Understanding position and rotation in this context

I am watching various videos related to understanding rotation in particular but it isn’t quite sinking in. I need a solution to solve a particular need and an example for this might help me understand the bigger picture. I am trying to place an avatar/player relative to my avatar and sure I can move and rotate it but not where I want without a lot of trial and error which means I don’t quite understand the formulas.

Imagine a baseball diamond with my avatar on the pitcher’s mound. I am facing second base. I can teleport a player to 3rd base (that formula works well enough). I would like to apply simple adjustments to place an avatar on 1st and 3rd base and even half way between those. Also behind me so essentially in a circle around me with each avatar facing me.

I don’t quite get what I multiply and what I add (though positional offset is easy to understand). A formula would be great but a tutorial that explains “arbitrary position and rotation” would be even better. I don’t really need “here is how to rotate an object around an object” I’m not animating anything and I’d like to know what to apply from my reference point to place an avatar just about anywhere on a plane around me.

Thanks.

I think I know what would help… perhaps someone knows about a Unity scene/project that shows a visualization of position and rotation of objects. Something that would allow for easy manipulation of the methods and values would be super cool.