Does playing at home influence referees' decisions?
Answering that question may depend on which side fans are on for a given match, and what the outcome of the game is. But there is growing evidence that referees do inadvertently tip the balance in the home side's favor more often than not.
In this article from The Guardian, Sean Ingle discusses the ways in which a home crowd can help their team receive fewer cards, as well as increase injury time if the home side needs more time to get a result.
These results are not only present in English and German soccer, the countries highlighted in the article, as evidence from other sports, including the NBA, also supports the hometown bias.
Still, given the frequent complaints leveled at officials from fans of home teams, the bias isn't the sole determinant of outcome, and obviously has a larger impact on some contests than others. Furthermore, if cheering for one's team and trying to coerce favorable decisions from referees is a hallmark of attending games for fans, the article notes that the impact of fans on actually helping the team perform looks to be negligible, at least statistically.
Don't let that hold you back from heading to the stadium and cheering on your local team, though – you could help give the home team the slightest of edges.