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

An ANN Model For Individual Ratings in Group Competitions 3
Fig. 1 The Bradley-Terry Modle as a Single-Layer ANN
The scale specific parameters are historical only and can be changed to the
following:
1
Pr(A def B) = . (3)
1 + e−(θA−θB) Substituting w for θ in (3) yields the single-layer artificial neural network
(ANN) in figure 1. This single-layer sigmoid node ANN can be viewed as a
Bradley-Terry model where the input corresponding to subject A is always
1, and B, always −1. The weights w A and w B correspond to the Bradley-
Terry strengths θ A and θ B —often referred to as ratings. The Bradley-Terry
ANN model can be fit by using the standard delta rule training method
for single-layer ANNs. This ANN interpretation is appealing because many
types of common extensions can be added simply as additional inputs to
the ANN.