I've always wondered this. I knew off the bat that Hagler was a converted southpaw, because his right was clearly his dominant. I know this is not always the case as some right handed fighters best punch is the hook. But Joe frazier so dominant with his left, I can't help but wonder.
He damaged his left elbow as a child and it he could never straighten his arm properly after that. It's been suggested that it partially explains his power. But, no, he's right-handed.