| Relative to other team games, the contribution of individual team
members to the overall team performance is more easily quantifiable
in cricket. Viewing players as securities and the team as a portfolio,
cricket thus lends itself better to the use of analytical methods
usually employed in the analysis of securities and portfolios. This
paper demonstrates the use of stochastic dominance rules, normally
used in investment management, to analyze the One Day International
(ODI) batting performance of Indian cricketers. The data used span
the years 1989 to 2005. In dealing with cricketing data the existence
of 'not out' scores poses a problem while processing the data. In
this paper, using a Bayesian approach, the 'not-out' scores are first
replaced with a conditional average. The conditional average that
is used represents an estimate of the score that the player would
have gone on to score, if the 'not out' innings had been completed.
The data thus treated are then used in the stochastic dominance analysis.
To use stochastic dominance rules we need to characterize the 'utility'
of a batsman. The first derivative of the utility function, with respect
to runs scored, of an ODI batsman can safely be assumed to be positive
(more runs scored are preferred to less). However, the second derivative
needs not be negative (no diminishing marginal utility for runs scored).
This means that we cannot clearly specify whether the value attached
to an additional run scored is lesser at higher levels of scores.
Because of this, only first-order stochastic dominance is used to
analyze the performance of the players under consideration. While
this has its limitation (specifically, we cannot arrive at a complete
utility value for each batsman), the approach does well in describing
player performance. Moreover, the results have intuitive appeal.
KEY
WORDS: Bayesian, utility function, batting average, conditional
average, geometric distribution.
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