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

12 Joshua Menke, Tony Martinez
group g on field f. The following change to the chosen field inputs, f A and
f B , extends this to handle uneven groups:
N A
f A =
N A + N B
(16)
N B
f B =
N A + N B
(17)
Therefore, the field inputs are the relative size of each group. The full model
including the field inputs then becomes:
Output = Pr(A def B) =
1
1 + e −(wA−wB+θ fAf A−θ fB f B) . (18)
The weight update after each comparison on field f then extends the deltarule
update from (8) to include the new parameters:
∆θ fA = η(1 − Output) (19)
∆θ fB = −η(1 − Output). (20)
3.5 Rating Uncertainty
One of the problems of the given model is that when an individual partipates
for the first time, their rating is assumed to be average. This can result
in incorrect predictions when a newer individual’s true rating is actually
significantly higher or lower than average. Therefore, it would be appropriate
to include the concept of uncertainty or variance in an individuals rating.
Glickman (Glickman, 1999) derived both a likelihood-based method and a
regular-updating method (like Elo’s) for modeling this type of uncertainty
in Bradley-Terry models. However, his methods did not account for finding