In my first post about Elo ratings in football I posted the code for a R function where you could adjust the ratings to account for home field advantage. The method is simple: Some extra points are added to the home teams rating when the match predictions (which is based on the ratings) are calculated. My implementation did only support giving a the same fixed amount of extra points to all teams in all games. In other words it is assumed that all teams have the same home field advantage, and that the home field advantage does not change over time. This is of course unrealistic if the point of the ratings is to give as accurate predictions as possible. Still the method is used in the FIFA Women’s World Ranking and in the World Football Elo Ratings.
I know of two ways to implement a more dynamic (and more realistic) home field advantage. The ClubElo ratings (which is perhaps the best football rating site out there), developed by Lars Schiefler, let the home field advantage change over time, similar to how the ratings change. This is done by updating the home field advantage after each game based on the home team’s performance. An article on the ClubElo site describes the details very well.
A rather different method is used in the pi-rating system, developed by Anthony Constantinou. Each team have two ratings, one describing performance when playing at home, the other when playing away. The cool thing about the way this is done is that the two ratings for a team are not calculated separately from each other. It is not the case that only the home matches are used to calculate the home rating and away matches to calculate the away rating; After each match both ratings are updated. The home rating for the home team is updated almost like the regular Elo ratings, and the away rating is then also updated based on how much the home rating has changed, scaled by a factor. That way the two ratings are allowed to deviate from each other, giving rise to an adaptive, team specific home field advantage. The procedure is of course also applied to the away team’s ratings.
The pi-ratings, by the way, are interesting in other ways besides the method for determining the home field advantage. Instead of the ratings being somewhat arbitrary numbers, like most Elo systems, the pi-ratings directly models goal differences. The details are described in the paper Determining the level of ability of football teams by dynamic ratings based on the relative discrepancies in scores between adversaries. A draft of the paper is also available at the pi-ratings website. While I am at it, I can also recommend Constantinou’s other papers on football prediction.