A study out of Britain finds that there is a demonstrable and significant advantage given to home teams by referees w/r/t to red and yellow cards. This is true even when controlling for a really staggering number of variables.
Apparently, for sports fans, it's not just in our heads the refs really do favor the home teams. I'd love to see brain scans of referees looking at fouls without context, and then with people cheering for one side or the other. Ie, give refs a video of two teams playing, help them with cheers and boos to know which team is home and which is away and then show them the clips. Then simply flip the color of the jerseys for the control. See if it's reproducable in the lab, and also see what parts of the brain, and what stress reactions there are in the body. Finally it'd be interesting to see how quickly the decisions are made. Does a call going against the home team take longer to process and make. Is there an internal delay that slows this down? Man, I wish I had the time and money to study all the random things I find interesting.