- Student Participants
- John Holodnak (Ohio Northern)
- Chandler May (Harvey Mudd)
- Daniel Moeller (Notre Dame)
- 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
- 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
- Details are in this
- 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