There are a few things to account.
A team playing at home will have:
– a terrain advantage: even in multi-million $ stadiums, there is an ever so slightly difference in the grass/material covering the court. While in “low ranking” matches we’d need a much bigger difference in the flooring’s quality to alter the quality of the game done by the players, at high level matches, that few millimeters of difference or in humidity or whatever can change the team’s play’s quality. Playing at home means that you’re playing on the very same ground you have trained on.
– a public advantage: while in big competitions supporters may do the move to cheer their team, they are rarely going to outnumber the locals coming to cheer their team. Your public knows you. Through time, the people cheering you on will be more and more “familiar” with you, even though you wouldn’t be able to recognize any of them in the street. You start to enjoy their specific energy, their way of lifting you on. Playing as the invite, you might have some supporters of yours in the stadium, but you’ll mostly have supporters of other team(s), people that are not as familiar to you as your supporters. This has a huge effect: the result of a game is a lot of technic, but there is a non-negligible part that comes from the strength your supporters breathe in you.
Specifically for hockey, home “ice” advantage means you get what’s called last change. This means the visiting team has to put their players out first, and the home team gets to see who comes out before deciding who to send out to counter. It’s why you see some matchups change depending on where it’s played.
Less subconscious mental effort is spent by the home team – since the surroundings are familiar they can easily filter out extraneous stimuli and distractions, whereas visiting team needs to focus harder to filter these out.
Kinda like when you are driving a new route, the trip feels longer and more arduous. If you’re driving the same route day in day out you filter out most of the crap around you, since your brain knows it doesn’t need to pay attention, and even long drives can feel quick
Home field advantage is influenced by the following factors:
1. Crowd support
2. Familiarity with the environment
3. Travel fatigue
4. Referee bias
The following article goes into details and looks at the statistics of home field advantage in soccer: https://graspthegame.com/soccer/fields/home-advantage-in-soccer/
Interestingly, it seems that advantages will differ depending on the level of competition, the country and between men’s and womens sports. It also shows that home field advantage is slowly becoming less important over time.
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