On accommodating the factors influencing the sports results by splitting the order effect in paired comparison experiments

Pak.j.stat.oper.res. Vol.VIII No.1 2012 pp91-100
On accommodating the factors influencing the sports results by splitting the order effect in paired comparison experiments
Nasir Abbas
Department of Statistics,
Government Postgraduate College Jhang, Pakistan [e-mail] Muhammad Aslam
Department of Statistics,
Quaid-i-Azam University Islamabad, Pakistan [e-mail] Abstract
The results of sport contests depend upon a lot. In this article, an attempt is made to accommodate the factors influencing the sports-results by proposing a model for paired comparison experiments that splits the order effect into its components. The proposed model can be used to separately study the effects of all the components of the order effect. We study only two components of the order effect as a special case. The maximum likelihood estimates of the worth parameters are found and the plausibility of the proposed model is checked. Real dataset is collected on five top-ranked one-day-international cricket teams and is used to illustrate the estimation procedure.
Keywords: Bradley-Terry model; Goodness of fit; Home advantage; Maximum likelihood (ML) estimates; Paired comparisons; Ranking; Toss-result effect.
1. Introduction
In the method of paired comparisons (PC), treatments (stimuli, options, objects, items, individuals etc) are presented in pairs to judges (raters, respondents, jurists, panelists etc) that are asked to pick the better one on the basis of sensory evaluation. If allowed, they may declare a tie rendering the two objects equal in worth when the difference between their worth is less than a certain critical or threshold value. By repeating this experiment a fixed number of times on balanced or un-balanced pattern under similar conditions, the PC dataset is generated and is expressed as a preference matrix. This preference matrix is analyzed through the PC models. The PC models quantify the qualitative preferences in the form of

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