Page 47 - Contributed Paper Session (CPS) - Volume 3

CPS1943 Nandish C. et al.
these methodologies fail to ensure that the players are maximally
distinguished and provide an easy selection strategy among close competitor.
In this paper, we propose a methodology that maximally discriminates the
individual players, overcoming the shortcoming of the existing methods. The
players can be easily ranked on the basis of their averages, ignoring the
consistency (variability), of the performance variables under consideration.
This mechanism is justifiable when all the players are equally consistent with
respect to all the performance variables. Likewise, the players could be rated
according to their consistencies when they are indistinguishable with respect
to their average performance. However in reality, there is dissimilarity among
the players, with respect to both averages and consistencies of the
performance variable. Moreover, multiple performance variables may be
considered to develop an efficient rating mechanism. In such cases,
maintaining the trade-off that exists between the averages of the
performances of the players and their respective variations is important but
difficult. Furthermore, there could be significant correlations between some of
the performance variables. This issue is not appropriately dealt with in any of
the subjective or objective methods available in the literature. Our proposed
methodology attempts to address all these aforementioned issues. We
propose a new methodology for the player rating scheme in Section 2. In
Section 3, we present the real-life data analysis on the performance of players
in the Indian Premier League, considering both batsmen and bowlers. In
Section 4, we present a simulation study of our proposed methodology. We
end with some concluding remarks in Section 5.

2. Modeling Methodology
In order to develop an effective player rating scheme, let us consider that
we have a total of n players, each player has played matches for =

()
1, . . . , . Let us define to be the value corresponding to the performance
of the -th player, in the -th match, for the -th performance variable, for
= 1, . . . , . A typical data structure is represented in Table 1. In order to rank
the individual players by associating a score with each of them, we will take a
weighted average of the performance variables. Let us denote Yij as the score
of the -th player in the -th match, which is formally written as:

()
= ∑

=1
where is the weight corresponding to the -th performance variable, and

() ()
() −
= () () is the normalized value of the -th performance

−

variable for the -th player in the -th match. Note that the aforementioned
normalization of variables is only for the sake of easy interpretation.
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