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Prediction and modelling of competitive sports outcomes has received muchrecent attention, especially from the Bayesian statistics and machine learningcommunities. In the real world setting of outcome prediction, the seminal\'{E}l\H{o} update still remains, after more than 50 years, a valuable baselinewhich is difficult to improve upon, though in its original form it is aheuristic and not a proper statistical "model". Mathematically, the \'{E}l\H{o}rating system is very closely related to the Bradley-Terry models, which areusually used in an explanatory fashion rather than in a predictive supervisedor on-line learning setting.  Exploiting this close link between these two model classes and some newlyobserved similarities, we propose a new supervised learning framework withclose similarities to logistic regression, low-rank matrix completion andneural networks. Building on it, we formulate a class of structured log-oddsmodels, unifying the desirable properties found in the above: supervisedprobabilistic prediction of scores and wins/draws/losses, batch/epoch andon-line learning, as well as the possibility to incorporate features in theprediction, without having to sacrifice simplicity, parsimony of theBradley-Terry models, or computational efficiency of \'{E}l\H{o}'s originalapproach.  We validate the structured log-odds modelling approach in syntheticexperiments and English Premier League outcomes, where the added expressivityyields the best predictions reported in the state-of-art, close to the qualityof contemporary betting odds.

Modelling Competitive Sports: Bradley-Terry-\'{E}l\H{o} Models for Supervised and On-Line Learning of Paired Competition Outcomes