Here, some quick vizualizations of Braun's usage and results this season for you.
His usage, primarily against other teams top lines. His results:
Brings goals against down, what the Leafs need. Also picks up PK time but I have a feeling you'll let me by with that. He's doing pretty well on an awful team, and playing an awful lot, for a 3rd pair guy.
Just in general, Braun is also a big defenseman who throws a good amount of hits. The kind of guy who excels in the playoffs once refs are a bit looser.