A Bradley-Terry Artificial Neural Network Model for Individual ...

6 Joshua Menke, Tony Martinez
thousands of comparisions and competitors. In addition, as mentioned, it is
impossible to fit a model this way if new individuals can be added at any
point. Elo and (Glickman, 1999) have both proposed methods for approximating
a simultaneous fit by by adapting the Bradley-Terry model after
every comparison. This also allows for new individuals to be inserted at any
point in the model. However, neither of these methods has been extended to
extract individual ratings from groups. The model presented here does allow
individual ratings to be determined in addition to providing an efficient
update after each comparison.
3 The ANN Model
The section proceeds as follows: it first presents the basic framework for
viewing the Bradley-Terry model as a delta-rule trained single layer ANN
in 3.1, then the next section, 3.2 will show how to extend the model to
learn individual ratings within a group, 3.3 extends the model to allow
different weights for each individual based on their contribution, 3.4 shows
how the model can be extened to learn “home field” advantages, 3.5 presents
a heuristic to deal with uncertainty in an individual’s rating, and 3.6 gives
another heuristic for preventing rating inflation.
3.1 The Basic Model
The basis for the Bradley-Terry ANN Model begins with the ANN shown
in figure 1. Assuming, without loss of generality, that group A is always the