Methods for sports ranking

Mentor: Dr. Braxton Osting, UCLA Mathematics

Any ranking method in sports (of which there are many) must address several inherent challenges, including (i) not all teams play all other teams, (2) there are inconsistencies in the data, i.e., team A beats team B, team B beats team C, and team C beats team A, and (3) the ``strength of schedule'' varies amongst the teams. Although this is an old problem, there have been several recent advances in both the methodological approach to the problem and the interpretation of the error in the solution (see the references below). In particular, the L2-HodgeRank method seeks a ranking which can be interpreted using the Hodge decomposition for edge-flows on graphs, while methods utilizing the L1-norm seek a ranking which has sparsest error. We'll continue to develop some of these ideas and apply them to generating sports rankings.

  • X. Jiang, L.-H. Lim, Y. Yao, and Y. Ye, Statistical ranking and combinatorial Hodge theory, Math. Program. Ser. B 127 (2010), no. 1, 203-244.
  • A.N. Hirani, K. Kalyanaraman, and S. Watts, Least squares ranking on graphs, (2011) submitted.
  • B. Osting, J. Darbon, and S. Osher, Statistical Ranking using the L1-norm on graphs, (2012) submitted.