# Football Forecasting - Offense/Defense Model - EdsCave

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## Football Forecasting - Offense/Defense Model

Football Forecasting

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)) +/- HomeAdvantage/2

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  - HomeAdvantage/2

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-problems, independently estimating both the home team's socre and the visiting team's score.

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 0.001-0.01.   The result of this algorithm are sets of offensive and defensive parameters for each tema that can be plugged into the model equation above for predicting each team's scores.  As an example of the algorithm's accuracy, the following graph shows the weekly and cumutive ability to call winning teams one week out for the 2014 NFL season:

While this model's game-calling accuracy (64% for the 2012 season) is comparable to that of the MOV model, this is not what I consider its most important feature. For fans, the parameters for team offensive and defensive strength may be far more interesting than the predictions, and could be the basis for some serious discussion, as they allow one to compare team offensve and defneisve strength ni a two-dimensional manner.  The figure below is a graphic representation of the offensive (fb\$OFF) and defensive (fb\$DEF) model parameters plotted for each team. Note that having a good offensive rating does not automatically result in a correspondingly good defensive rating, and vice-versa. These values were calculated on the basis of all games in the 2014-2015 season.

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.

DISCLAIMER !

Professional odds-makers have better predictive methods and algorithms than this one. This algorithm will NOT let you beat the odds in a consistent manner in Las Vegas-style gambling.