There's a multitude of ways to look at these things. Whilst there's some discussions about "objective" ways to look at things, I'd suggest the following:
Umpiriing decisions for / against at home vs away for the same team. This would usually balance out whether a teams style of game sees a benefit from "the home town" umpires giving them more leniency/or more free kicks than away umpires do.
Win/loss record is usually higher for a team at home than away
Crowd noise has always been something which either consciously or subconsciouly impacts on umpires decisions. Less of a factor in Australia, but there's places overseas where the referees have had things thrown at them (basketball world cup, the home fans threw coins at the referees and visiting team), several referees have been murdered in Sth America (including one being beheaded by irate fans). Those types of factors have inflienced refereeing decisions, Umpires in Australia get securty guards to walk them through crowds for a reason, but maybe not to avoid beheadings.
Playing away takes more out of you physically. Earlier morning/late night flights, sleeping in hotel rooms or your own bed, disruption of normal routine at home, etc.
There may also be less support staff around you away than at home. Sure all the necessary people go, but maybe not everyone. In the old days of the NBL (I gave up following closely when the Titans slaughtered the memory of NMGiants) only a couple of clubs had won both games of the Doomsday Double (Adelaide/Perth in consecutive nights).
Familiarity with your home ground vs those who don't play there often. This is probably the one thing that negates a lot of Home Ground Advantage for Melbourne based teams. Clubs tend to play at your venue multiple times a year, so the "mysticism" of the venue is gone. There's also very little fatigue or disruption from playing "away" at a venue in Melbourne vs playing away interstate. Look at things like humidity, heat, wind (getting used to kicking with one blowing around a ground), firmness of the ground.
Home Ground Advantage is definitely a thing, but I'd argue more situational for Melbourne based clubs than permanent.
