Links:

My home page

My college football rankings

R 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 assign numeric id’s to the five teams as A=1, B=2, C=3, D=4 and E=5.

The R code below will rank the five teams based on the season above. Simply paste all of the red code into R to run.

#David Mease 2006

#http://www.davemease.com/football

#the code below runs my simple example

#to run for different data, simply edit only the variables number_of_teams, number_of_games and input_matrix

number_of_teams<-5

#note: if you have an extra collect-all team for all non-Division 1A teams as I do for real data

#then this single team *should* count as 1 toward the total numbers of teams

#and it should be treated as a regular team throughout

number_of_games<-8

input_matrix<-matrix(0,number_of_games,2)

#the input matrix has two columns and one row for each game

#the first column is team id for the winner of the game and the second column is the team id for the loser

#the team id's should begin with 1 and be sequential

#for those of you familiar with R, you could instead create a data file containing

#this information and read it in using read.table or read.csv

input_matrix[1,]<-c(1,3)

input_matrix[2,]<-c(1,5)

input_matrix[3,]<-c(2,1)

input_matrix[4,]<-c(2,5)

input_matrix[5,]<-c(3,4)

input_matrix[6,]<-c(3,5)

input_matrix[7,]<-c(4,5)

input_matrix[8,]<-c(4,5)

#the data matrix has one column for each team and one row for each game

#the column for the winner of each game has a 1 and the column for the loser has a negative 1

#the data matrix is created from the input matrix automatically by this code so

#you only need to modify the input matrix

data_matrix<-matrix(0,(number_of_games+2*number_of_teams),number_of_teams)

for (i in 1:number_of_games) {

data_matrix[i,input_matrix[i,1]]<-1

data_matrix[i,input_matrix[i,2]]<-(-1)

}

for (i in 1:(number_of_teams)) {

#every team beats the virtual team exactly once

data_matrix[(number_of_games+i),i]<-1

#every team losses to the virtual team exactly once

data_matrix[(number_of_games+number_of_teams+i),i]<-(-1)

}

model<-glm(rep(1,(number_of_games+2*number_of_teams))~data_matrix-1,family=binomial(link=probit))

summary(model)

The essential part of the output from R is:

Estimate Std. Error z value Pr(>|z|)

data_matrix1 0.2615 0.6489 0.403 0.687

data_matrix2 0.5813 0.7468 0.778 0.436

data_matrix3 0.1519 0.6423 0.237 0.813

data_matrix4 -0.0411 0.6634 -0.062 0.951

data_matrix5 -0.9732 0.6697 -1.453 0.146

The five values in the “Estimate” column are used to rank the five teams:

Team Theta Rank

A .2615 2nd

B .5813 1st (Best)

C .1519 3rd

D -.0411 4th

E -.9732 5th (Worst)