Probabilistic modelling and inference of home effect in sports matches
DOI:
https://doi.org/10.5902/2179460X85273Keywords:
Home win, Distribution approximation, Home cooking, Soccer, Sports statisticsAbstract
A point based random variable (r.v.) built to obtain the home ground effect in soccer leagues was recently proposed by Paludo, Figueireido e Ferreira (2023). It is the points' relative diference between home and away and it was named D. Once it was proposed it's necessary to know its distribution to make inferences. D is composed by the linear combination of 4 r.v. and it was assumed that the problem origins of two independent multionomial r.v.. From the distributions definitions we have obtained expectation and variances and based on this, we have developed two approximations, one by normal and the other by the binomial distribution. Subsequently it was conducted a simulation study to evaluate of the approximations and applications were presented to exemplify new inferences possibilitaded by this paper. The simulated D values from both hypothetical and observed vectors presented low percentages of adherence to the binomial distribution. In the greater part of analyzed situations, the data was expressively adhered to the normal distribution, and this was the selected distribution. The applications using distributions have showed differente possibilities of use for inferences, including one when there are differente number of home and away matches. It was possible to represent properly the r.v. that will permit to make inferences around D.
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