tac lasers in most cases?  Probably. But 20 Tac lasers are better than 20 IR pulse in nearly every cases because they have more range and they will overcome the dissipation of most ships before they can fire back. You cannot compare them one to one because they do not scale the same way because the mechanics are different. Saying a single beam is weak is stating the obvious, that's how they are supposed to work.

That would be like comparing Missiles and Projectiles weapons' ability to deal 100K damage! It's obvious individual missile racks can't do that because of limited ammo, but 20 of them together would reach that goal much faster than most stack of 20 projectile weapons.

[xenoargh]

You'll note that Missiles aren't even on the menu for this; comparing them requires a few different mechanics be considered; we're in total agreement on that

Anyhow, what I've said is much, much, much easier to simply show you with a mod built to demonstrate it clearly and without noise, obviously.  I'll get it done.

[Thaago]

Oh, and Thaago... give IR Pulse Lasers 1000 range.  Get back to me about how great Tac Lasers are. 

...

Yeah. I'm done with this one. I do not find your math valid or your arguments compelling.