How are backgammon players' ratings actually calculated? ($15)

I am interested in finding out the **mathematical details / formulas**
(as opposed to vague / high-level information) behind the backgammon
rating system (each player is assigned a rating; by beating a higher
rating than yourself you score more points than if you beat a lower
ranked player, etc.).

I am interested in the backgammon system only (not the chess one which
may looks similar but differs in ways important to what I am trying to
get at).

Again, mathematical details required.  I want to be able to calculate
ratings myself based on the information found.

Clarify a little please... are you referring to a specific internet
backgammon site, a specific real-life league, or what?