College of Liberal Arts & Sciences
Samuel Burer - Colloquium Speaker
Abstract:
We investigate the sensitivity of the Colley Matrix (CM) rankings—one of six computer
rankings used by the Bowl Championship Series—to (hypothetical) changes in the outcomes of
(actual) games. Specifically, we measure the shift in the rankings of the top 25 teams when the
win-loss outcome of, say, a single game between two teams, each with winning percentages below
30%, is hypothetically switched. Using data from 2006–2011, we discover that the CM rankings
are quite sensitive to such changes. To alleviate this sensitivity, we propose a robust variant of
the rankings based on solving a mixed-integer nonlinear program, which requires about a minute
of computation time. We then confirm empirically that our rankings are considerably more robust
than the basic CM rankings. As far as we are aware, our study is the first explicit attempt to make
football rankings robust. Furthermore, our methodology can be applied in other sports settings and
can accommodate different concepts of robustness besides the specific one introduced here.