Albrecht Matrix Hybrid
Encyclopedia
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
.
Sports rating system
A sports rating system is a system that analyzes the results of sports competitions to provide objective ratings for each team or player. Rankings are then derived by sorting each team's ratings and assigning an ordinal rank to each team starting with the highest rated team earning the #1 rank...
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
Turnover (football)
In American football, a turnover occurs when the team with the ball loses possession of the ball, which is then gained by the other team. The two events that are officially classified as "turnovers" are fumbles or interceptions In American football, a turnover occurs when the team with the ball...
, field goal
Field goal (football)
A field goal in American football and Canadian football is a goal that may be scored during general play . Field goals may be scored by a placekick or the now practically extinct drop kick.The drop kick fell out of favor in 1934 when the shape of the ball was changed...
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
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...
model. In the Performance rating, point margins are converted into probabilities based on the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
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
Elo rating system
The Elo rating system is a method for calculating the relative skill levels of players in two-player games such as chess. It is named after its creator Arpad Elo, a Hungarian-born American physics professor....
.