next up previous
Next: Technical Issues Up: Ratings Previous: Introduction

Soccer Ratings

The rating system I have developed for soccer teams is a dynamic generalized linear model (see eg. Multivariate statistical modelling based on generalized linear models by Ludwig Fahrmeir and Gerhard Tutz) based on the Bradley-Terry model for paired comparisons, which is also known as a logistic model. The basic formula relating ratings to winning probabilities (ignoring ties) is

displaymath19

where P is the probability that the home team wins, tex2html_wrap_inline23 is a parameter representing the home field advantage (specifically, its the log odds for a home team victory when the two teams are evenly matched), and tex2html_wrap_inline25 is a scale parameter chosen so that a rating difference of 100 points corresponds to a probability of 2/3 of victory for the higher rated team at a neutral site, ie.

displaymath29

tex2html_wrap_inline31 and tex2html_wrap_inline33 are the home team rating and the away team rating, respectively.

Here is a brief table of winning probabilities for the higher rated team, ignoring home field effects:

		Diff    Prob

		  0 	0.500
		100 	0.667
 		200 	0.800
 		300 	0.889
 		400 	0.941
 		500 	0.970
 		600 	0.985
 		700 	0.992

For the 1995 NCAA men's and women's Division I teams, the home team wins about 60% of the time, which corresponds to

displaymath35

To put it a different way, the home field advantage corresponds to a rating difference of close to 60 points in this system.



Albyn Jones
jones@reed.edu
Wed Jun 19 15:59:37 PDT 1996