this ain't soccer or football - home field for the most part means squat. Now this is a little weird since baseball has the most severe home field advantage (the last at-bat as well as parks of different shapes) but that does not make it less true. What is home field advantage? The ability to have a Game 5 or Game 7 at your house. So what has happened in the annals of deciding games this century:
2015: Road team won both wild card games, KC and Toronto won LDS home Game 5, Mets won LDS road Game 5 ... (home teams 2-3 overall)
2014: Royals won home wild card, Giants won road wild card, Giants won WS Game 67 on road ... (home 1-2 in season ... 3-5 overall)
2013: Rays won road wild card, Pirates won home wild card, Cardinals won home LDS Game 5 ... (home 2-1 ... 5-6 overall)
2012: Orioles, Cardinals won road wild card, Yankees won home LDS, Tigers won road LDS, Cardinals, Giants won road LDS, Giants won home LCS ... (home 2-5 ... 7-11 overall)
2011: Tigers won LDS home, Cards won LDS road, Brewers won LDS home, Cards won WS home (home 3-1 ... 10-12 overall)
2010: Rangers won LDS road (home 0-1, 10-13 overall)
2008: Rays won LCS home (home 1-0, 11-13 overall)
2007: Red Sox won LCS home (home 1-0, 12-13 overall)
2006: Cards won LCS road (home 0-1, 12-14 overall)
2005: Angels won LDS home (home 1-0, 13-14 overall)
2004: Astros won LDS road, Red Sox won LCS road, Cards won LCS home (home 1-2, 14-16 overall)
2003: Red Sox won LDS road, Cubs won LDS road, Marlins won LCS road, Yankees won LCS home (home 1-3, 15-19 overall)
2002: Twins won LDS road, Giants won LDS road, Angels won WS home (home 1-2, 16-21 overall)
2001: Mariners, Yankees, Diamondbacks won LDS home, Diamondbacks won WS home (home 4-0, 20-21 overall)
2000: Yankees won LDS road (home 0-1, 20-22 overall)
So home teams are 20-22 in deciding games ... not much of an advantage. Now this does not mean teams with home field are not more likely to win than those without (I did not test that) ... of course they are, but that is because they have better records (at least the division champs do) and thus are likely better teams in the first place.
Getting the team ready - healthy or whatever - trumps home field by a lot.