At least with home matches they are more motivated to play more all out because they want to give the best for the supporters who do support them in the stands. On the other hand, the presence of supporters will also ultimately provide a greater intimidation for the away team considering that we know that with the cheers or chants given by supporters apart from bringing enthusiasm to the club being supported, this could also make the mentality of the opposing players weaken.
But in the end this is only a small part of the supporting instrument because it remains regardless of home or away the match is determined through the performance of the players in 90 minutes of matches that can be decisive. Performance on the field is an important factor in this case if indeed a match is to be won.
Anyway, home matches have an advantage and a greater chance of winning because the support of the fans will provide encouragement for the players they support so that they can achieve the expected results. But this depends on the club being supported if the support is a lower level club or mid-table home matches cannot be a benchmark because stable performance affects their appearance on the field not only by the screams and songs of fans, but if the support is a big club like PSG then the home match will make that club a favorite for bettors and there is also no doubts about winning and usually big clubs rarely lose when playing at home.
Yes, it's true that the players' appearance is number one. If the players' performances are mediocre and they don't have more motivation to achieve victory then it will be difficult to achieve, and in the end the fans will be disappointed if the club they support loses or only achieves results. draw, therefore the home match is not always the benchmark because the club's performance is an important factor in achieving victory.