Damage Falloff

Damage Falloff is a mechanic that affects the damage of guns outside of their optimal range.

Description

Every gun has two falloff ranges, falloff start and falloff end. When hitting an enemy within the weapon's falloff start range, the shot will experience no damage falloff and will simply deal the full amount of damage. Beyond the falloff start range, damage will fall linearly such that it would reach zero at the falloff end range - however, the damage can never fall below 10% of its initial value. Beyond the falloff end range the weapon will always just deal 10% of its initial damage.

Formula

The formula for the damage a bullet does ($d(x)$) at a range $x$ is given by:

$d(x) = \begin{cases} d, & \text{if } x \le \text{start} \\ d \frac{\text{end} - x}{\text{end} - \text{start}}, & \text{if } \text{start} < x < \frac{9 \text{end} + \text{start}}{10} \\ 0.1 d, & \text{if } x \ge \frac{9 \text{end} + \text{start}}{10} \end{cases}$

Where $\text{start}$ is the falloff start range, $\text{end}$ is the falloff end range, and $d$ is the initial damage of the bullet. Note the unusual terminals for where falloff ends, this is due to the fact that the linear falloff would reach zero by the falloff end range, but is not allowed below 10% of the initial value, thus falloff actually ends slightly before falloff end.

Falloff Ranges by Weapon

Melee weapons never experience damage falloff.

Main Weapons

Weapon	Falloff Start (m)	Falloff End (m)
Shelling S49 Pistol	9	45
Shelling Nano Burst Pistol	7	47
Bataldo 3RB HEL Revolver	10	80
Raptus Treffen 2 Machine Pistol	5	35
Raptus Steigro HEL Autopistol	5	55
Accrat Golok DA Bullpup Rifle	10	65
Van Auken LTC 5 SMG	6	55
Accrat STB PDW	5	47
Accrat ND6 Heavy SMG	7	60
Van Auken CAB F4 Carbine	10	65
TR22 Hanaway DMR	50	100
Hanaway PSB Double Tap Rifle	40	90
Malatack LX Assault Rifle	10	70
Malatack CH 4 Burst Rifle	20	85
Drekker Pres MOD 556 Rifle	22	80
Buckland SBS III Sawed-off Shotgun	6	40
Bataldo J 300 HEL Shotgun	4	40
Bataldo Custom K330 Slug Shotgun	6	40

Special Weapons

Weapon	Falloff Start (m)	Falloff End (m)
Malatack HXC Heavy Assault Rifle	12	80
Drekker CLR Short Rifle	8	58
Buckland S870 Shotgun	4	40
Buckland AF6 Combat Shotgun	5	45
Drekker INEX Drei Scattergun	4	30
Buckland XDIST2 Choke Mod Shotgun	15	80
Mastaba R66 Revolver	12	80
Techman Arbalist V Machine Gun	15	80
Techman Veruta XII Machine Gun	15	80
Techman Klust 6 Burst Cannon	15	80
Omneco EXP1 HEL Gun	15	90
Shelling Arid 5 High Caliber Pistol	8	65
Drekker Del P1 Precision Rifle	30	70
Köning PR 11 Sniper	60	100
Omneco LRG HEL Rifle	40	80

Example Calculations

Range at which the High Cal Pistol stops bodyshotting Strikers

Assuming this range is somewhere within the linear falloff region, we know that the total damage inflicted by a bodyshot ($D(x)$) at some range $x$ is:
$D(x)=d{\frac {{\text{end}}-x}{{\text{end}}-{\text{start}}}}$

Rearranging for $x$ gives:
$x={\text{end}}-{\frac {D(x)}{d}}\left({\text{end}}-{\text{start}}\right)$

For the shot to exactly kill, we need $D(x)$ to be equal to the Striker's health (20). So substituting in all our values we have:
${\begin{aligned}x&=65-{\frac {20}{30.1}}\left(65-8\right)\\&=27.13\end{aligned}}$

The High Cal Pistol will bodyshot Strikers out to 27.13m. Any distance beyond this, and the damage will fall below this breakpoint.

Range at which the Pistol stops three-shotting Strikers

Assuming this range is somewhere within the linear falloff region, we know that the total damage inflicted by a headshot and two bodyshots ($D(x)$) at some range $x$ is:
$D(x) = d \left(\text{Precision Multiplier(Pistol)} \cdot \text{Headshot Multiplier(Striker)} + 2\right)\frac{\text{end} - x}{\text{end} - \text{start}}$

Rearranging for $x$ gives:
$x = \text{end} - \frac{D(x)}{d \left(\text{Precision Multiplier(Pistol)} \cdot \text{Headshot Multiplier(Striker)} + 2\right)} \left(\text{end} - \text{start}\right)$

For the shots to exactly kill, we need $D(x)$ to be equal to the Striker's health (20). So substituting in all our values we have:
$\begin{align} x &= 45 - \frac{20}{4.64 \left(0.8667 \cdot 3 + 2\right)} \left(45 - 9\right)\\ &= 11.27 \end{align}$

The Pistol will three-shot Strikers out to 11.27m. Any distance beyond this, and the damage will fall below this breakpoint.

As a quick sanity check, we could verify that one shot still breaks the head at this range. The damage of a single shot at this range is:
$\begin{align} d(11.27) &= d \frac{\text{end} - x}{\text{end} - \text{start}}\\ &= 4.64 \frac{45 - 11.27}{45 - 9}\\ &= 4.347 \end{align}$
Which, when headshotting a Striker, deals $4.347 \cdot 0.8667 \cdot 3 = 11.3$ damage, which is still enough to break the Striker's head (the head having 10HP).