Shotgun spread

Deadline 0.25.2 spread math, defaulting to the stock R870 00 buck setup.

Ammo presets

12g 00 buck, 9× 00_buck_piece.

Hit region

Flat frontal silhouette, so each pellet counts once against one part.

barrel_deviation

buck_barrel_deviation

Use buck deviation

spread_multiplier

spread_factor

Higher pulls pellets toward center, lower toward the edge.

Target distance

Projectiles

Seed

Game formula

input = use_buck_deviation ? buck_barrel_deviation : barrel_deviation max = tan(input / 100) * spread_multiplier dir = Vector2(rand(-1, 1), rand(-1, 1)).Unit vec = dir * max * (rand(0, 1) ^ spread_factor) final = (barrelCFrame * CFrame.Angles(vec.X, vec.Y, 0)).LookVector

Hit probability

F(r) = (r / max) ^ (1 / spread_factor) theta = atan(t) + k*pi/2, t ~ U(-1, 1) P(part) = E_theta[F(r_out) - F(r_in)] P(hit) = sum P(part) over region E[hits] = n * P(hit) P(1+ hit) = 1 - (1 - P(hit)) ^ n

Integrated exactly, not sampled. Verified against a 4,000,000 pellet Monte Carlo run.

Impact pattern

Max radius

Avg radius

Max angle

Avg angle

hit

miss

aim center

max cone

hit region

character parts

Hit chance per pellet

Expected hits

Chance of 1+ hit

This seed