Estatística Aplicada à Vantagem de Casa no Futebol

Abstract

The Brazilian Série A usually has higher home advantage than, for example, the European leagues and the factors that explain this pattern remain not completely cleared. To provide a better comprehension of those factors, we believe that the first issue is to obtain the home effect metric that permit observe the year to year variation of each club and that is based in points. One of the most important study in this subject, obtained an average home advantage for the seasons that was corrected by ability and the study didn't bring the information of each season by methodological reasons. Then, our objective is to develop a metric to obtain the home effect based on points, that does not need an ability correction and that bring an information for a team in every season. To achieve this objective, we conducted two studies, one in Chapter 4 and other in the Chapter 5. Chapter 4 has the objective of propose a metric to obtain the home advantage based in points. This Chapter started transforming a well-known metric to a new metric. So, we have used data from Série A of Campeonato Brasileiro from 2003 to 2020 as a study application. As a result, the new metric was named d and it was obtained accomplishing the points we had expected to. As a solution, it was developed a test for d to verify if there is enough information to affirm if there is a home effect avoiding random effects as when a team win few points. Based on this test, we have obtained from 43 teams in 370 participations that: 259 had positive home effect, 1 negative and 110 had no effect. Moreover, d has permitted to visualize graphically the team's individual behavior though the years in the competition. Chapter 5 treated d as a random variable (v.a.) D and we described its distribution and some important characteristics as population mean and variance. Besides, as it was not possible to obtain the exact distribution of D, we obtained 2 approximations of the distribution of D: a binomial and a normal one. To evaluate and to decide which approximation was the best, we conducted a simulation study. As the main result, D was well approximated by the normal distribution and so we used it in applications with real data. Knowing the proper distribution permit to conduct statistical inferences over the v.a. D and has permitted some applications using well known tests. So, as a general conclusion we have developed a v.a. D to measure the home effect and we have studied its distribution, which is approximately normal and permit to build inferences.