I would expect Stand Your Ground laws to cause an uptick in violent crime when first instituted.
Why? Because potential victims would be facing down attackers instead of being legally required to run. Criminals not used to that tactic are going to suddenly be facing off against someone who might have gotten away.
I think after a few successful self defense shootings though the word will spread that someone who doesn't run may be packing.
In states where you are practically required to run away I think the situation will remain worse, while SYG has promise to reduce crime over time. I think legally requiring someone to be a victim is a travesty in of itself, regardless of whether SYG contributes or reduces crime.