It is the same way a football fan thinks he helped his team win by watching on the sidelines while the players do the work and give you the illusion of participation.

Shouting racist slurs at the opposition, making monkey noises and throwing bananas is surely why my team won the match! Couldn’t have done it without us.

The thrill of victory, without the agony of defeat.

Thats what $200 for a ticket to any N*L sunday football event buys you.

T-shirts are extra, and if we win, we sell more of them.

The hard working, professional, polite members of society benefit from the release I think.

isn't "home match" usually more favorable? Like you usually play better when you play in your home country.

There is some evidence of that, where the closer the crowd is to the field the more likely the referees are to call in the home team's favour. There was a study on this, probably close to a decade ago now.