So far I looked at 10 games in the EPL (May 2 to May 4, 2015), Serie A (May 2 to May 6, 2015), La Liga (May 8 to May 11, 2015), and MLS (May 15 to May 17, 2015). The odds could have changed between when I looked at them and the start of the game, but hopefully not by much. Two MLS clubs play an MLS game tomorrow before the ones I looked at. For each game I gathered the ratio odds for the favorite, the points per game for each club, and the points per game differential. Then I calculated 11 correlations. Each one was between the ratio odds and the points per game differential or the points per game differential + a home field advantage from 0.1 to 1.0 in increments of 0.1. The correlations are negative because the bigger the points per game differential, the less profit you make from betting on the favorite. For the EPL the correlation peaked at a home field advantage of 0.4 points per game. For Serie A and La Liga the correlation peaked at a home field advantage of 0.5 points per game. Because MLS has more parity between clubs, the correlation peaked at a home field advantage of 0.8 points per game. MLS has fewer games where the better club is better by enough to be favored away. For MLS the correlation without any home field adjustment was a very weak -0.0562. For the EPL the correlation without any home field adjustment was -0.6063, which is bigger than the MLS correlation with a home field advantage of 0.4 points per game. I might look at the record of the home club compared to the better club in games with winners where the better club (measured by points per game) was away and compare leagues that way.
Familiarity. Travel. Support from home fans. Pressure from home fans on referees. Hostility towards opponents and officials. Sometimes: climate, geographical location.
Based on what henryo posted, the average points per game is 1.651 for the home club and 1.090 for the away club.
Base on 332,276 games played Worldwide since 1960s, should be quite accurate... http://aragon.ws/teamstats/leagues.php
A lot of things contribute to home field advantage. Something about the field itself can be a home field advantage. It's up to the home field coach has to find out what that is and make it an advantage for his team. Winds, sun, narrow field, players ability, how they play on it, etc. On fans they could have an effect, but it's not as big as the fans think. Unless they start throwing things at the opponents player or lasers in their eyes. Or anything else they can think of to intimate a player and their teams fans.