  We study the ranking of individuals, teams, or objects, based on pairwise
comparisons between them, using the Bradley-Terry model. Estimates of rankings
within this model are commonly made using a simple iterative algorithm first
introduced by Zermelo almost a century ago. Here we describe an alternative and
similarly simple iteration that provably returns identical results but does so
much faster -- over a hundred times faster in some cases. We demonstrate this
algorithm with applications to a range of example data sets and derive a number
of results regarding its convergence.
