Summer 2009 REU Project

      Who's #1? The Science Of Building Ranking Systems

    Student Participants
    • John Holodnak (Ohio Northern)
    • Chandler May (Harvey Mudd)
    • Daniel Moeller (Notre Dame)

    Advisors
    • Carl D. Meyer (Faculty Advisor, NC State)
    • Ralph Abbey (Graduate Student Advisor, NC State)

    Project Description
    • Every day our lives are touched or influenced by some kind of ranking system. For example, the heart of Google's search engine depends on their innovative PageRank concept to rank the importance of web pages. Voting systems are ways to rank candidates running for an office. The BCS ranking systems determine who gets to play for the national championship in NCAA football. These are only a few of the innumerable places where mathematical models are created for ranking a set of competing entities. The purpose of this project is to investigate the scientific techniques used to create a variety of different ranking schemes. The ultimate goal is to try to build some new and innovative ranking models that can outdo some of the standard ones. While the applications are not necessarily tied to sports ranking, the abundance of sports data and statistics is a good place to start, so our project will begin by examining mathematical models for ranking sports competition, and we will build from there.
    • The tools employed are elementary probability, networks and graphs, linear algebra, and number crunching, so some elementary knowledge in these areas would be helpful.

    Conclusions & Results
    • We analyzed several different sports ranking models, applying them to the NFL. We then used three different approaches to examine whether rushing yards or passing yards is a better indicator of team strength. Each approach provided evidence that rushing yards is a better indicator of team strength than passing yards.
    • We learned about four different ranking models and the theory behind them.
    • We compared the four models and discovered that they are competitive with each other and with ESPN analysts (Chris Mortensen and Mike Golic).
    • We examined the correlation between score differences and rating differences and discovered that it was not strong enough to provide any significant conclusions.
    • We worked on optimizing hindsight accuracy and concluded that optimized hindsight accuracy did not imply optimized foresight accuracy.
    • We compared rushing yards and passing yards as measures of strength.
    • We looked at which performed better in the four models.
    • We determined that differences in rushing yards more closely correlates with differences in scores than passing yards.
    • We saw that teams that out-rushed their opponents were more likely win than teams that out-passed their opponents.
    • Details are in this article.

    Presentations
    • The article "Rush vs Pass: Modeling the NFL"
    • The poster presentation given at the Joint AMS MAA Mathematics Meeting, San Francisco, CA, January, 2010 and the Eighth Annual North Carolina State University Undergraduate Summer Research Symposium, McKimmon Center, NC State University, July 2009.

    Final Report