Both SR and MMR are influenced by stats (below diamond). “Well, the amount of MMR (and SR) you go up or down isn’t simply a matter of whether you won or lost … As a minor factor, we also do evaluate how well you played the heroes you used in a match.” – Scott Mercer, Overwatch Forums
This was updated to remove the effect below diamond (Overwatch Forums), as well as other various changes, but performance affecting SR has never been removed, and has been restated recently (Groups and Matchmaking in Overwatch).
For the full story, see How Competitive Skill Rating Works (Season 12), performance modifier section.