Home field advantage truly lies in the MLB where each and every stadium is unique. To understand how this came to be we need to look at the beginnings of baseball. While baseball respects the tradition of having defined rules for their infield, there is no rules saying what the outfield needs to looks like. This gave us strange looking outfields since the teams were trying to fit their stadiums into tiny spaces while keeping the infield the standard size.
If any sport can truly claim that they have a home field advantage its baseball.