Albrecht Matrix Hybrid
The Matrix Hybrid is a college football rating system that was developed by Scott Albrecht in 2006, and has been revised several times since. The hybrid rating is a compilation of the Matrix-Performance and Matrix-Elo ratings. The Performance rating uses location and point margin to rate teams, and the Elo rating uses location and win/loss outcome. Variations of these ratings also adjust for luck (an exceptional number of turnovers, field goal successes or failures, etc.), how well a team matches up against its opponents, and allow a team's performance to trend over time.
Both ratings are based on a probabilistic iterative-fitting model. In the Performance rating, point margins are converted into probabilities based on the standard deviation of a team's performance from its "mean". In this case, a probabilistic model gives greater weight to points score in close games. For the Elo rating, probabilistic outcomes of one and zero are assigned to wins and losses, respectively. An iterative method has the distinct advantage when dealing with only wins and losses that a best fit short of infinity can be found for undefeated and winless teams. The Matrix-Elo was inspired by the Chess Elo rating system.
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