Home court advantage usually refers to the greater quantity of fans available to cheer for you when at home. The boost in morale along with the inherent familiarity make "home" the best venue to play...or fight. When we are talking about pitting heroes and villains from different Universes against each other, home court means even more.
Examples:
In the Star Wars Universe, Jedi and Sith can become closer to the force through training and meditation. In the Star Trek Universe, the force doesn't exist. If Darth Maul challenges Data to a duel on the USS Enterprise, does he still have the powers of the dark side or does is he confined to the physics of his new surroundings?
On the Earth of Dragon Ball Z, Goku uses Chi as the source of his power. Can he become a Super Sayian in Coast City or will he be no match for Green Lantern?
Within DC is an Anti-matter Universe in which evil is more likely to win--the inverse of DC proper where the good guys always prevail. The home court in this case directly determines the outcome of the battle.
For Combatic purposes, the arenas chosen will have a neutral effect on the powers of the ...