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## [Statistics] Analysing weapons balance with weapon values alone

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Saturday, May 23rd 2015, 2:01am

### [Statistics] Analysing weapons balance with weapon values alone

Disclaimer: This is not meant to be 100% serious analysis on weapon balance. More like a "could this work?" attempt so there are ton of assumptions that might be borderline valid! Also I originally wrote this at 2am so might be full of brainfarts.

Basic idea: For every pro weapon has it also has a con. Sum of pros and cons zero out each other = balanced. (Especially when comparing to weapons inside same class)

Assumptions:
• Weapon variables inside certain class (eg. assault rifles) follow normal distribution.

-> Combining these opens up possibility to calculate z-values for different variables of weapons per class and then sum them up to see if they indeed zero eacother out. If sum of z-products is >0 or generally above others then there's an indication of stronger weapon, and opposite if sum <0.

Problems:
1. Assumption of normal distribution. Weapons tend to have very discrete steps for damage, especially when comparing between weapon classes
2. "True effect" of a variable is usually very dependant with other variables. Eg. Damage output can be higher if RoF is high enough even with small damage values etc.
3. Some variables have more "true effect" then other variables. Eg. Initial speed rarely effects much compared to damage values.

(1) prevents us from really comparing weapons between different classes (eg. carbines vs snipers), which already is somewhat rational. For (2) we need to figure out more refined variables calculated from basic ones and for (3) we need to define good coefficients per variable to simulate the "true effectiviness". Thanks to z-values we don't have to worry about the scale of refined variables so that makes things bit easier.

I haven't done much thinking past this other than some rough ideas on what kind of refined variables we should have. For example damage values are calculated as a integral from distance 0m - 100m which counts in all the damage variables but is not the best way to do it as weapons usually are restricted to certain range, Spread values need to be squared as they are a radius of a circle, RoF needs to be counted in many of the variables (dmg, spread/recoil inc) and so worth.
Figuring out refined variables is somewhat easy but coefficients need more thinking as they can alter the result rather vividly. Also they most likely need per-class coefficients (moving spread > standing spread for SMGs while carbines prefer standing spread?). See following quick plots of same weapons with different coefficients and variables included (BFH secondary weapons):

### "plot2"

(G17 derps up as it has very high RoF in files but is semi-fire only). Plot1 is with dmg, spread, recoil and reloadval. Plot2 is with dmg, reloadval and firstshot_mul. Plot2 seems to agree more with general picture of what weapons are better in subjective opinions.
Way differents results for these two different "coefficient sets". Granted, other one was missing spread and recoil completely but it still is really based on those coefficients.

If I get interested enough in this I might even do quick online tool based on database on Symthic where people can put their own coefficients and variables and check these results themselves.
• 3VerstsNorth - Analysis of game mechanics in BF4 (tickrates, effects of tickrate, etc)
• InterimAegis - Weapon comparisons/scoring.
• leptis - Analysis of shotguns, recoil, recoil control and air drag.
• Veritable - Scoring of BF4/BF1 firearms in terms of usability, firing and other mechanics.
• pmax - Statistical analysis of BF4 players/games.
• Miffyli - Random statistical analysis of BF4 battlereports/players and kill-distances. (list is cluttered with other threads).
Sorry if your name wasn't on the list, I honestly can't recall all names : ( . Nudge me if you want to be included

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Saturday, May 23rd 2015, 3:10am

When I was compiling my "big list," I noticed that the assigned SIPS values have a very strong correlation with the assigned RoF values, especially for guns shooting the same "bullet."

To wit: BF4 Weapon charts (Damage, accuracy, etc.) | Symthic

FAMAS, 1000RPM, 0.13 SIPS
AEK / MTAR, 900RPM, 0.117 SIPS
ACW, 880RPM, 0.114 SIPS
F2K / M16 / M4, 800RPM, 0.111 SIPS

So on and so forth, continues to the bottom

AKU-12, 680RPM, 0.088 SIPS
AK-12 / G36C / Type-95 twins, 650RPM, 0.085 SIPS
SAR-21, 600RPM, 0.078 SIPS

I noticed that this causes slight issues when, thanks to 3VN's research, various RPMs actually function the same for a quite long burst time. So, if the damage output is actually the same thanks to the engine limitations, then the higher SIPS is actually not "nerfing" anything. It is purely detrimental, which is probably not something the devs intended.

Anyway, this is on a slight tangent but just something I noticed after spending way too much time at Multi-Comparison

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Saturday, May 23rd 2015, 4:44am

### Quoted from "Veritable"

I noticed that the assigned SIPS values have a very strong correlation with the assigned RoF values

You do realize that it's been known for a while now that SIPS is calculated based on

(ROF * projectile_type) / 7700

and now SDEC uses the same system as well.

### Quoted from "Rezal"

Please, it is obviously ROF*N/7700 for SIPS and ((770/(ROF*N))^2)*10.5 for SDEC, where N=1 for normal bullets, N=1.25 for heavier (RPK, UMP-45), N=1.33 for heavy and 0.9 for most PDWs (9mm, MPX, SR2), SIPS only though. Light PDWs are a bit weird so far. 0.889 for decrease, about 0.8 for increase.
Data Browser

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"Skill" may indeed be the most magical of words. Chant it well enough and any desire can be yours.

Are you a scrub?

### Quoted from "blahdy"

If it flies, it diesÂ.

Can't get a title

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: Dec 23rd 2013

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Saturday, May 23rd 2015, 5:44am

Why is there Hardline in this when talking about BF4 weapon balance?

### Quoted from "Miffyli"

(3) we need to define good coefficients per variable to simulate the "true effectiviness".

This has already been somewhat started in Veritable's All-Kit thread. From my own experience and talking to other people ranking different variables of usability, recoil comes out on top, with reload speed and bullet velocity following respectively. Also, people seem to value RoF and damage (i.e. DPS/TTK) a lot more than spread.
something something Model 8 bestgun

### Quoted from "Pastafarianism"

Next, wanna try adding a guy that you KNOW is bad, and just testing to see that? Example: PP-2000 (god I so wanna love this gun, and yet...)

### Quoted from "Pastafarianism"

Example: PP-2000 (god I so wanna love this gun, and yet...)

Yes, it comes in last so far, but that is mostly because I'm making it shoot at 100m ADS - Not Moving as one of the criteria. Even then, between 50-100m Not Moving, when you include Useability, it is only 1.37% worse than the MTAR-21. Within 50m then it even beats the A-91.

Have a look, vs. the A-91 Carbine:

Using it with Muzzle Brake and Compensator is a wash in terms of overall performance. Comp is SLIGHTLY more accurate, while MB is SLIGHTLY more easy to use. Their overall scores are basically tied, with MB just ahead. I guess either can be recommended.

### Quoted from "Pastafarianism"

But... You can't be counting for the fact that it takes 9 bullets to kill at "long" range... Don't you dare tell me my A-91 is worse than a 9 BTK 650 RPM mediocre PDW.

Also. Just go heavy barrel. The recoil is low enough.

### Quoted from "Zer0Cod3x"

Well, technically...

Comparing a PP2K with HB and an A-91 with comp and stubby (as you suggested in an earlier post), at 50m not moving, the A-91 is only better by 4 damage per hitrate. While at 75m and 100m, surprisingly the PP2K does better than the A-91 (I'm pretty damn surprised as well).

And 10m and 50m moving the PP2K also does more damage per hitrate than the A-91. At 25m the A-91 is only better by about half a bullet's damage as well.

In addition, the PP2K has a much larger mag size and substantially less recoil. And it looks hella awesome. So comparing the A-91 to a PDW is of some worth after all, as the PP2K is better (technically, not practically) than the A-91.

Mind blown.

### Quoted from "Pastafarianism"

I... I...

*cries in a corner*

### Quoted from "Veritable"

Zer0Cod3x explained it very well. If you look at the raw numbers right here on Symthic Comparison, you can see how that happened:

A-91 vs PP-2000 | BF4 Weapon Comparison | Symthic

A-91's "23%" RPM advantage only afforded it 1 extra round.

Velocities are wash.

V-Recoil are wash (and this is HBar on PP2k vs. A-91 without).

Hipfire and ADS - Moving are better on the PP2k, but it's a PDW and not the surprising part.

The surprising part is that, as equipped (and we see above that PP2k HBar has almost same V-Recoil as A-91 without HBar so why not?), the PDW performs better at 50 - 100m than a bloody Carbine. Why?

SIPS, 42% better on the PP2k.

And here is the most important part. ADS - Not Moving Spread, 0.35 vs. 0.2, 43% improvement.

Without HBar then of course the PP2k loses, which is why when I add all the attachments together for an Overall Ranking, it would slot below the A-91. Run HBar on it, though, then... I'm sorry

### Quoted from "Pastafarianism"

@Veritable
@Zer0Cod3x
I... I...
But...
Wha...
I AM HAVING AN EXISTENTIAL CRISIS IN SCHOOL BECAUSE OF YOU TWO.

FUCK YOU NERDS AND YOUR FANCY NUMBERS

SEXY RUSSIAN BULLPUPS FTW.

In all seriousness, thank you both so much for giving me the numbers. I still don't want to accept them. You have led the horse to water. I still need to drink.

The only man who ever reported his own post!

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Saturday, May 23rd 2015, 11:24am

Well, that's an interesting introduction, it would need some refining.
To me, spread, velocity and RoF determine optimal range of use,
Recoil, reload speed and velocity determine ease of use.
I use these two axes to choose the easiest weapon to use at the intended ranges of the map.
On second thought, this might be off topic.
Stats thingy

### Quoted from "Cheapnub"

I'm a battlefield player, good sir. I don't play metro.

### Quoted from "Suiizide"

PC is no longer PC master race. It's PC mustard race, because consoles need to ketchup :'D

### Quoted from "Riesig"

DICE gave so much into making commander better, but lemmings be lemmings I guess.

### Quoted from "MrT3a"

As a good guy that don't want to use overly glitched weapons, I'll quit using the MTAR and switch to the ACWR until it's fixed

The world needs more people like you

+1, I think we're all in agreement that more MrT3as would be an awesome thing
Although if that was the case they'd use up so much of the world's awesome that there'd be none left for the rest of us!

### Quoted from "CobaltRose"

yes, I know, I'm a big-ass hypocrite

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Saturday, May 23rd 2015, 12:03pm

### Quoted from "Zer0Cod3x"

Why is there Hardline in this when talking about BF4 weapon balance?

Because it can be applied to either one as they are practically the same game and I only had BFH weapons available at this time.

I also realized the "Big List" was pretty much something very similar to this, but I still decided to write this up in case something comes out from it. The Big List is better and more refined at the moment tho.

This could be kind of used as a weapon selection method. You input your coefficients, eg. you favor for more accurate but less damage weapons -> higher coff for spread and recoil and less for dmg, and then the system outputs that graph based on those coeffs, giving a quick way to compare weapons.
• 3VerstsNorth - Analysis of game mechanics in BF4 (tickrates, effects of tickrate, etc)
• InterimAegis - Weapon comparisons/scoring.
• leptis - Analysis of shotguns, recoil, recoil control and air drag.
• Veritable - Scoring of BF4/BF1 firearms in terms of usability, firing and other mechanics.
• pmax - Statistical analysis of BF4 players/games.
• Miffyli - Random statistical analysis of BF4 battlereports/players and kill-distances. (list is cluttered with other threads).
Sorry if your name wasn't on the list, I honestly can't recall all names : ( . Nudge me if you want to be included

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Saturday, May 23rd 2015, 8:36pm

@NoctyrneSAGA

I must have missed that, so thanks for quoting it! I'm not surprised though, as the correlation is so strong that it's pretty obvious it was derived from a formula, and since there are a whole bunch of people here way smarter than I am, I'm not surprised it has already been found.

My point still stands though that thanks to 3VN's investigations, the 900RPM of the MTAR-21 and AEK does not help it to shoot faster than the 880RPM ACW-R until the 28th (!?) bullet fired, so the higher SIPS value is a pure and meaningless nerf. Same thing for the 880RPM ACW-R vs. the 830RPM SG553, that the former only has an advantage from the 8th bullet on.

The upcoming high frequency updates will make that moot, and it can't come soon enough I suppose.

@Zer0Cod3x

Well, I'm sure he's well aware of it, as it's in his signature.... I'm not quite certain if it is deserving just yet, as I'm still refining it. I made some massive changes to the Google Sheets last night, but I won't have much time to work on it further until the end of this month, due to having to do real work. That coincides with the upcoming Spring Patch anyways. For now, still tweaking what to weigh and how much, so it spits out reasonable overall rankings.

@Miffyli

As you can see what NoctyrneSAGA quoted Rezal, and I suppose just playing around with BF4 weapon values so often, I'm sure you can see that it seems obvious DICE SE uses various formula in order to come up with basic weapon stats. Of course that gets refined further for balancing, but there are definitely correlations to RPM (despite how flawed it is), SIPS, V-Recoil, and H-Recoil to a lesser extent.

My other "interest" is baseball statistics, and they use scatter plots with trend lines. Something similar might be useful for what you are thinking of:

Or: Workbook: O-Contact/ISO_400_PAs_2002-2014

I learned a lot while compiling The Big List, if nothing else just having spent so much time with the values in Multi-Comparison. Here are what I found to be important at close range (up to 50m):

• DPS, which is RPM + bullet damage. You'd think the SCAR-H and ACE 52 shoot too slowly, but their high-damaging bullets more than make up for it.
• Reload speeds, maybe? But this is not so much "stats" as more about animations and related artistry.
• Accuracy-related stats like Starting Spread, SIPS and H-Recoil actually don't mean much, since the target is so close.

For longer range:

• Base Spread is ridiculously powerful, because it not only affects first-shot hit rate, but also subsequent shots hit rates due to the SIPS having a lower starting point.
• SIPS is next, as it allows you to land more shots over a longer burst.
• To the above, then the HBar that currently halves Base Spread and then LOWERS SIPS, is crazy good in this usage. Pair that with the Stubby, and you can shoot all day while standing still.
• H-Recoil will pull your aim point off target, especially in shorter bursts that you don't have time to react and pull it back. However, since you have to forego the HBar in order to run Comp, which is the only thing that curbs H-Recoil, I found it is rarely worth it to do so, unless you really have trouble with V-Recoil.
• Velocity makes the gun much easier to use, as you get lower bullet drop (within the same class and thus with the same gravity values) and also having to lead less vs. the ADADADAD guys. However, Velocity is probably one thing that DICE SE tried to take the "realistic values" approach. There seems to be no obvious relationship to Velocity, V-Recoil or others.

Hope this helps, and good luck with your endeavour!

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Saturday, May 23rd 2015, 10:37pm

### Quoted from "Veritable"

I noticed that this causes slight issues when, thanks to 3VN's research, various RPMs actually function the same for a quite long burst time. So, if the damage output is actually the same thanks to the engine limitations, then the higher SIPS is actually not "nerfing" anything. It is purely detrimental, which is probably not something the devs intended.

Would the increased update rates being tested in CTE help with this?
Who Enjoys, Wins

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Saturday, May 23rd 2015, 10:54pm

### Quoted from "BleedingUranium"

Would the increased update rates being tested in CTE help with this?

Yes, 3VN already made 60Hz and 120Hz tables at Rezal's request. He likes 60Hz.

BF4 shooting mechanics

In that case 900RPM > 880RPM at 13th round, but 880RPM > 830RPM already by the 4th round. Much more meaningful.

As an exclusive DMR user I don't have a dog in this fight... well maybe I should be against it because the lower the simulation rate, the better it is for low-RPM weapons which DMRs belong to... but as a logical guy who enjoys good balance, I'm glad to see High Frequency Updates happen.

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Saturday, May 23rd 2015, 11:14pm

@Veritable
Yeah I knew about the formulas etc but that shouldn't be used in these formulas as it's just for... checking balance, so to say. I am combining RoF with recoil/spread increase and so worth because higher RoF = spread and recoil increase more often. Other than that I figured out same as you wrote (base spread matters a lot, velocity matters etc) but I just haven't had time to refine or even start to think about things like penalties from movement. I still think your list is more comprehensive and this was just semi-random idea, but thanks for help anyways!