A Bradley–Terry artificial neural network model for individual ratings in group competitions

Abstract

A common statistical model for paired comparisons is the Bradley–Terry model. This research re-parameterizes the Bradley–Terry model as a single-layer artificial neural network (ANN) and shows how it can be fitted using the delta rule. The ANN model is appealing because it makes using and extending the Bradley–Terry model accessible to a broader community. It also leads to natural incremental and iterative updating methods. Several extensions are presented that allow the ANN model to learn to predict the outcome of complex, uneven two-team group competitions by rating individuals—no other published model currently does this. An incremental-learning Bradley–Terry ANN yields a probability estimate within less than 5% of the actual value training over 3,379 multi-player online matches of a popular team- and objective-based first-person shooter.