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SAS Code

 

Consider the following “season” involving a total of 8 games among 5 different teams, as described in the paper.

 

 

Game 1: Team A defeated Team C               Game 2: Team A defeated Team E

 

Game 3: Team B defeated Team A               Game 4: Team B defeated Team E

 

Game 5: Team C defeated Team D               Game 6: Team C defeated Team E

 

Game 7: Team D defeated Team E                Game 8: Team D defeated Team E

 

 

We will code five teams as A=1, B=2, C=3, D=4 and E=5.  We will use 0 as the code for the “generic” non-Division 1A team and use 200 as the code for the “virtual” team.  Note that the “generic” non-Division 1A team is not really needed here since it does not participate in any games.

 

The SAS code below will rank the five teams based on the season above.

 

options ps=600;

data football;

input winner loser;

cards;

1  3

1  5

2  1

2  5

3  4

3  5

4  5

4  5

0 200

1 200

2 200

3 200

4 200

5 200

200 0

200 1

200 2

200 3

200 4

200 5

;

data newfootball(keep=win x1-x6);

array x{6} x1-x6;

set football;

do i =1 to 6;

x(i)=0;

end;

if (winner <200) then x(winner+1)=1;

if (loser <200) then x(loser+1)=-1;

win=1;

proc logistic ;

model win = x1      x2      x3      x4      x5      x6   /noint link=probit;

run;

 

 

The output from SAS is:

                                        

 

              Parameter      DF    Estimate   

              x1            1           0   

              x2            1      0.2615   

              x3            1      0.5813   

              x4            1      0.1519   

              x5            1     -0.0412   

              x6            1     -0.9731   

 

 

 

The estimate for x1 corresponds to the “generic” non-Division 1 team and can be discarded, while the other five values are used to rank the five teams:

 

Team          Theta            Rank

 A            .2615            2nd

 B            .5813            1st (Best)

 C            .1519            3rd                              

 D           -.0412            4th

 E           -.9713            5th (Worst)