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As for baseball specific home edges.  It is important to remember that parks are built to cater to different strengths.  All year long the talk of what a great job Z has been doing pulling in LEFTY hitters because Safeco destroys most righties.  Well, that implies that the previous administration was NOT doing a good job of tailoring the team for the park.  If a park is tailored to help lefty bats, and kill righty bats, then you want a lot of lefty hitters AND lefty pitchers on your team.  If you end up with a team full of righties -- well, you're gonna have some serious home issues.
So, whereas football and basketball have identical playing areas, and the edge CANNOT come from park design, baseball can (and likely does), have very significant home edges that are based on matching personnel and park.
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That said, a large part of the game is defense.  And defensive players learn the intracacies of THEIR home park over time.  The more you play in Safeco, or the Metrodome, or Fenway, the more you learn to anticipate caroms and positioning of that park.  Some parks, learning the OF is more important, (Metro-bag), some places the infield is an adventure for visiting teams due to the specs of the local groundskeepers. 
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Ultimately, baseball is likely to have the smallest "psychological" skew for home/away because baseball is the one sport where the field changes in every venue, and where how you tailor your roster to the park impacts the aggregate numbers.