A Mathematical Rating System (UMAP)

This module develops a mathematical model for rating a group of contestants based on the results of several head-to-head competitions. The model utilizes only the schedules and results (either as wins and losses or points for and points against) of the participants, summarized in a ratings matrix. Under appropriate conditions, row reduction of the matrix produces the ratings. The ratings are not uniqely determined, since the matrix will always have at least one dependent row. However, the difference between any two ratings is uniquely determined, enabling a precise ranking of participants and use of the model for prediciton of future results. Applications of the model include sports leagues and taste tests. College football and baseball examples are discussed in the module.

Table of Contents:

INTRODUCTION

POINT-SPREAD RATINGS

WIN RATINGS

THEORY

APPLICATIONS

OTHER RATING SYSTEMS

ANSWERS TO SELECTED EXERCISES

REFERENCES

ABOUT THE AUTHOR