I always assumed the main benefit to starting with a reliever was that you can start with a reliever with opposite splits of the "starter" that would come in for the 2nd inning. If you have Rich Hill up in your rotation,the opposition would pack the line up with righties, and the top of the line up is where you put your best hitters, for obvious reasons. But if you bring in a right-handed reliever to start the game, you either get an inning of good match ups, or you cause a bunch of early-game, non-double-switch PH/defensive switches (unless the other team is also starting the game with a reliever) OR at the least, you force the other team into putting their best split-dependant hitters lower in the order. Am I thinking of this wrong? I think the make up of the bullpen plays a lot into how beneficial it can be.