Bradley-Terry models and "retrodictive" ranking
University of Warwick and the Alan Turing Institute
The Bradley-Terry model for pair comparisons, and its extensions, are widely used in various scientific and social-science research contexts, as well as in some very non-academic domains such as predictive modelling in sports. A recent paper of Aldous (2017) highlights some interesting aspects of the models, from an applied probability perspective. In this talk I will discuss some key elements of so-called "retrodictive" modelling via Bradley-Terry-type models, where the aim is to report informatively on the relative standings of (say) soccer teams in the present season, rather than to predict future outcomes. A crucial constraint is that a retrodictive ranking should respect the structure and scoring system of a competitive league, such as the double round-robin structure and 3-1-0 points system that is used worldwide in soccer leagues. The current season of the English Premier League will illustrate.
Aldous, D J (2017). Elo Ratings and the Sports Model: a Neglected Topic in Applied Probability? https://www.stat.berkeley.edu/~aldous/Papers/me-Elo-SS.pdf