Publication Date
Spring 5-8-2024
School
College of Arts and Sciences
Major
Mathematics
Keywords
tennis analytics, feasible generalized least squares, homogeneity tests
Disciplines
Applied Statistics
Recommended Citation
Ugona Santana, Ernesto, "Testing the Hypothesis that Tennis Points are Independent and Identically Distributed Using Statistical Methods" (2024). Senior Honors Theses. 1444.
https://digitalcommons.liberty.edu/honors/1444
Abstract
Most research on the probability of winning a tennis match is based on the assumption that the points are independent and identically distributed, treating each point as a Bernoulli trial with fixed probability of success. This assumption, however, seems to contradict experience. Players' performance appears to fluctuate as the match progresses due to the psychological effect of past performance. To test this counterintuitive yet central assumption, previous research has attempted to test the independence hypothesis. However, there exists a research gap in evaluating the identicality-of-distribution hypothesis, a question of broader scope than that of independence. Hence, the purpose of this study is to test the hypothesis that tennis points are identically distributed throughout a server’s match. This objective is accomplished by initially identifying, through appropriate homogeneity tests for sparse data, deviations from the base distribution, with the goal of developing a forecasting model that accounts for perturbations in the distribution.
