This predictive model works on estimating two numerical characteristics per team, an Offensive Strength Factor (Off(t)) and a Defensive Strength Factor (Def(t)). The model assumes that the score (S) achieved by a team 'A' when playing against team 'B' is given by:
S(A) = Meanscore * (Offense(A)/Defense(B)) +/-
where Meanscore is a common mean score factor for all games played. To account for differences between 'home' and 'visitor' team performance, an additional 'home advantage' factor is added (for the home team) or subtracted(for the visiting team) to the equation. Because there are separate home and visitor scores, each is computed independently:
Home_Score = Meanscore * Home_Offense_Factor/Visitor_Defense_Factor + HomeAdvantage/2
Visitor_Score = Meanscore * Visitor_Offense_Factor/Home_Defense_Factor -
The offensive strength factor can be interpreted as the ability for a given team to score points, where the defensive strngth factor can be interpreted as the ability to prevent the opposing team from scoring points. The effect on a given score is determined by the ratio of one team's offensive strength to the other team's defensive strength. This model effectively breaks each game into two sub-
The challenge is in finding sets of coefficents (Meanscore, HomeAdvantage, Offense and Defense ratings) that fit the scoring data from previous games. One can use an iterative method shown below, which is similar to that shown for estimating the MOV model parameters.
In the above algorithm, as in the MOV fitting algorithm, 'eta' is the learning rate constant, and will typically be set in the range of 0.001-
While this model's game-
I have also put some of these throught s down in a short PDF technical memo A Method for Determining Relative Offensive and Defensive Strengths of Football Teams (PDF) with respect to ranking teams two dimensionally.