Methodology/Recoil Mechanics

Gunsmith Physics • Keyframes & Angular Displacement

Recoil Mechanics & Pattern Compounding

Recoil in Wardogs is driven by per-shot angular impulse curves extracted from Unreal Engine DA_*_Stats data assets. Each round applies a discrete Pitch (vertical climb) and Yaw (horizontal drift) vector, modified by attachment compounding, mechanical barrel dispersion, and target engagement distance.

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1. Unreal Engine Recoil Data Architecture

In Wardogs, weapon recoil is built on Epic Games' Gameplay Ability System (GAS). When inspecting the game's compiled .pak archives, assets utilize standardized engine prefixes:

Prefix	Unreal Engine Type	Role in Recoil & Handling	Extracted Asset Example
DA_	Data Asset	Authored base recoil pitch and yaw keyframe curves	DA_M4_Stats, DA_AK74_Stats
GE_	Gameplay Effect	Modifier blueprints compounding handling multipliers	GE_MUZL_, GE_FGRP_, GE_MAGZ_*
GA_	Gameplay Ability	Executable state machines governing firing, reload, and ADS	GA_Weapon_Fire, GA_Weapon_Reload

Each weapon possesses an authentic per-shot angular impulse array:

\vec{R}_i = (\text{rawYaw}_i, \text{rawPitch}_i)

rawPitch (y): Vertical barrel climb in degrees (positive = upwards deflection).
rawYaw (x): Horizontal barrel drift in degrees (positive = rightward kick, negative = leftward kick).
Pitch Clamp (pitchMax): Ceiling boundary capping maximum cumulative vertical climb.
Yaw Boundaries (yawMinMax): Lateral limits preventing unbounded horizontal deflection.
Post-Pattern Drift: When continuous fire exceeds the authored curve keyframes, the engine transitions into steady-state procedural jitter via a deterministic pseudo-random walk generator.

2. Macro Recoil Path vs. Micro Stochastic Dispersion

A common question regarding Wardogs gunplay is whether recoil patterns are 100% identical on every spray. In the engine, recoil is a hybrid system comprising a fixed, predictable macro trajectory combined with stochastic micro variation:

The Macro Pattern (Deterministic)

The core recoil impulse curve is fixed and authored directly in game assets. Every time a weapon is fired, the muzzle climbs, pulls, and kicks along this exact sequence of angles.

This is the repeatable recoil pattern that skilled players learn and counteract through muscle memory (pulling down and opposite to lateral drift).

The Micro Variation (Stochastic)

Two sprays are never 100% pixel-identical because of four stochastic factors:

Shot-to-Shot Random Deviation: Physical angular cone perturbation (RandomDeviationDegree) rotating the impulse.
MOA Barrel Spread: An inherent cone dispersion radius centered on each recoil node.
Post-Pattern Jitter: Procedural random walk if magazine capacity exceeds curve keyframes.
Shotgun Buckshot: Random radial distribution of 8 pellets within the choke cone.

3. Shot-to-Shot Random Angular Deviation (RandomDeviationDegree)

In the game source data (WDWeaponStatsData), individual bullet trajectory is governed by a dedicated physical property: RandomDeviationDegree. Unlike unitless multipliers, this value is a geometric angle measured in degrees (°).

Before applying the recoil impulse vector to the player's aim, the engine calculates a stochastic angular perturbation vector scaled by this envelope:

\mathbf{\vec{\Theta}_i = \underbrace{\left( \vec{R}_{\text{base}}[i] \circ \vec{M}_{\text{attachments}} \right)}_{\text{1. Scaled Base Pattern}} + \underbrace{\vec{\Delta}_{\text{dev}}(\text{RandomDeviationDegree})}_{\text{2. Directional Jitter Cone}} + \underbrace{\vec{\Delta}_{\text{MOA}}(\text{WeaponAccuracy})}_{\text{3. Mechanical Barrel Spread}}}

The angular perturbation envelope rotates the instantaneous impulse direction $\theta_{\text{base}} = \operatorname{atan2}(Y, X)$ within symmetric bounds:

\mathbf{\theta_{\text{final}} = \theta_{\text{base}} \pm \delta, \quad \delta \sim \mathcal{U}[0, \text{RandomDeviationDegree}]}

◔The “Arrow on a Clock” Analogy

A common point of confusion is whether a RandomDeviationDegree of 35° adds a full 35 degrees directly to horizontal yaw. It does not. If 35° were added directly to yaw, a single round would violently whip the crosshair by nearly an eighth of a full circle (at 25 meters, a 35° deflection would miss the target center by over 17 meters), violating the engine's hard yaw clamp of ±22.5°.

Instead, visualize an arrow representing the recoil kick vector of an individual bullet:

Length of the Arrow (Magnitude): Small, typically around 0.8° to 1.2° of angular climb.
Direction of the Arrow: The predefined recoil curve points this arrow almost straight up at 12:00 (with a slight authored tilt to the left or right).

RandomDeviationDegree does not make the arrow longer. Instead, it tilts the orientation of the arrow on the clock face:

High Jitter: SUPER-45 (±35°)

The arrow can tilt randomly up to ±35° from 12:00 (between roughly 11:00 and 1:00 on the clock face).

Low Jitter: M4 Carbine (±10°)

The arrow tilts only up to ±10° from vertical (between 11:40 and 12:20 on the clock face).

Trigonometric Resolution on Screen Yaw and Pitch

Because the recoil impulse is only about 1.0° in length, tilting it by an angle $\theta_{\text{tilt}}$ resolves into Cartesian crosshair offsets via basic trigonometry:

\mathbf{\Delta \text{Yaw} = \|\vec{R}_{\text{impulse}}\| \times \sin(\theta_{\text{tilt}}), \quad \Delta \text{Pitch} = \|\vec{R}_{\text{impulse}}\| \times \cos(\theta_{\text{tilt}})}

For a 1.0° impulse on the SUPER-45 tilted at the maximum 35°:

\mathbf{\Delta \text{Yaw}_{\text{max}} = 1.0^\circ \times \sin(35^\circ) \approx \pm 0.573^\circ}

The resulting crosshair wobble on screen is only about half a degree (±0.57°), not 35 degrees.

Per-Shot Stochastic Sampling Sequence

Each bullet in a continuous burst samples a fresh uniform angle $\theta_{\text{tilt}} \sim \mathcal{U}[-\text{RandomDeviationDegree}, +\text{RandomDeviationDegree}]$ :

5-Shot Burst Example:Shot 1: +14° (slight right)•Shot 2: -31° (kick left)•Shot 3: +3° (near true vertical)•Shot 4: -19° (drift left)•Shot 5: +35° (max drift right)

Weapon Class	Firearm	Source Data Asset	RandomDeviationDegree
Sniper Rifles	AMR 50, MK22, SV-98, Mosin, Scout	DA_SR_04, DA_MK22, DA_SV98	4.0°
DMR	SKS	DA_SKS_Stats	5.5°
DMR	BMR (RFB), SVD	DA_RFB_Stats, DA_SVDM_Stats	10.0°
Assault Rifles	M4, Bushmaster M17S	DA_M4_Stats, DA_WEPN_032	10.0°
Assault Rifles	Galil	DA_WEPN_029_Stats	12.0°
Assault Rifles	AK-74M	DA_AK74M_Stats	13.0°
Assault Rifles	KH-2002, A-91, T-21	DA_KH2002, DA_A91, DA_TAR21	15.0°
Assault Rifles	FAL	DA_WEPN_030_Stats	16.0°
Submachine Guns	MP5	DA_WEPN_026_Stats	10.0°
Submachine Guns	AMP-9, PP-19 Vityaz	DA_MP9_Stats, DA_SMG_03	15.0° – 17.0°
Submachine Guns	SUPER-45 (Vector)	DA_Vector_Stats	35.0°
Light Machine Guns	M249 SAW, PKM	DA_M249_Stats, DA_LMG_02	20.0°
Shotguns	M500, MP43	DA_M12G_Stats, DA_MP43_Stats	24.0° – 28.0°
Sidearms / Pistols	GGX-17, GGX-18, Judge, M1911, Deagle	DA_G17_Stats, DA_Pistol_*	10.0°
Archery	Compound Bow	DA_Bow_Stats	2.0°

4. Attachment Multiplicative Compounding

Equipped attachments (Muzzle devices, Foregrips, Sights, and Magazines) modify vertical climb and horizontal drift multiplicatively using Unreal Engine MultiplyCompound attributes:

\mathbf{\text{verticalRecoilMult} = \prod_{k=1}^n \text{verticalMultiplier}_k}

\mathbf{\text{horizontalRecoilMult} = \prod_{k=1}^n \text{horizontalMultiplier}_k}

The adjusted angular deflection vector for shot $i$ is:

\mathbf{\theta_{\text{yaw}, i} = \text{rawYaw}_i \times \text{horizontalRecoilMult}}

\mathbf{\theta_{\text{pitch}, i} = \text{rawPitch}_i \times \text{verticalRecoilMult}}

Compounding Example: M4 Carbine

Equipped Muzzle: Flash Hider (-16% climb → 0.84x)
Equipped Foregrip: Vertical Grip (-30% climb → 0.70x)
Equipped Extended Mag: 60-Round Drum (+8% recoil penalty → 1.08x)
Composite Multiplier: $0.84 \times 0.70 \times 1.08 = 0.63504 \implies \mathbf{36.5\%\text{ Net Climb Reduction}}$

5. Trigonometric Projection to Target Distance

Because recoil impulses act as angular deflections at the barrel muzzle, linear physical displacement on a flat target down-range increases with target distance $d$ (in meters):

\mathbf{\text{Displacement}_{\text{cm}} = d \times \tan\left(\frac{\theta^\circ \times \pi}{180}\right) \times 100}

Small-Angle Approximation & Linear Distance Scaling

For small angular deflections typical of rifle recoil ( $\theta < 5^\circ$ ), the small-angle approximation holds: $\tan(\theta) \approx \theta\text{ (in radians)}$ . Consequently, linear target displacement scales almost purely linearly with distance:

At 25m, a $1.2^\circ$ pitch climb produces: $25 \times \tan(1.2^\circ) \times 100 \approx 52.36\text{ cm}$
At 50m, the same $1.2^\circ$ climb produces: $50 \times \tan(1.2^\circ) \times 100 \approx 104.72\text{ cm}$ (exactly double)
At 100m, the climb produces: $100 \times \tan(1.2^\circ) \times 100 \approx 209.47\text{ cm}$ (exactly quadruple)

6. Minute of Angle (MOA) Barrel Dispersion Physics

In addition to directional climb, every firearm exhibits mechanical barrel dispersion defined in Minute of Angle (MOA). One MOA corresponds to $\frac{1}{60}^\circ \approx 0.0002908882\text{ radians}$ , producing a spread of 2.9089 cm per 100 meters.

The radius of the circular spread cone in centimeters at distance $d$ is:

\mathbf{r_{\text{spread}} = \frac{\text{MOA}_{\text{effective}} \times 2.9089 \times \left(\frac{d}{100}\right)}{2}}

where $\text{MOA}_{\text{effective}} = \max(0.4, \text{baseMoa} \times \text{spreadMult})$ .

To model a true uniform circular disk distribution without artificial clustering at the center pip, the radial distance is sampled using the square root of a uniform pseudo-random variable $u_2 \sim \mathcal{U}[0, 1)$ :

\theta_{\text{jitter}} = u_1 \times 2\pi, \quad r_{\text{jitter}} = \sqrt{u_2} \times r_{\text{spread}}

\mathbf{\Delta X_{\text{jitter}} = r_{\text{jitter}} \cos(\theta_{\text{jitter}}), \quad \Delta Y_{\text{jitter}} = r_{\text{jitter}} \sin(\theta_{\text{jitter}})}

7. Combined Cartesian Target Impact Coordinates

In the simulation engine (weaponBuilderEngine.ts), the total Cartesian impact coordinate $(X_{\text{cm}}, Y_{\text{cm}})$ relative to center mass $(0, 0)$ combines macro recoil projection, shot-to-shot angular deviation jitter, and barrel MOA dispersion:

\mathbf{X_{\text{cm}} = \left[ d \times \tan\left(\frac{(\theta_{\text{yaw}} + \delta_{\text{yaw}}) \cdot \pi}{180}\right) \times 100 \right] + \Delta X_{\text{jitter}}}

\mathbf{Y_{\text{cm}} = \left[ d \times \tan\left(\frac{(\theta_{\text{pitch}} + \delta_{\text{pitch}}) \cdot \pi}{180}\right) \times 100 \right] + \Delta Y_{\text{jitter}}}

Shot Execution Sequencing:

Initial Shot (i = 0): Recoil displacement is exactly zero ( $\theta_{\text{yaw}} = 0, \theta_{\text{pitch}} = 0$ ). The bullet strikes point-of-aim modulated only by tight cold-barrel MOA dispersion ( $0.4 \times r_{\text{spread}}$ ).
Subsequent Shots (i ≥ 1): Displaced by cumulative angular climb/drift, rotated by the shot's $\text{RandomDeviationDegree}$ envelope, projected across distance $d$ , plus stochastic MOA barrel spread.

8. 12-Gauge Buckshot Pattern Simulation & Choke Constriction

Shotgun ballistics operate on multi-pellet conical cloud expansion. A standard cylinder bore produces an 18.0 cm radius (36.0 cm diameter) pattern at a reference distance of 15 meters:

\mathbf{r_{\text{pattern}} = 18.0 \times \left(\frac{\max(5, d)}{15.0}\right) \times \text{spreadMult}}

Pellet Array Geometry (8 Pellets Total):

1 Core Pellet: Concentrated tightly within $r \le 0.25 \times r_{\text{pattern}}$ of the aim point.
7 Perimeter Pellets: Distributed radially across $r \in [0.55, 1.0] \times r_{\text{pattern}}$ with equidistant angular pacing and radial jitter.

Choke Attachment	Spread Multiplier	Pattern Radius @ 15m	Total Pattern Diameter
Stock Cylinder	1.00x	18.0 cm	36.0 cm
Improved Cylinder Choke	0.80x (20% tighter)	14.4 cm	28.8 cm
Full Choke	0.60x (40% tighter)	10.8 cm	21.6 cm

9. Canvas Screen Projection & Perspective Scaling

In the visual target simulator (RecoilTargetCanvas.tsx), physical centimeters are converted to viewport pixels using an inverse perspective scale:

\mathbf{\text{pxPerCm} = \left(\frac{\text{baseConstant}}{d}\right) \times \text{zoomLevel}}

Screen coordinates on the HTML5 canvas are mapped directly from physical offsets:

\mathbf{\text{canvasX} = \text{centerX} + (X_{\text{cm}} \times \text{pxPerCm})}

\mathbf{\text{canvasY} = \text{centerY} - (Y_{\text{cm}} \times \text{pxPerCm})}

Why Down-Range Dispersion Visually Widens:

Physical displacement on target grows with distance ( $X_{\text{cm}} \propto d$ ), while the apparent scale of the target silhouette on the shooter's retina/screen scales inversely ( $\text{pxPerCm} \propto \frac{1}{d}$ ).

Increasing the distance slider accurately reflects how a target shrinks in angular size relative to the weapon's spray pattern, illustrating why tight recoil compensation becomes exponentially more demanding at extended ranges.

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