Parameter estimation in large dynamic paired comparison experiments

Paired comparison data in which the abilities or merits of the objects bein g compared may be changing over time can be modelled as a non-linear state space model. When the population of objects being compared is large, likeli hood-based analyses can be too computationally cumbersome to carry out regu larly. This presents a problem for rating populations of chess players and other large groups which often consist of tens of thousands of competitors. This problem is overcome through a computationally simple non-iterative al gorithm for fitting a particular dynamic paired comparison model. The algor ithm, which improves over the commonly used algorithm of Elo by incorporati ng the variability in parameter estimates, can be performed regularly even for large populations of competitors. The method is evaluated on simulated data and is applied to ranking the best chess players of all time, and to r anking the top current tennis-players.