Links:
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)