As in orthodox, he manages to avoid hearns right hand and can fire back with left hooks and his own right hand. In the southpaw stance round 1, his face bloodied by hearns cutting right hands. Was this another factor? Also Hagler tried to outbox ray Leonard I think the southpaw position if I remember when he should of started orthodox and he wouldn't gave way the first few rounds. A mistake that cost him the fight.
Regarding the Hagler-Leonard fight, I think you have it the wrong way round - Hagler started orthodox, and many people claim that he lost those early rounds and it cost him the fight. Personally, I thought he was doing okay against Leonard in the orthodox stance. If he lost some early rounds it was more due to Leonard being good and mobile than because of Hagler's stance. Leonard began to tire and get caught more, and move less, as the fight progressed and Hagler's punches took their toll. I thought Hagler narrowly deserved the decision.