Armchair analysts and sports scientists have come up with all sorts of theories to explain why playing at home helps. In 2007 a study investigated the influence of crowd noise on referees in the English football Premier League. It showed that some were more likely to flash yellow cards and award penalties against touring players than the hosts, because they relied on the split-second rise in the home crowd's roar as a cue to determine if a tackle deserved punishment. In the most recent season of the Spanish football Liga, two-thirds of all penalty kicks were awarded to the home team. Biased referees are not the only worry for visiting teams. Hectic travel schedules can tire them out and unfamiliar conditions can spook them. Foreign teams sometimes struggle against Bolivia at its Hernando Siles stadium, which lies at a headache-inducing altitude of 3,636 metres (11,932 feet). A bit of gamesmanship also comes in handy. One successful London football club reputedly offers a cramped away-team dressing room with low kit-lockers and high shirt-hangers.
Do these factors really make a difference? The numbers suggest that they do. In the latest English football season, the top 20 clubs enjoyed a home success rate of 50%, while their victory rate on the road was 32%. In 12 of the past 19 World Cups the host nation has made it to the semi-finals and six times it has gone on to win. The effect can be seen in other sports too. Before the start of the London Olympics in 2012, UK Sport, a government agency, pored over the results of more than 100 big tournaments across 14 Olympic sports and predicted that the London home advantage would boost Britain's medal haul by as much as 25%. As it turned out, Britain bettered its 2008 performance by winning 18 more medals (10 of them gold), an improvement of 38%. At the Beijing games, China won 59% more medals than it had done at the 2004 Athens games. Russia topped the medal table in Sochi; in the previous winter Olympics it had come sixth.
http://www.economist.com/blogs/economist-explains/2014/06/economist-explains-6
I think to some extent this is also true for the NFL but not aware of any study.
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