Right hand shooting, right side of support. This combination maximizes your cover or concealement.
Right hand shooting, left side of support. This will expose more of you as a target, if that's what someone has in mind for you.
Overhead view of a shooter taking it left handed to maximize his cover.
If I had been a little more patient and focused, I could have taken maybe 2 more inches off the side to side. What I noticed is that the side to side movement would make this position beneficial for tracking moving targets. When positions have inherent directional instability, it usually works to work with it and control it rather than trying to eliminate it. At any rate, this is significantly better than what I do from offhand with no support.