Kendrick Savage |
School: University Of Mississippi
Major: Mathematics Mentor: Dr. James Reid Expected Graduation Date: May 2006 Organizations & Honors:
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ABSTRACT
A Matrix Eigenvalue Approach to Team Rankings
| A fundamental problem in ranking sports teams is the incomplete nature of most competitions where some teams play each other and some do not. It is challenging to compare teams that do not play each other. An example of this phenomenon is the controversy surrounding the selection of the 2003 NCAA Division 1 Football Champion. Both Louisiana State University and the University of Southern California were named champions by different polls. A reason for the uncertainty as to which of these teams should be higher ranked is the fact that they did not play each other. In fact most of the NCAA Division 1 teams do not play each other as there were 117 such teams in 2003 but each team played roughly 12 games. Hence each team only plays roughly 10% of all the other Division 1 teams. This situation is analogous to the problem of ranking web pages where some pages are linked to each other but the vast majority of web pages are not. The internet search engine Google assigns a rank to each web page called the pages “pagerank”. The method Google uses is to model the importance of a particular page relative to the importance of pages that are linked to this particular page. The ranking vector of all web pages is an eigenvector of a matrix. Motivated by the success of the Google pagerank ranking scheme, we apply a similar ranking scheme based on eigenvectors to the 2003 NCAA Division 1 Football Season. We will find the Division 1 School with the largest ranking in the real positive eigenvector of largest modulus. The results of this research will have applications to practical personnel assignment problems. The incomplete information available is the common difficulty of each of these problems: ranking web pages, ranking sports teams, matching job applicants to positions. |