# 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