Page 49 - Contributed Paper Session (CPS) - Volume 3

CPS1943 Nandish C. et al.
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the players, with respect to the average score = ∑ , for =

=1
1, . . . , , in the descending order.

2.1 Variable Selection
While dealing with sports and related fields, which have a variety of
quantitative aspects serving as performance attributes, selecting the most
important ones is a crucial task. It may so happen that a certain subset of
variables might be insignificant. The information contained in them, might
already have been incorporated by some other variables. This might
particularly happen in case of higher correlation among variables. In such an
event, their corresponding weights might be close to zero. Therefore, using all
the available variables will make the model unnecessarily cumbersome. In
order to deal with such issue, we propose a variable selection technique to
choose a suitable subset of variables for adequately explaining the final score.
However, there is an involved cost of forfeiting the optimal solution and
settling for a reasonable sub-optimal solution.
In order to choose an optimal subset of variables, from the complete set
of available ones, we propose a backward subset selection technique. Since
our methodology involves solving a constrained maximization problem,
presented in equation (2), the maximum value of the objective function is
attained when we use all the variables to obtain the full model () with
variables. Subsequently, dropping variables one by one leads us to sub-

optimal solutions. In this method, we begin to generate the models () s, for
= – 1, … ,1, each time by dropping the variable corresponding to the
lowest associated weight. Having noted the corresponding values attained by
(2) for all the models, we generate a scree plot of these values versus the
number of variables rejected. In order to determine the appropriate number
of variables, we plot the value of the objective function against the number of
variables rejected, known as a Scree plot. We look for a knee (bend) in the
Scree plot thereafter, to decide on a suitable number of variables.

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