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All that, and I forgot to include ... the home pitcher is pitching on a mound that he gets to throw off of routinely. How much of hitter home edge is actually pitcher road-mound issue?
Summary of home/road factors in baseball NOT present in NFL/NBA:
Mound (home pitcher has edge)
Defense (home fielders have edge)
Park (team can be tailored to park - so home hitters CAN have edge)
Then, of course, there is the actual travel and living out of suitcases.