Random Walker Rankings for NCAA Football
Return to RWR Blog
Beginning & Disclaimer
Can monkeys rank teams?
What was wrong with the old BCS formula?
Want More Random Walker Ranking Details?
In addition to the rants on this collection of web pages,
we have written a pair of scholarly, academic articles about
ranking with random walkers. The now somewhat amusingly misnamed
"Division I-A Football" article (it was properly named when it
was submitted; and the Michigan Wolverines
hadn't famously lost to Appalachian State Mountaineers,
an FCS née I-AA program)
discusses a number of issues in greater depth
than covered on this website, including the community structure of
the football matchups network and its influence on rankings,
ideas about choosing a good p value, and the improved properties
of the RWFL ranking system.
''Random Walker Ranking for NCAA Division
I-A Football,'' T. Callaghan, M. A. Porter and P. J. Mucha,
Mathematical Monthly, 114, 761-777 (2007) [originally made available as arxiv.org/physics/0310148].
Each December, college football fans and pundits across America debate
which two teams should meet in the NCAA Division I-A National
Championship game. The Bowl Championship Series (BCS) standings employed
to select the teams invited to this game are intended to provide an
unequivocal #1 v. #2 game for the championship; however, this
selection process has itself been highly controversial in four of the
past six years. The computer algorithms that constitute one part of
the BCS standings often act as lightning rods for the controversy, in
part because they are inadequately explained to the public. We
present an alternative algorithm that is simply explained yet remains
effective at ranking the best teams. We define a ranking in terms of
biased random walkers on the graph formed by the schedule of games
played, with two teams (vertices) connected by an edge if they played
each other. Each random walker moves from team to team by selecting a game
and "voting" for its winner with probability p, tracing out a
never-ending path motivated by the "my team beat your team"
argument. We study the statistical properties of a collection of such
walkers, relate the rankings to the community structure of the
underlying network, and compare these rankings for recent NCAA
Division I-A seasons. We also discuss the algorithm's asymptotic
behavior, illustrated with some analytically tractable cases for
round-robin tournaments, and discuss possible generalizations.
''The Bowl Championship Series: A
Mathematical Review,'' T. Callaghan, P. J. Mucha and M. A. Porter,
Notices of the
American Mathematical Society 51, 887-893 (2004).
Abstract: We discuss individual components of the college
football Bowl Championship Series. Comparing with a simple algorithm
defined by random walks on a biased graph, we attempt to predict whether
the proposed changes will truly lead to increased BCS bowl access for
non-BCS schools. We conclude by arguing that the true problem with
the BCS Standings lies not in the computer rankings, but rather in