Original Title: Brute-force approach to BF4 gun balance & optimal attachments, burst sizes, and aim targets, November 10th 2013

Author: 3VerstsNorth

**Motivation**

In-game experience and testing are critical for having a feeling about the performance of different weapons and attachments. However, subjective Âfeeling-basedÂ testing or even the player stats cannot tell whether some weapon is 5 or 10 % more effective than another. Most importantly, because learning near-perfect recoil compensation patterns takes a lot of time, it is impossible to just test all combinations to find out what weapon and attachments have * statistically the greatest potential for an expert user even though they can be more difficult to use than some other* .

**Model and simulation settings**

Realistic models of shooting can help here: it is fairly straightforward to map the shooting outcome across the parameter space by brute-force simulations.

I coded a simulation platform using Symthic weapon stats and the algorithms described in Algorithms for the Shooting Mechanics in BF4. I present here the first results for non-moving ADS shooting. I will do the same for moving and/or HIP shooting (requires just clicking a button or two), but I would like to have some community feedback on the visualization, conditions, sensibility etc. stuff so that the next iteration better serves the community needs.

**The parameters explored here**

(i) all combinations of attachments

(ii) all distances from 5 to 100 m (5 m step)

(iii) all burst sizes from 2 to 10 shots/burst

(iv) all aim locations from stomach to head (5 cm step, see figure below)

As the outcome measure, I used T100.

**Definition of T100**

T100 is defined so that the model shoots bursts at the aim location and keeps track of the elapsed time and accumulated damage. When the accumulated damage is equal or greater than 100, the accumulated time is recorded (and the rest of the shots in that burst are discarded). These times are then averaged across many bursts to get a reliable estimate (now 100000 shots).

In short, **T100 is the realistic in-game time in milliseconds that it takes to cause 100 damage to a target.** T100 does not consider the magazine size and time taken to reload the weapon. (It would be easy to incorporate mag size and reload time in another metric if it is seen relevant.)

## Assumptions and parameter decisions

(i) Hitbox sizes and their relationships are as shown above. I will gladly use a more accurate target model when it is available.

(ii) Spread and recoil recovery are ignored (assumption of 100% recovery during inter-burst interval).

(iii) Inter-burst interval (the time from the end of one burst to the start of the next burst) is fixed to 150 ms. I this this represents a fair estimate of considering the demand for recoil recovery and reasonable mouse clicking rate. Educated opinions are welcome!

(iv) Recoil is either taken as is, without any compensation, or with ÂperfectÂ compensation so that vertical recoil is set to 0 and the *mean* horizontal recoil is subtracted from horizontal recoil.

(v) Bullet drop with gravity is excluded although muzzle speed is included in the time estimates.

(vi) Burst-mode shooting and burst-only weapons are excluded and treated later in a separate analysis.

(vii) Single-mode shooting is excluded: minimum burst size is 2.

### Results

Ok, I want first to show all the data and then dissect out some major findings. The tables below show the smallest mean T100 values for each full-auto primary weapon (rows) in the game in their corresponding groups for each distance (columns). The values are smallest with respect to attachment combinations, burst size, and aimpoint.

**Scale of the simulations**

To find the optimal parameters for minimum T100, 100000 shots were simulated for 36 guns, 20 distances, 22 aimpoints, 14 shots/burst, 12 attachment combinations, 2 recoil comp. modes, 2 inter-burst intervals, and 3 conditions (base ADS, move ADS, move HIP) so far: (36 * 20 * 22 * 14 * 12 * 2 * 2 * 3 = 31933440 times the 100000 shots.)

**How to read the tables**

For an example, please look at the top-3 ARs below.

At the distance of 40 m and in the row for SCAR-H, the cell shows the following information:

**265 2.4
175 h p 2**

**1. The first row shows the expected optimal performance of the gun. Optimal = smallest T100.**

The first number is the mean T100: it will take on average **265 milliseconds** to inflict at least 100 damage.

The second number is the mean “B100”: it will take on average **2.4 bullets** to inflict the damage sufficient for the T100 above.

**2. The second row shows that parameters that give the optimal T100.**

The first number, here 175, indicates the height of the aim location in cm between 80Â

190 cm (see the model above). Roughly, 90 cm indicates aiming at the low-edge of the stomach hitbox, 145 cm at the middle of the chest hitbox, and 175 cm at the middle of the head hitbox. So, with SCAR-H, aim at the face!

The letters indicate the attachments that give this smallest T100: here heavy barrel and potato grip.

h: heavy barrel

c: compensator

m: muzzle brake

a: angled grip

p: potato grip

e: ergo grip

Top-2 attachment combinations and their use percentage are shown under the weapon name.

The last number, here 2, indicates the optimal burst size.

**3. The color of the hitbox shows how good or bad the T100 value at this distance is with respect to the mean T100 of this weapon group** ( - (T100 - MeanT100) * 100% ). See also the color bars above the full tables. Green colors show that the gun kills faster than average and reddish colors suggest that you will hit the dirt first.

The second column shows the balance percentage (see 5. above), <%>, averaged across all distances. The guns are sorted by this number so that the overall best, fastest-killing guns are in the top. For SCAR-H, the value -22.6 means that across all distances with optimal parameters, SCAR-H will kill the target 22.6% faster than an average AR.

**Optimal and Fixed-burst/aim Tables**

There are two kinds of cuts into the data below. For each playstyle, the **optimum** tables show what are the optimal aim locations, attachments, and burst sizes in any single * condition* (say non-moving/moving ADS/HIP). Fixed-burst/aim tables are fixed to 3-shot bursts (burst RoF used where applicable) aimed at mid torso (130).

**2x2 Playstyle variables**

Inter-burst Interval (IBI)

For each condition, two factors define are four playstyle categories. First, the inter-burst interval (IBI): If you are a fast clicker and proficient in maintaining *aim* AND controlling the recoil between bursts while micro-bursting, IBI 100 ms (= 100 ms interval between bursts) is your category. Typical click rates with IBI 100 ms are ~5 Hz. If you overall prefer longer bursts, take more time to control the aim, or are not pro in *controlling the recoil between bursts* , look into IBI 300 ms. Typical click rates there are 1-2 Hz, depending on burst sizes ofc.

**Recoil Compensation**

Second, recoil compensation: There are now two categories for recoil compensation within bursts. “Perfect compensation” assumes that the player can, well, perfectly control the vertical recoil including the first shot multiplier. In perfect compensation, the trend (mean drift) of the horizontal recoil is also compensated. “No compensation” means that there just is no compensation. Note how this influences aim location, attachments, and burst sizes. I’d say most players are somewhere in between these categories depending on how difficult subjectively the gun is to control. Perfect compensation for the most difficult guns (thinking of ~~The bitch~~ heavy barreled SCAR-H…) can even for the best players be difficult enough to make easier guns more effective in game!

**Notes**

Note that recoil compensation between bursts is always assumed perfect => pick your IBI accordingly. Finally, note also (again) that all simulations assume perfect aim. Whether someone is capable of aiming at the middle of the head hitbox of a moving target while compensating for the flight time of the bullet is not considered here. For other headshot considerations, see below.

## pre-CR/SA tables

## Assault

## Assault, stationary ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Assault, moving ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Assault, moving HIP

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Engineer

## Engineer, stationary ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Engineer, moving ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Engineer, moving HIP

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Support

## Support, stationary ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Support, moving ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Support, moving hip

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Carbines

## Carbines, stationary ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Carbines, moving ADS

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Carbines, moving hip

Perfect compensation IBI 100 ms

No compensation IBI 100 ms

Perfect compensation IBI 300 ms

No compensation IBI 300 ms

## Future Directions

(i) How to estimate recoil compensation difficulty? High vertical recoil is more difficult to compensate than small vertical recoil but can this be quantified? The same goes for high vs. low FSM or any FSM in high-vs.-low RoF gun. I think we need realistic models for recoil compensation, or specifically the mouse movement trajectories that expert players can make to compensate for FSM, vertical recoil, and the horizontal trend. This, as far as I see, necessarily involves measurements with players using simulated in-game-like gun and mouse mechanics.

(ii) Should we include noise into the aiming? No-one has 100% jitter-free mouse control. Variability in the aimpoint would probably decrease the relative effectiveness of aiming at the head.

(iii) Doing the tables separately for stationary and moving conditions is easy. How to construct the optimal compromise or to choose the single optimal attachment combination for both stationary and moving gameplay? For example, would it make sense to search for the weapon and single attachment combination that gives the best overall performance for short-range (5 - 15 m) moving HIP, medium-range (15 - 50 m) moving ADS, and long-range (50 - 100 m) stationary ADS accuracy?

(iv) When the approach is validated, I’m going to make the simulation and visualization programs freely available. These data would benefit from a live (web page) user interface.

(v) Opinions, critique & feedback, please!

### T100 probability distributions and Headshot considerations

**Probability distributions**

Let’s look at the probability distributions of T100 values to see what is behind the mean T100 value shown and used in the tables.

The top panels show for AEK-971 the temporal distribution of T100 values (y-axis) for each distance (x-axis) so that the probability is color coded (red, p=1; yellow, p=0.5; green, p=0.2). The gun was shot with perfect recoil control from stationary ADS at mid-torso (130 cm) and at the middle of the head hitbox (175 cm) in bursts of 3 shots with 100 ms in between the bursts. The red bins in short distances show that at this distance and latency after the first shot, the target is dead (accumulated total damage > 100) with 100% confidence (p = 1). The slanted striped structure reflects individual shots, inter-burst intervals, and the increasing bullet flight time.

For comparison, the bottom panels show the mean T100 values and the 50% (median), 75%, and 90% percentiles. For example, the 75% percentile simply shows that 75% of the T100 values are equal or smaller. 75% percentile of T100 thus indicates that 3/4 of targets are dead by that time.

The same plots for SCAR-H:

show that

**Headshot considerations**

The explore in more detail which guns should be used for headshots and which not, I looked at the penalty in T100 compared to the optimal T100 for each aimpoint (vertical) and distance (horizontal). The data are from simulations with perfect recoil control, stationary ADS, at least three shots / burst, and the ‘noob’ inter-burst interval of 300 ms.

For AUG A3,

it is pretty clear that in ranges from 50 to 100 m the optimal approach is to aim at mid torso (130 cm)

But with CZ-805,

the gun has all the potential for the player to go for headshots. 2-shot microbursting would be even more accurate and kill faster, but I wanted to show that also 3 shot bursts do the trick.

Summarizing the T100 penalty for all ARs we see a nice transient from AUG A3 that works best with torso shots to CZ-805 and SCAR-H that can reward a skilled player with reliable headshots for fast kills with few bullets.

The number next to the gun name is the difference between head and torso mean T100 values in the 55-100 m distance range.

### Attachment Considerations

There has been a lot of discussion on whether one should learn to use the statistically optimal attachments vs. using those that make the gun easier to use (i.e., optimizing the attachments with the human factor in mind). I plotted below the effects of different attachment combinations on T100 with keeping the aimpoint and burst size as free parameters. So, the plots describe as realistically as possible the effective time to kill for optimal human usage of the gun.

For a single gun, ACE-23, the table looks like this for **Base ADS** (100 ms inter-burst interval and perfect compensation of H Recoil trend and V Recoil).

Reading instructions

Rows: Attachments (see first post for abbreviations)

Columns: Distances (m)

1st column: Mean (across distances) T100 penalty for non-optimal attachment (%).

In the row of the optimal attachment (here > 5 m: **h p** ): Top row in each cell: mean T100 (ms) and mean Bullet Cost (bullets). Bottom row in each cell: aimpoint, attachment, burst size.

In the rows of suboptimal attachments: Top rows: T100 penalty (ms) and mean Bullet Cost penalty (bullets). Bottom rows, as above.

The cell color indicates in % the relative magnitude of the T100 penalty (see color bar above the chart).

So, for example, at 40 m, ACE-23 with **h p** kills in T100=319 ms and uses 3.4 bullets aimed at the lower part of the head hitbox in 5-shot bursts. If one used **h e** , T100 penalty would be 6 ms and increase bullet cost by 0.7 bullets: the benefit of potato grip § over the ergo grip (e) is pretty negligible. On the other hand, someone using the muzzle brake (m) and angled grip (a), would get the kill 83 ms later. Whether this is this a significant number is very personal. At 60 m, the penalty for the inaccuracy of m a is already 225 ms (~50% increase in time-to-kill!) and the optimal aimpoint is shifted to upper torso (135). So, please have a look at this:

For **Moving ADS** , the table looks like this (the effect of ergo (e) is obvious…):

For other **ARs** , the effects are very similar in shape but quite different in size. See some guns below (your favorite(s) available at request):

M416 (ADS, base), M416 (ADS, move)

AK-12 (ADS, base), AK-12 (ADS, move)

AEK-971 (ADS, base), AEK-971 (ADS, move)

M16A4 (ADS, base), M16A4 (ADS, move) (Note! Estimated with a fixed burst size (3) no shit sherlock *and* aimpoint (145)!)

FAMAS (ADS, base), FAMAS (ADS, move)

Some carbines:

AK5C (ADS, base), AK5C (ADS, move)

ACW-R (ADS, base), ACW-R (ADS, move)

ACE 52 CQB (ADS, base), ACE 52 CQB (ADS, move)

In the plots below, the mean relative (in %) T100 penalty is plotted for distance ranges of 20-40 m and 45-80m for each AR.

**Base ADS 45-80 m:**

**Base ADS 20-40 m:**

**Moving ADS 45-80 m:**

**Moving ADS 20-40 m:**