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## An integrated Index of Lethality for full auto weapons

Hey! If this is your first visit on symthic.com, also check out our weapon damage charts.
Currently we have charts for Battlefield 3, Call of Duty: Black Ops 2, Medal of Honor: Warfighter and Call of Duty: Modern Warfare 3

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Sunday, December 27th 2015, 10:16pm

### An integrated Index of Lethality for full auto weapons

VERSION 3 (FINAL)

This thread cames from the discussion with @Miffyli (creative discussion!!!) about which is the parameter to describe a dimension in a weapon (Thread Multidimensional Analysis). This is just an exercise to integrate individual parameters of weapons in an index and doesnÂ´t pretend to be THE RANKING of weapons because those rankings depend strongly on the set initial conditions.

Philosophical principle: A gun is better than another if it wins in an individual engagemet (is faster delivering the damage>100), and the measure of that is the probability of delivering it.

The case analyzed is: full auto weapons (55 weapons), ADS, naked gun (or fixed attachements such as PDWs) and perfect aiming. Other strategies (microbursts, auto or manual), recoil correction or different points of aiming for each weapon to optimize the bursts are not considered. Time to ADS is not considered.

Weapon Features are taken from @Veritable table (Thanks!!!), filling some gaps (Base values of Hrec and Spread). When discrepancies are found with Symthic stats, these values are taken (mainly AS VAL and GROZA).

1th step: Generate 2,000 bursts of 10 rounds for every weapon in 10 m intervals up to 100 m (these weapons havenÂ´t significant results further than 50 m). Evaluate if each bullet hits and where (stom., chest, head or missed). Register the damage.

That means: 20,000 bursts for each weapon, 1,100,000 total burst, 11,000,00 ÂvirtualÂ shots.

The methodology here:

### Spoiler

The coordinates (angular) of the bullet ÂiÂ in a burst are:

RECOIL

Xri=Xi-1+ random [Hleft, Hright]; (no recoil in first shot)
Yri= Yi-1+ RecoilV.FSM.random [0,95,1,05]

FSM=1 except i=2 (no recoil in first shot)

Note that Random numbers has to be the same in X and Y to be consistent.

MaxSpread is not reached with 10b Burst.

TOTAL CARTESIAN COORDINATES AT DISTANCE ÂDÂ

Xi=Xaim+D.TAN(Xri+Xsi)
Yi=Yaim+D.TAN(Yri+Xsi)

HITBOX

Head 0.20m (width) x 0.30 m (height), damage multiplier = 2,13
Chest 0.50m (width) x 0.30 m (height), damage multiplier = 1
Stomach 0.50 m (width) x 0.40 m (height), damage multiplier = 0.93

Arms and legs are not considered (the burts go mainly upward).They are similar to Test Field targets. Defensive spec is not considered.

The aiming point was X=0 and Y=0,35, centered in the intuitive center of mass of torso.

EXCEL was used.

This is not new, because it follows in the footsteps of Hitrater, Simplot and Plotic.

2nd step: Classified by distance, register on each individual burst: Total Damage, Number of Bursts that produces DMG> 100, Number of Bullets that hits the target, Number of Shots (not bullets, because some of them may be missed) that causes DMG> 100, Time to Kill (where DMG> 100) and many other parameters. This analysis within the burst is new.

This TTK is different than common TTK in Symthic because it takes into account missed bullets and time to reach the target (velocity of bullet). In fact it is:

TTK=(Distance/Vbullet)+(60/ROF-1).(Nshots to kill-1)

Note that the first shot is done at Time=0 and I compute total shots to kill instead of bullets on target to kill. An analysis of sensibility shows that Vbullet has
importance at range to change the TTK.

3th step: Get the statistical parameters for the above values for each set of 2000 bursts at a given distance (Mean, Standard Devt., quartiles, max., min, etcÂ).

The analysis shows that the relevant parameters are:

- Probability the burst is effective (DMG> 100)= Efective Bursts/Total Bursts
- TTK defined as above.

We have the following graphs.

Mean DAMAGE in the bursts / DISTANCE

Average Mean DMG/DISTANCE by class.

PDW are OP and out of its natural position (as powerful as carbines).

Probability of DMG>100/DISTANCE

TTK (seconds) /DISTANCE

No Data means probability DMG>100=0

This post has been edited 11 times, last edit by "leptis" (Jan 6th 2016, 2:02pm)

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Sunday, December 27th 2015, 10:32pm

4th step: Compare the weapons in pairs. That is, huge 55x55 matrices at each distance, with the probability to win.

The algorithm is explained here because it is a combinatorial problem.

### Spoiler

We have to compute

Kill-Fail
Fail-Kill
Fail-fail

If Prob1 is the probability of effective burts at a DISTANCE for Weapon1 (faster; lower TTK) and Prob2...etc... Weapon2 (slower, higher TTK)

WEAPON1 wins with probability=Prob1
WEAPON2 wins with probability=(1-Prob1).Prob2 ; When Weapon1 fails.
Both fail with probability=(1-prob1).(1-Prob2)

There is other not computed case (kill-kill) with very, very small probability (tipically where TTK curves crossing).

The sum of the rows gives us the sum of winning percentage and column and the percentage of losses.

Actually this is not rigorous because it presumes the frecuency of use of weapons is uniform (the engagements are not equi-probable). But we donÂ´t know it, so...

Average values are calculated.

Here you see an image of a matrix and a sample of 4 weapons to understand how it works.

Now we have the integrated probablity to win for each weapon against other ones. Here you see the results for AR

The "waves" are due to curved option.

Note that it shows there are good weapons for CBQ (F2000 or ACE23) and good ones for long range (SAR-21). The results are fully consistent.

5th step: Are all distances of combat equally probable?. We know they are not. We have the @Miffyli curves of probabilities of engagement. We weight the results for each distance with that probability, we add the probabilities weighted, we convert that to the scale 0-10 .... and FINALLY!!! we have THE INTEGRATED INDEX OF LETHALITY (sorry for the name!!!:-)) that integrates ROF, RECOIL, SPREAD, DAMAGE (D) and BULLET VELOCITY (no weighted values are shown to compare the effect of weighting.Scale 0-10).

Next steps: Which are the probability that you could produce that results?. It depends on the availability of ammo, which depends on the size of the magazine and reload time .... but sorry, I'm exhausted now :-).

This post has been edited 10 times, last edit by "leptis" (Jan 6th 2016, 1:47pm)

Symthic Developer

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Sunday, December 27th 2015, 10:40pm

Woah I still can't comprehend how you can do something like this with Excel. Sure it's possible but damn I'd grind my teeth to dust if I had to do something like this.

I like how M60 is very similar in non-weighted and weighted area ( @ViperFTW :v ). Interesting results we got here, can weapon guys say if these results are agreeing with other knowledge of weapons? ( @Rezal ?)
• 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

Rezmer

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Sunday, December 27th 2015, 10:52pm

[Aristocrat's Shoes]

### Quoted from "Darktan13"

TLDR -
Teamwork is where players function by themselves, but their effectiveness is multiplied when they work together. Not a checklist of "did we bring a healer so we can start playing?"

Can't get a title

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: Dec 23rd 2013

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Sunday, December 27th 2015, 11:09pm

Interesting how the first eight weapons are all heavy hitters.
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.

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Sunday, December 27th 2015, 11:19pm

### Quoted from "Miffyli"

Woah I still can't comprehend how you can do something like this with Excel. Sure it's possible but damn I'd grind my teeth to dust if I had to do something like this.

I like how M60 is very similar in non-weighted and weighted area ( @ViperFTW :v ). Interesting results we got here, can weapon guys say if these results are agreeing with other knowledge of weapons? ( @Rezal ?)
lol !!!!

I use Excel because it allows progress while thinking and allows tests such as "What if", automatic graphics and be very aware of what is being done, but...to avoid to do 55 sheets, some manual labor of copy and paste has to be done:-).

The reason of M60 results is in this graph:

Non-weighted

As you see M60 have more stable values for short distances. This is because it doesnÂ´t "suffer" with the weighting.

@Rezal

I will specifically study the reason for JS2 position. :-)

This post has been edited 5 times, last edit by "leptis" (Dec 28th 2015, 7:26pm)

Can't get a title

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Monday, December 28th 2015, 1:29am

@leptis

Why are there so many large calibre bullet guns at the top?
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.

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Monday, December 28th 2015, 11:20am

This is some fine work. I'm a little curious as to how much burst fire mode can play into the equation. Some weapons (AK-12, AN-94, AKU-12) have higher rates of fire for burst mode.
I assume they would have somewhat increased scores.

When I look at the JS-2 numerical stats, it has a lot of damage potential up close, but as it gets further and further away, it drops off considerably. If you used a heavy barrel with it, it has better long distance capabilities, but it still suffers. Just about any PDW would have the same shortcomings.
I love the math behind the statistics
It's possible to find me online at almost any given time, due to the fact that my schedule is hectic and rather non-existent.

Who needs sleep anyways?
(PC/PS4 gamer)

Various bf4 spreadsheets: (nothing special, just raw data from the Symthic website put into a spreadsheet to analyze all values at once)

### Spoiler

BF4_Weapons_enhanced_UPDATED_2016
Soldier Equipment:
Interactive Damage Table
Unsuppressed Sniper Rifle Bullet Drop Charts
bf4_sniper_guide
Suppressed Sniper Rifle Bullet Drop Charts
Suppressed bf4_sniper_guide
More user friendly Unsuppressed Sniper Rifle Bullet Drop Chart
Friendlier Sniper rifle Bullet Drop Chart
More user friendly Suppressed Sniper Rifle Bullet Drop Chart
Friendlier Suppressed Sniper Rifle Bullet Drop Chart

This post has been edited 2 times, last edit by "lope_a_dope" (Dec 28th 2015, 11:43am)

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Monday, December 28th 2015, 12:00pm

Woa nice charts but some questions:

- TTK=(Distance/Vbullet)+(60/ROF-1).(Nshots to kill-1)

What's the Nshots value do I understand it correctly with "needed shots to kill?"

- by the "Probability of DMG>100/DISTANCE"

the M249 support line drops below zero? bug or intended?

- by the TTK (seconds) /DISTANCE

The AR graph is missing you have the carbines twice

- the last grahp the "INTEGRATED INDEX OF LETHALITY"

how should I understand the weighted/no weighted values?? sorry English is not my native language so dunno if I translate it correctly for me because in bf4 weapons don't have any weight

Smoked Salmon Best Salmon

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Monday, December 28th 2015, 5:17pm

I think you ought to include time-to-ads in your TTK numbers, and then allow for weapons with viable hipfire to be reflected in your rankings as weapons that do not need to ADS within a certain distance.

I have no idea how to implement this, but this may solve Rezal's issue with your rankings.

### Quoted from "Girtablulu"

how should I understand the weighted/no weighted values?? sorry English is not my native language so dunno if I translate it correctly for me because in bf4 weapons don't have any weight

Weight:

### Quoted

Noun: a body's relative mass or the quantity of matter contained by it, giving rise to a downward force; the heaviness of a person or thing

Verb: to attach importance or value to

He's using the second definition. In this case, his rankings have been biased based on what kind of engagements we expect to see in a game. So, the U100 unweighted is ranked more highly than the weighted U100, because it is found that the ranges in which the U100 excels are not common.

Platoon Marble Duck

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"you obviously don't know what an argument is as there is only one person battling. Do you really fucking think I want subs? You think you can act all big and powerful just because you sit on a computer at least 6 hours a day like the probably nerdy unwanted retard you are with 4.3k subs? You think 4.3k subs is a lot? LOL you need medicine man. I don't want any subs as i just have a google account for other media and writing comments. Think twice before you act. You even said in your video you aren't that great of a player, and the comments agree you aren't. Maybe you should once again think twice before you act, stop being such an annoying, ignorant bastard that everyone wants to shut up, and god, literally, just shut up. Your voice gave me a headache :sÃ¯Â»Â¿"

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You started playing bf3 and never touched bfc1/2. Please do yourself a favor and shutdown your generic cod channel down"

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"stfu cunt, BF3 was way better end of discussion"

"Stfu man, you're be littleing the most looked upon Battlefield Youtuber. No one cares about you, how much of an ego you have, or quite frankly your opinion. It's a fucking game.... Does it really fucking matter? Pathetic man."

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"please talk like a normal person and not like a professional"

This post has been edited 1 times, last edit by "marbleduck" (Dec 28th 2015, 5:23pm)