A Parametric Control Chart for Monitoring Individual Batting Performances in Cricket

Abstract

A control chart is developed specifically for monitoring batting performances in cricket. Issues associated with the need to retain extreme values and limited sampling opportunities are overcome by using a parametric approach to obtain theoretical quartiles from the distribution of individual batting scores. A mixed distribution, named the Ducks 'n' Runs distribution, is proposed. A beta distribution models zero scores (ducks) and a geometric distribution describes the distribution of non zero scores (runs). This suitability of this probability distribution model is demonstrated using data from New Zealand first class batsmen in domestic three day cricket over a four year period. Changes in the process (player performance) are detected using rules adapted from the supplementary rules for Shewhart control charts.

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