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Olympic Game Medal Count Analysis

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OLYMPIC GAMES MEDAL COUNT ANALYSIS SUMMER AND WINTER OLYMPIC GAMES A Thesis Presented to the Faculty of California State Polytechnic University, Pomona In Partial Fulfllment Of the Requirements for the Degree Master of Science In Mathematics By Jiaxin Si 2018 SIGNATURE PAGE THESIS: OLYMPIC GAMES MEDAL COUNT ANALYSIS SUMMER AND WINTER OLYMPIC GAMES AUTHOR: Jiaxin Si DATE SUBMITTED: Fall 2018 Department of Mathematics and Statistics Dr. Adam King Thesis Committee Chair Mathematics & Statistics Dr. Hoon Kim Mathematics & Statistics Dr. Alan Krinik Mathematics & Statistics ii ACKNOWLEDGMENTS First and foremost, I would like to show my deepest gratitude to my supervisor, Dr. Adam King, a respectable, responsible and resourceful scholar, who has provided me with valuable guidance in every stage of the writing of this thesis. Without his enlighten- ing instruction, impressive kindness and patience, I could not have completed my thesis. His keen and vigorous academic observation enlightens me not only in this thesis but also in my future study. I shall extend my thanks to Mr. King for all his kindness and help. I would also like to thank all my teachers who have helped me to develop the fundamental and essential academic competence. My sincere appreciation also goes to the teachers and students from Cal Poly Pomona who participated in this study with great cooperation. iii ABSTRACT More than 35,000 medals have been awarded at the Olympics since 1896. The IOC (International Olympic Committee) retrospectively awarded gold, silver, and bronze to athletes based on their rankings. The dataset we used covers Summer Olympics from 1896 to 2012 and Winter Olympics from 1924-2014; each year includes a row for every Olympic athlete that has won a medal since the frst games. Also, this dataset has each IOC country’s population and GDP in 2012 to 2014. This report has four main analysis parts. The frst part introduces the base information about Olympics. In the second part, we explore the basic analysis about Summer and Winter Olympics. The third part consists of joint analysis of both the Summer and Winter the Olympic Games. The fourth part, involving the number of medals in the Summer Olympics and the Winter Olympics, will be explored. At the same time, in order to reveal the relationship between the number of medals and the basic characteristics of each country average high temperature in winter and GDP per capita were introduced in 2012 and 2014. The relationship between the average high temperature in winter and GDP per capita affects the number of medals a country obtains. iv Contents 1 Introduction 1 1.1 The Olympic Game and Olympics Spirit . 1 1.1.1 Olympics Game . 1 1.1.2 Olympics Spirit . 2 1.2 The History of The Olympic Games . 2 1.3 The Importance of Olympic Games Statistics . 2 1.4 Economic and Social Impact on Olympic Games . 3 2 Exploratory Data Analysis 5 2.1 The Basic Statistical Analysis of Summer . 5 2.1.1 Statistics of Each Sport Event . 5 2.1.2 Statistics of Medals . 8 2.1.3 Statistics of the Historical Hosting Cities . 12 2.1.4 Statistical Analysis of the Characteristics of Winners . 13 2.1.5 Comparison of Medals on the Same Gender in Different Countries 17 2.2 The Basic Statistical Analysis of Winter . 17 2.2.1 Statistics of Each Sport Event . 18 2.2.2 Statistics of Medals . 19 v 2.2.3 Statistics of the Historical Hosting Cities . 21 2.2.4 Statistical Analysis of the Characteristics of Winners . 23 2.2.5 Comparison of Medals on the Same Gender in Different Countries 25 2.3 The Joint Analysis of the Olympic Games . 27 2.3.1 Examining the Same Countries’ Summer and Winter Olympic Performance . 27 2.3.2 Strong Repeat Performances by Certain Countries in Certain Sports 29 2.3.3 Comparing Performance of Men and Women within the Same Country . 34 3 Main Data Analysis 36 3.1 Data Set . 36 3.1.1 Data Description . 36 3.1.2 Method for Making Model . 37 3.2 Statistical Model for Analysis in Summer Olympic Games in 2012 . 39 3.2.1 Relationships of Single Variables with Medal Count in 2012 . 39 3.2.2 Medal Count Prediction Using GDP and Average High Winter Temperature . 43 3.3 Statistical Model for Analysis in Winter Olympic Games in 2014 . 53 3.3.1 Relationships Between Medal Count and Single Variables in 2014 53 3.3.2 Predicting Winter 2014 Medal Counts using GDP and Average High Temperature in Winter . 56 3.3.3 Summary of Winter Olympic Games Analysis . 63 4 Conclusion 65 vi List of Figures 2.1 The total number of events each summer year. 6 2.2 The total number of disciplines each summer year. 7 2.3 The total number of medals of top fve countries in each year. 10 2.4 The sex difference between men and women. 16 2.5 The number of winner about men and women in the same Summer Olympic Games. 16 2.6 The total number of disciplines increase year by year in winning games. 18 2.7 The total number of medals of top fve countries in each winter year. 20 2.8 The top fve countries from 1924 to 2014 each medal compared. 21 2.9 The sex difference between men and women. 24 2.10 The number of winning men and women in the same Summer Olympic Games. 24 2.11 The number medal of men and women in same country. 26 2.12 The number medal of men subtract the number of medals women in the same country. 26 2.13 Each Country Medals of Ranking about Summer and Winter Different . 28 2.14 The winter sports event which the USA has advantages. 30 2.15 The summer sports event which the USA has advantages. 30 vii 2.16 The winter sports event which the RUS has advantages. 32 2.17 The summer sports event which the RUS has advantages. 32 2.18 The winter sports event which the GER has advantages. 33 2.19 The summer sports event which the GER has advantages. 33 3.1 The relationship each country log of base two GDP of billion dollar match with the number of the medal in 2012. 40 3.2 The relationship between country log of base two with GDP and number of the medal in 2012. 41 3.3 The relationship between each country average high temperature Winter and number of the medal in 2012. 42 3.4 The relationship between the log of base GDP in billion and average high temperature Winter and number of the medal in 2012. 43 3.5 Each country an actual number of medals and predicted number of medals in 2012. 46 3.6 Each country actual number of medals and predicted number of medals 2012. 46 3.7 Diagnostic plots for the regression of the number of medals on the log of base two GDP in billion dollar GDP and square of the log of base two GDP in billion dollar GDP and cube of the log of base two GDP in billion dollar and temperature . 47 3.8 Each country actual number of medals and predicted number of medals 2012. 49 3.9 Each country an actual number of medals and predicted the number of medals in 2012. 50 viii 3.10 Diagnostic plots for the regression of number of medals on square of the log of base two GDP billion U.S. dollars and temperature. 51 3.11 Fitted using Smoothing Splines the residual values of the log base two GDP billion U.S. dollars in 2012. 51 3.12 Fitted using Smoothing Splines the residual values of the temperature in 2012. 52 3.13 Each country actual number of medals and predicted number of medals 2012. 52 3.14 Each country an actual number of the medals and predicted number of medals 2012. 53 3.15 The relationship each country log of base two GDP of billion dollar match with the number of medal in 2014. 54 3.16 The relationship between country log of base two with GDP and number of medal in 2014. 55 3.17 The relationship between each country average high temperature Winter and number of medal in 2012. 56 3.18 The relationship between log base 2 of GDP in billions and average high temperature in Winter and number of medals in 2012. 57 3.19 Each country actual number of medals and predicted number of medals 2014. 58 3.20 Diagnostic plots for the regression of the number of medals on the log of base two GDP in billion dollar in 2014. 59 3.21 Each country actual number of medals and predicted number of medals 2014. 60 ix 3.22 Diagnostic plots for the regression of number of medals on square of log of base two GDP billion U.S. dollars and temperature. 61 3.23 Fitted using Smoothing Splines the residual values of the log base two GDP billion U.S. dollars in 2014. 62 3.24 Fitted using Smoothing Splines the residual values of the temperature in 2014. 62 3.25 Each country actual number of medals and predicted number of medals 2014. 63 x List of Tables 2.1 2012 Compare to 1896 Adding 28 Disciplines . 8 2.2 Each year the number of Bronze Medals, Gold Medals and Silver Medals. 9 2.3 List each country with the total number of medals. 11 2.4 List each year Summer Olympics in which city. 13 2.5 List three different kinds of medals total number of Summer Olympics in men and women.
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