Bradley-Terry models and "retrodictive" ranking
 
David Firth
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. 
 
Reference:
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
 
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