Visualizing the non-normal pattern of archery
I recently read an article published in 2012 by Technical Archery that focused on understanding why archery shot patterns did not follow a Gaussian distribution. The article summarized that the non-normal distribution was, "consistent with a two dimensional error model where the archer's shots have normally distributed errors in both the horizontal and the vertical."
Predicted shooting results for 2000 arrows showing the distribution of shots from the center with a standard deviation in both the X and Y direction of 1.
Source: Technical Archery
The model they created showed that archery shots will typically form a doughnut-shape around the bullseye when accounting for errors in the X, Y, and Z directions. Below is a visualization of the shooting error model of 2000+ shots Technical Archery produced. It was created using QGIS and Mapbox GL. The data is available at the bottom of the article page.