重大勝利是否能增加職業男網選手之信心 - 政大學術集成

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(1)國立政治大學會計學系碩士班碩士論文. 指導教授：林良楓博士. 重大勝利是否能增加職業男網選手之信心政治. 大. 立. ‧ 國. 學. Can a Major Win Enhance a Professional Tennis Player’s Confidence?. ‧. n. er. io. sit. y. Nat. al. Ch. engchi. 研究生：中. 華. 民. 國. 一. i Un. v. 林俊佑百零四. 撰年. 七. 月.

(2) 謝辭能夠完成這本論文，首先要感謝的是指導老師的林良楓老師。謝謝老師在繁忙的生活中仍然每週撥空和我們 meeting、指導我們論文中碰上的任何問題，同時也謝謝老師不厭其煩地幫我修飾文章，才讓英文程度不甚好的我也能完成一本英文論文。除了論文上的幫助，也很謝謝老師提供我找工作方面的建議。非常慶幸能有林良楓老師作為我的指導教授。另外要感謝郁傑和鄭宇淳，沒有你們在統計和資料搜集上的幫助，這論文不知道什麼時候才寫得完。此外，也很感謝同門的呂晉，雖然最後論文方向完全不同，不過有人能一起 meeting 順便罩著我，讓我更踏實了一點。. 政治大樣。剛來到政大人生地不熟的，好險有志軒、郁傑和敏雄幾個老朋友，讓我能快速適立兩年的碩士生活結束地太快，途中遇上了許多人、許多事，就像一場奇幻冒險一. ‧ 國. 學. 應不熟悉的政大、不熟悉的商學院。謝謝パソナ實習的夥伴們，實習時一起遊玩、回國後仍常天南地北地聊天、提供我許多建議與幫助。Jan and spring break bxxches,. ‧. thanks for the unforgettable and crazy semester, hanging out with you guys is the best:) 會研. sit. y. Nat. 學長姐、學弟妹以及 102 級的各位，和你們一起上課、唸書以及一起出遊的日子，都. n. al. er. io. 讓我的碩士生涯更加的充實，謝謝你們。. i Un. v. 最後要感謝我的家人，全力支持我的每一個決定、每一個任性，突然從歷史跳槽. Ch. engchi. 到會計、決定到日本實習甚至決定到日本工作，你們都沒有多說什麼而默默地支持我，才讓我能順利地走到這一步，有你們在我身旁是我最幸運的事。.

(3) 摘要本研究欲比較網球技術與心理素質與網球比賽勝率之關聯性，以及不同天分之男網選手的差異，並檢驗重大勝利能否影響選手之生涯。實證結果顯示，大多數的網球技術都和比賽勝率顯著地正相關，而有天分的選手於大多數網球技術之表現優於天分較差的選手。另外也發現選手得到 ATP 之賽事冠軍後，可以提升網球技術與心理素質；但在得到大滿貫(Grand Slam)賽事冠軍之後卻會退步。本研究結果亦顯示雖然攻擊、防守與心理素質對選手的比賽結果都有很大影響，但在贏得 ATP 級冠軍之前攻擊技術是影響比賽勝率最大的因素；而贏得大滿貫賽事冠軍之後防守技術則成為最重要. 政治大. 的勝率影響因素。研究結果顯示獲得重大勝利之後確實會增加職業男網選手之信心。. 立. ‧. ‧ 國. 學. 關鍵字：心理素質、高天分網球選手、網球. n. er. io. sit. y. Nat. al. Ch. engchi. II. i Un. v.

(4) Abstract This study tries to examine the tennis skills and mental toughness associated with winning percentages, compare the performance difference between talent players and less talent players, and find out how a major win can affect players career. The empirical results suggest that most of the tennis skills and mental toughness are positively and significantly associated with winning percentage. Talent players have better performance than those less talent players in most of tennis skills. The study also finds that players can improve offensive and defensive skills and mental toughness through winning an ATP title, but get worse after. 政治大. winning a Grand Slam title. The research findings suggest that before winning an ATP title. 立. offensive skill is as important as defensive skill for a player to gain more winning percentage,. ‧ 國. 學. however, after winning a Grand Slam title defensive skill is the most important skill to win more winning percentage, although defensive skill and mental toughness are still play an. ‧. important role for winning more percentage. The research concludes that a major win does. y. Nat. n. al. er. io. sit. enhance a player’s confidence.. Ch. engchi. i Un. Keywords: Mental toughness, Talent tennis player, Tennis. III. v.

(5) Table of Contents Table of Contents .....................................................................................................................IV List of Tables ............................................................................................................................. V Chapter 1 Introduction ........................................................................................................ 1 1.1 Motivation .............................................................................................................. 1 1.2 Research Purpose and Problems ............................................................................ 1 1.3 Organization of the Research ................................................................................. 2 Chapter 2 Literature Review............................................................................................... 3 2.1 Introduce of Association of Tennis Professionals .................................................. 3. 立. 政治大. 學. Research Design................................................................................................. 9 Hypotheses Development ...................................................................................... 9 Data Collection .................................................................................................... 10 Variables Description ........................................................................................... 11 Research Method ................................................................................................. 14 Empirical Results ............................................................................................. 16 The Descriptive Statistics .................................................................................... 16. ‧. sit. y. Nat. Chapter 3 3.1 3.2 3.3 3.4 Chapter 4 4.1. Tennis Matches Related Literature ........................................................................ 5 Talent Identification Background and Related Literature ...................................... 6 Background and Related Literatures of Sport Psychology .................................... 7. ‧ 國. 2.2 2.3 2.4. n. al. er. io. 4.2 Tennis Skills and Winning Percentage ................................................................. 21 4.3 Talent Players Perform Better Than Less Talent Players ..................................... 25 4.4 A Major Win Enhance a Player’s Performance ................................................... 32 Chapter 5 Conclusions and Suggestions........................................................................... 42 5.1 Conclusions .......................................................................................................... 42 5.2 Suggestions and Limitations ................................................................................ 43 References ................................................................................................................................ 44. Ch. engchi. IV. i Un. v.

(6) List of Tables Table 2.2.1 Summary of ATP Tours and Grand Slam Games .................................................... 4 Table 4.1.1 Descriptive Statistic of the Main Variables Examined of ATP Data ..................... 17 Table 4.1.2 Summary of Strong Hand per Year ....................................................................... 17 Table 4.1.3 Pearson Correlation Coefficient of All Variables .................................................. 18 Table 4.1.4 Summary of Descriptive Statistics of Grand Slam Tournaments .......................... 19 Table 4.1.5 Pearson Correlation Coefficient of Grand Slam Tournaments .............................. 20. 政治大 Table 4.2.2 Standardized Estimate Value and the Results of F-test of ATP Tours ................... 23 立 Table 4.2.1 Regression Results of ATP Tours .......................................................................... 22. ‧ 國. 學. Table 4.2.3 Regression results of Grand Slam Tournaments ................................................... 24 Table 4.2.4 Standardized Estimate Value and the Results of F-test of Grand Slam. ‧. Tournaments ..................................................................................................................... 24. Nat. sit. y. Table 4.3.1 The Regression Results of Groups Divided by Talent .......................................... 26. n. al. er. io. Table 4.3.2 Comparison of the Variance Means of 3 Groups .................................................. 27. i Un. v. Table 4.3.3 ANOVA Statistical Results of Groups................................................................... 28. Ch. engchi. Table 4.3.4 Mean Difference between Groups ........................................................................ 29 Table 4.3.5 Regression Results by Talent ................................................................................ 31 Table 4.3.6 Standardize Estimate Values and F test of 3 Groups from Table 4.3.5 ................. 31 Table 4.4.1 Regression Results Before and After Winning the First ATP Title ....................... 33 Table 4.4.2 ANOVA testing results of Before and After the First ATP Title............................ 34 Table 4.4.3 Regression Results of Before and After the First ATP Title .................................. 35 Table 4.4.4 Integrate Coefficients Comparison of Defensive, Offensive and Mental Toughness Before and After Winning the First ATP Title.................................................................. 36 Table 4.4.5 Comparison of the Mean of Before and After the First ATP Title ........................ 36 V.

(7) Table 4.4.6 Regression Results for Winning the First Grand Slam Title ................................. 38 Table 4.4.7 Comparison of the Mean of Before and After the First Grand Slam Title ............ 38 Table 4.4.8 ANOVA Testing Results of Before and After the First Grand Slam Title ............. 39 Table 4.4.9: Regression Results Before and After Winning the First Grand Slam Title .......... 41 Table 4.4.10 Integrate Coefficient Comparison of Defensive, Offensive and Mental Toughness Before and After Winning the First Grand Slam Title ................................... 41. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. VI. i Un. v.

(8) Chapter 1. Introduction. 1.1 Motivation Tennis is one of the most popular sports of the world, and there are already many studies about tennis. Although, a few studies provided the evaluation of tennis players’ performance, however, no study focuses on tennis skills with respect to winning a tennis game. Many sports stars were believed to have a natural talent for a specific sport, such as LeBron James and Michael Jordan (6 NBA champions holder) for basketball, Carl Lewes, (9. 政治大. gold medals holder of Olympic Games), for Track and field athlete, and Jimmy Connors (all. 立. time record of 105 ATP single titles holder) and Roger Federer (all time record of 14 Grand. ‧ 國. 學. Slam single titles holder) for tennis. The common point of those professional players is that they were known as natural talent players and they started to enhance their career after a. ‧. major achievement.. sit. y. Nat. er. io. 1.2 Research Purpose and Problems. al. n. iv n C This paper tries to find out the tennis and talent associated with tennis winning h eskills ngchi U opportunities. Accordingly, the study tries to answer the following 3 questions. How players’ tennis skills and mental toughness affect their winning opportunities? Do talent players present better tennis skills and mental toughness than those of less talented players? Does a tennis player improve his offence and defense skills as well as mental toughness after a major win?. 1.

(9) 1.3 Organization of the Research This research process as follows. Chapter 2 introduces the background information of the Association of Tennis Professionals (ATP) and some literature reviews about tennis skills, talent players in respect to players’ performance. Chapter 3 discusses the methodologies used in this research. Chapter 4 describes the data and results of the research models, and Chapter 5 summarizes and concludes the finding of the research.. 立. 政治大. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 2. i Un. v.

(10) Chapter 2. Literature Review. 2.1 Introduce of Association of Tennis Professionals The Association of Tennis Professionals (ATP) was formed in September 1972, and organized the worldwide tennis tour for male professional players. The name of organization was ATP TOUR in 1990, and in 2001 changed into ATP, and then in 2009, it changed into the current name ATP World Tour. ATP is governing 5 levels of the tournament, which are ATP World Tour Finals, ATP World Tour Masters 1000, ATP World Tour 500 series, ATP World. 政治大 replaced Tennis Masters Series tournaments, ATP International Series Gold and ATP 立. Tour 250 series and ATP Challenger Tour. This structure was once changed in 2009, and. ‧ 國. 學. International Series with ATP World Tour Masters 1000, ATP World Tour 500 series, ATP World Tour 250 series. ATP also provides two ranking systems, Emirates ATP Rankings1 a. ‧. 52-weel rolling ranking, and the Emirates ATP Rankings Race to London2, a year to date. Nat. sit. y. ranking. There is the other organization, International Tennis Federation, who is governing. n. al. er. io. the 4 Grand Slam games and ITF Men’s Circuit.. Ch. i Un. v. In this study, the ATP games are defined the results of 4 Grand Slam games, ATP World. engchi. Tour Masters 1000, ATP World Tour 500 series, and ATP World Tour 250 series. The data of ATP World Tour contain all 4 levels from 1995 to 2014; while due to data limited Grand Slam data only include Australia Open 2015 and the other 3 Grand Slam 2014 records. A summary of ATP tours and Grand Slam tournaments is listed in table 2.1.1.. 1. Emirates ATP Rankings is used for determining qualification for entry and seeding in all tournaments. Within the ATP Rankings period consisting of the past 52 weeks, points are accumulated, except for ATP World Tour Finals, whose points are dropped following the last ATP event of the year. The player with the most points by season's end is the World Number 1 of the year. 2 Which is used for determining qualification for entry and seeding in all tournaments. Within the ATP Rankings period consisting of the past 52 weeks, points are accumulated, except for ATP World Tour Finals, whose points are dropped following the last ATP event of the year. The player with the most points by season's end is the World Number 1 of the year. 3.

(11) Table 2.2.1 Summary of ATP Tours and Grand Slam Games Event category. Contains. Grand Slam. Australian Open in, French Open in, Wimbledon in and the US Open. ATP World Tour Finals. Barclays ATP World Tour Finals. 立. 政治大. ‧ 國. 學. ATP World Tour Masters Indian Wells, Miami, Monte-Carlo, Madrid, Rome, Canada, Cincinnati, 1000 Shanghai and Paris. 2,000. ITF. 1100 to 1500. ATP (2009-present). 1000. ATP. 500. ATP. 250. ATP. n. al. er. sit. y. Nat. Championships, Barcelona Open, Halle Open, Queen's Club Championships, German Open, Washington Open, China Open, Japan Open, Vienna Open, Swiss Indoors. io. Governing body. ‧. Rotterdam Open, Rio Open, Mexican Open, Dubai Tennis ATP World Tour 500 series. Winner's ranking points. i n U. v. ATP World Tour 250 series. 39 Tournaments. ATP Challenger Tour. 178 Tournaments. 80 to 125. ATP. ITF Men's Circuit. 534 Tournaments. 18 to 35. ITF. Ch. engchi. 4.

(12) 2.2 Tennis Matches Related Literature Studies of professional tennis are mostly focused on the prediction of the outcomes of the match. For instance, del Corral and Prieto-Rodríguez (2010) tested whether the difference in rankings between individual players are good predictors for Grand Slam outcomes. They used probit models and bootstrapping techniques to examine data from 2005 to 2008. The results denoted that the most relevant variable is the ATP or WTA rankings. McHale and Morton (2011) employed a forecasting model based on the Bradley-Terry model without relying on the official ranking, but based on the results of past matches, the length of time. 治政 after past matches and the surface of contest to predict match 大winners. Their model revealed a 立 better prediction than that of ranking model. Knottenbelt, Spanias and Madurska (2012) ‧ 國. 學. applied a hierarchical Markvo model to estimate of the probability of each player winning a. ‧. professional singles tennis match. When using their model with a data set of historical match. sit. y. Nat. statistics and bookmakers odds, the model yields a 3.8% return on investment over 2173 ATP. io. er. matches played. Several other predicting models for tennis matches outcomes have been also. al. presented over the years (Boulier and Stekler, 1999; Clarke and Dyte, 2000; Klaassen and. n. iv n C Magnus, 2003; Scheibehenne and Broder, McHale and Morton, 2011) h e2007; ngchi U. Moreover, there are also several studies applying Data Envelopment Analysis (DEA) methodology to evaluate the efficiency of professional tennis plays. Ramon, Ruiz and Sirvent (2012) applied the DEA model that use no input specifications and nine performance outputs. The result denoted similar rankings as the official ATP rankings. Halkos and Tzeremes (2012) also evaluated the performance of professional tennis players by using DEA approach. The evaluation indicated 39 out of 229 male tennis players are efficient under CRS assumption, and a highly competitive environment of professional tennis was revealed. Chitnis and Vaidya (2014) employed DEA model to measure the performance of professional tennis 5.

(13) players. They concluded that the DEA approach of measuring performance of an individual tennis player is quite different from the conventional method adopted by ATP World Tour Rankings. Chitnis and Vaidya also found that tennis is a game where not only physical but also psychological factors of a player are tested continuously and hence identifying the weaknesses and potential areas for improvement becomes necessary. In addition, there are other studies of tennis focus on different topics such as measuring the best player in the history, creating a new ranking system or classifying tennis players. Radicchi (2011) considered all matches played by professional tennis players between 1968. 政治大 professional players. As a result, total win and win against top players are the most relevant 立. and 2010, and a diffusion algorithm was applied to the tennis contact network in order to rank. ‧ 國. 學. factors and Jimmy Connors is determined as the best player ever with Ivan Lendl and John McEnroe following behind. Baker and McHale (2014) conducted a research that a dynamic. ‧. paired comparison model is used to measure who’s the best player of the Open Era of men’s. Nat. sit. y. professional tennis since 1968. And the result suggested that Roger Federer is the best player,. n. al. er. io. with Bjorn Borg and Jimmy Connors close behind. There are also studies showed other. i Un. v. ranking system differ from the official ATP one, and provide more information about which. Ch. engchi. player is better. (Dahl 2012; Han, Xie, Li, Zhu, and Wang, 2014). 2.3 Talent Identification Background and Related Literature Talent identification is a big business in every way such as sport, art and even education. Researches of these fields are attempting to find a way to identify the best talent. Bloomfield, Fricker and Fitch (1995) defined effective elements of talent identification like strength, power, flexibility and speed. Bompa (1999) revealed that in the late 1960s and early 1970s, researchers in many East European countries tried to find talent identifications, which can be underpinned with scientific theory and evidence. Moreover, Lykken (1998) indicated that 6.

(14) psychological factors such like persistence, and the capacity to concentrate and confidence is also important. Abbott, Button, Pepping and Collins (2005) revealed that many TI models overemphasis on early identification rather than the development of potentially talented performers. The concept of the talent is revised as a complex, dynamical system in which future behaviors emerge from an interaction of key performance determinants such as psychological behaviors, motor abilities, and physical characteristics. Papic, Rohulj and Plestina (2009) present a fuzzy exert system for scouting and evaluation of young sports talent, and the results show high reliability and accuracy of the developed system which makes the possibility of wrong selection of sports and the time losing in training of. 治政 inappropriate sports reduced significantly. These studies reveal 大 that not only physical factors 立 are highly related to talent identification but also have to consider psychological factors ‧ 國. 學. which are keys to performance of athletes.. ‧. 2.4 Background and Related Literatures of Sport Psychology. sit. y. Nat. n. al. er. io. Weinberg (2014) indicated that stress can be either positive and helpful to performance. i Un. v. or negative and harmful to performance, and how it works is depend on the control of the. Ch. engchi. stress. A major source of stress is uncertainty, and one of the most effective ways to get control over stress is to develop confidence. Sport psychologists define self-confidence as the belief that one can perform as wanted. To build self-confidence is important to one’s performance. At the end of 2004, Andy Roddick said about Roger Federer (winner of the most Grand Slam singles titles in men’s tennis), “He’s got an aura about him in the locker room. Mentally, he’s so confident right now. A lot of his success right now is between the ears.” These comments by Roddick are echoed by Federer himself, who has said, “I believe strongly in my capabilities. There’s a lot of confidence as well, with my record over the past few years. I’ve built up this feeling on big points that I can do it over and over again. Things 7.

(15) are now just coming automatically.”3 Another example from elite tennis player is that Jimmy Connors once said, “The whole thing is never to get negative about yourself. Sure, it’s possible that the other guy you’re playing is tough and that he may have beaten you the last time you played, and okay, maybe you haven’t been playing all that well yourself. But the minute you start thinking about these things you’re dead. I go out to every match convinced that I’m going to win. That’s all there is to it.”4 Moreover, Bandura (1997) revealed that level of self-confidence can be raised by the. 政治大. performance accomplishment if the experiences are successful.. 立. Additionally, mental toughness, other psychological factor, is considered related to. ‧ 國. 學. performance. Dewhurst, Anderson, Cotter, Crust and Clough (2012) found out mental toughness is related to outcome performance measures in sport and other competitive. ‧. situations. And mentally tough individuals have an enhanced ability to prevent unwanted. y. Nat. io. sit. information from interfering with current goals. Newland, Newton, Finch, Harbke, and. n. al. er. Podlog (2013) revealed that basketball performance can be partially predicted by mental. Ch. i Un. v. toughness. Similarly, Gonzalez-Diaz, Gossner and Rogers (2012) indicated that career. engchi. success is significantly related individual critical ability which is how a player response to the importance of the situation. And it also shows that some aspects of the critical ability are related to psychological skills that are difficult to learn, but still can be improved by training, or simply through experience. In consequence, these studies suggested that mental toughness and self-confidence have positive affect to the performance. Both psychological factors can be improved by several way, and one of them is the success experience form the past.. 3 4. Weinberg, R. S., & Gould, D. 2014. Foundations of Sport and Exercise Psychology, 6E. Human Kinetics. Weinberg, R. S., & Gould, D. 2014. Foundations of Sport and Exercise Psychology, 6E. Human Kinetics. 8.

(16) Chapter 3. Research Design. 3.1 Hypotheses Development This study tries to examine whether a tennis player can improve his offence and defense skills as well as mental toughness after a major win. As many researchers tried to use ATP rankings or modified ranking (del Corral and Prieto-Rodríguez, 2010, Ramon, Ruiz and Sirvent, 2012) to predict the outcome of the matches. The logic behind a higher ranking play has a higher probability to win the match is that a higher ranking player should have better. 政治大. tennis skills and has a better chance to win the match. Therefore, based on this idea, the first hypothesis of the research is:. 立. ‧ 國. 學. Hypothesis 1: Players have no significant difference in their tennis skills and mental toughness.. ‧. sit. y. Nat. Base on Bandura (1997) and Dewhurst, Anderson, Cotter, Crust and Clough (2012). io. er. made an assumption of a player with better talent will have better performance than players. al. without talent. However, it is very difficult to define who is a talented player. The study. n. iv n C arbitrarily defined that a player won hishfirst ATP title within e n g c h i U 3 years after turned pro.. Therefore, players are divided into 3 groups, group 1 with players get their first ATP title within 3years after they turned pro.; group 2 with players get their first ATP title over 3 years after they turned pro.; and group 3 with players who never win a ATP title during his professional career. Though this kind of classification has never been used by any studies, Filipcic, Panjan and Sarabon (2014) suggested that there is always a way to classify professional tennis players into several groups with clear boundaries. Another reason for the study to make this classification is due to the extremely competitive environment of men professional tennis match. Most of the player can’t even win an ATP title for their whole career, while some of them can win it in their early career. Therefore, the second hypothesis 9.

(17) is players with better talent will perform better than those without. Hypothesis 2: There is no significant difference between talent players and less talent players with respect to tennis skills and mental toughness. Additionally, research also found that the performance of players are highly related to self- confidence and mental toughness which can be improved by the success experience in the past (Bandura, 1997, Dewhurst, Anderson, Cotter, Crust and Clough, 2012) . Therefore the second hypothesis is the performance of the player will be better after they win their first ATP champion. Due to the importance of the Grand Slam tournaments in professional tennis,. 政治大. two models are used with this hypothesis, one is the performance before and after winning. 立. first ATP title, and the other one is the performance before and after winning first Grand Slam. ‧ 國. 學. title.. Hypothesis 3: There is no significant change in tennis skills and mental toughness after a. al. er. io. sit. y. Nat. 3.2 Data Collection. ‧. player won his first ATP (Grand Slam) title.. n. iv n C 2 data sets are used and collected h from the official site e n g c h i Uof the Association of Tennis Professionals5, and the official site of 4 of the Grand Slam tournaments6, respectively. The ATP data set is collected from official site of ATP, with the players ranking in top 200 in the year end7 from 1995 to 2014, then the study removes players with total games played lower than 5, due to some of skill variables are missing. The Grand Slam data set is collected form official site of 4 Grand Slam tournaments, respectively.. 5 6. 7. Official site of ATP: http://www.atpworldtour.com/ Official site of Australia Open: http://2015.ausopen.com/index.html Official site of French Open: http://www.rolandgarros.com/en_FR/index.html Official site of Wimbledon: http://www.wimbledon.com/index.html Official site of US Open: http://2014.usopen.org/index.html The weekly ranking before Barclays ATP World Tour Finals of that year 10.

(18) 3.3 Variables Description Dependent variable Fred Hesse once suggested that playing percentage tennis is a wise tactic; and the player who plays this type of tennis will likely win.8 Base on this idea, therefore, the study uses winning percentage (WP) as the dependent variable, and is used for all models. Independent variables The independent variables are the skill statistics of the tennis player. These variables are used in most of the models. These independent variables are divided into 3 groups: offensive. 政治大. skills, defensive skills and mental toughness by their characteristics.. 立. (1) Offensive skills. ‧ 國. 學. A.. Service aces per game (AACE): According to Glossary of tennis terms at Tennis. ‧. Australia, “Ace: a service point won by the server because the receiver doesn’t. io. al. Double-Fault per game (ADF): A player can serve two times in each point, and will. iv n C loss the point if failed to serve the service box consecutively. ADF hthe e nballg into chi U n. B.. er. higher of this stat. means the better the offensive skill.. sit. y. Nat. return, or even touch, the ball9”. Therefore, ace is a pure offensive skill, and the. stands for both offensive and mentally skills, but related more to offense. C.. First serve percentage (FSER): The percentage of the first serve successfully serves into the service box. FSER stands for an offense skill. The higher the percentage is the higher chance wins the point.. D.. First serve points winning percentage (FSERW): Number of points won on first serve, divided by total number of first serves available, includes aces. FSERW. 8. Global Community Tennis Association Inc., Percentage Tennis, http://www.playtennisintheparks.com/pages/index.cfm?siteid=8105 9 http://www.tennis.com.au/learn/rules-and-scoring/glossary/a-h 11.

(19) stands for an offense skill, and the higher the percentage is the higher chance wins the game. E.. Second serve points winning percentage (SSERW): Number of points won on second serve, divided by total number of second serves available. SSERW stands for an offense skill, and has the same character with FSERW, but usually lower than it.. (2) Defensive skills A.. First serve return points won percentage (RET1S): Number of receiving first serve. 政治大 receiving first serve. FSERW stands for a defense skill, and the higher the 立. points won by a player, divided by total number of points when the player was. ‧ 國. B.. 學. percentage is, the higher chance wins the game.. Second serve return points won percentage (RET2S): Number of receiving second. ‧. serve points won by a player, divided by total number of second serves received.. sit. y. Nat. Return games winning percentage (RETGW): Number of receiving points won by a. io. al. n. player, divided by total number of points received. (3) Mental toughness A.. Ch. engchi. er. C.. i Un. v. Tie-break games winning percentage (TBWP): Number of tie-break games won divided by total number of tie-break games played.. B.. Break points converted percentage (BPW): Number of breakpoints won divided by total number of break points played in receiving games.. C.. Break points saved percentage (BPS): Number of breakpoints saved divided by total number of break points played in serving games.. 12.

(20) Control variables A.. Age of players (AGE): Used to examine whether the age of players related to winning percentage.. B.. Career of a player (CAR): The total years as a professional player in sample years.. Dummy variables A.. TOP: Equals 1 if a player ranks higher than 30, and 0 otherwise.. B.. BOTTOM: Equals 1 if a player ranks lower than 100, and 0 otherwise.. C.. Y2006-Y2014: Used to control year effects.. D.. PLAYR: Equals 1 if a player uses right hand as his dominated hand, and 0. 立. ‧ 國. IN3: Equals 1 if the players win their first ATP title in 3 years after turned. ‧. E.. 學. otherwise.. 政治大. y. sit. n. al. proxy of a relative less talent player. G.. Ch. engchi. er. NONE: Equals 1 if a player never won an ATP title, and 0 otherwise, which is a. io. F.. Nat. professional, and 0 otherwise which is a proxy of a talent player.. i Un. v. FTITLE: Equals 1 if the year is after the year winning first ATP title, and 0 otherwise.. H.. FGS: Equals 1 if the year is after the year winning first Grand Slam title, and 0 otherwise.. 13.

(21) 3.4 Research Method The study first tries to examine which skills associate with winning percentage, then test whether a talent player perform better than less talent player, finally, examine whether a major win can improve a player’s performance. The paper constructs 5 models to examine the above hypotheses. 3.4.1 Model Construction This study first examines which skills associate with the winning percentage. Model 1. 政治大 respectively. The differences between the two models are due to Grand Slam data does not 立 and Model 2 are used to examine the ATP torus and the Grand Slam tournaments,. ‧ 國. 學. have RET1S and RET2S, which are replaced them with RETGW. Since only one year data includes for Grand Slam tournaments, no year effect used in Model 2.. ‧. Model 1.. Nat. sit. y. WPATP=α+β1AACE+β2ADF+β3FSER+β4FSERW+β5SSERW+β6RET1S+β7RET2S+β8TBWP. n. al. er. io. 𝑖=14 +β9BPW+β10BPS+β11AGE+β12CAR+β13PLAYR+∑22 14 𝛽 ∑𝑖=6 𝑌200𝑖 +β23TOP+β24BOTTOM+ ε. Model 2.. Ch. engchi. i Un. v. WPGL=γ+δ1AACE+δ2ADF+δ3FSER+δ4FSERW+δ5SSERW+δ6RETGW+δ7TBWP+δ8BPW+δ9 AGE+δ10CAR+δ11PLAYR+ζ Secondly, Model 3 is used to test Hypothesis 2, whether the talent players perform better than those of less talent players.. Model 3. WPATP=η+θ1IN3+θ2NONE+θ3AACE+θ4ADF+θ5FSER+θ6FSERW+θ7SSERW+θ8 RET1S+θ9 𝑖=14 RET2S+θ10TBWP+θ11BPW+θ12BPS+θ13AGE+θ14CAR+θ25PLAYR+∑24 16 𝜃 ∑𝑖=06 𝑌20𝑖 +θ25TO P+θ26BOTTOM+ι. 14.

(22) Third, Model 4 and 5 are used to test Hypothesis 3, whether the performance differs before and after a player won his first ATP (Grand Slam) title. FTITLE (FGS) is the proxy of winning the first ATP (Grand Slam) title.. Model 4 WPATP=κ+λ1FTITLE+λ2AACE+λ3ADF+λ4FSER+λ5FSERW+λ6SSERW+λ7RET1S+λ8RET2S +λ9TBWP+λ10BPW+λ11BPS+λ12AGE+λ13CAR+λ14PLAYR+μ Model 5. 政治大. WPGL=ν+ξ1FGS+ξ2AACE+ξ3ADF+ξ4FSER+ξ5FSERW+ξ6SSERW+ξ7RET1S+ξ8RET2S+ξ9T. 立. BWP+ξ10BPW+ξ11BPS+ξ12AGE+ξ13CAR+ξ14PLAYR+ο. ‧. ‧ 國. 學. n. er. io. sit. y. Nat. al. Ch. engchi. 15. i Un. v.

(23) Chapter 4. Empirical Results. 4.1 The Descriptive Statistics 4.1.1 Descriptive Statistics of ATP Data Table 4.1.1 provides the summary of descriptive statistics of the ATP tours main variables. As shown in Table 4.1.1, the mean (median) of WP is 47.49% (45.83%) with maximum (minimum) amount of 95.29% (0%). Roger Federer in 2005 kept the maximum WP record, meanwhile the minimum WP records was kept by both Jiri Vesely and Dusan. 治政 Lajovic in 2013.The mean (median) of TBWP is 47.97% (50%) 大 with the maximum 立 (minimum) percentage of 100% (0%). The record of the maximum tie-break game winning ‧ 國. 學. percentage is kept by 35 players whose average tie-game played are 2.086, and the minimum. ‧. tie-break game winning percentage is kept by 85 players whose average tie-game played are. sit. y. Nat. 2.471. The mean (median) of AACE is 5.4743 (4.9) per game with the maximum (minimum). io. er. 20.6 (0) severed average per game. The maximum number is kept by Ivo Karlovic in 2007,. al. meanwhile the minimum number is kept by Di Wu in 2012 (with only 6 ATP matches. n. iv n C played). The mean (median) of BPW ish39.02% (39%) with e n g c h i U the maximum (minimum) percentage of 100% (10%). The maximum percentage is kept by Thiemo de Bakker in 2012 (with only 6 ATP matches played), meanwhile the minimum percentage is kept by Vladimir Voltchkov in 2005 (also with only 6 ATP matches played). The mean (median) of ADF, FSER, FSERW, SSERW, BPS, RET1S and RET2S are 2.8143 (2.7), 60.77 % (61%), 70.31% (70%), 50.02% (50%), 59.74% (60%), 28.5% (29%) and 48.79% (49%), respectively. The maximum (minimum) number of ADF, FSER, FSERW, SSERW, BPS, RET1S and RET2S are 11.5 (0.1), 74% (43%), 85% (52%), 61% (34%), 79% (14%), 40% (13%) and 58% (35%), respectively. 16.

(24) Regarding the control variables, the mean (median) of AGE is 26.42 (26) with the highest (youngest) year of 37 (17). The mean (median) of CAR is 8.0834 (8) year with the longest (shortest) years of 20 (0) Table 4.1.1 Descriptive Statistic of the Main Variables Examined of ATP Data Variables. Mean. Stdev.. Min. Q1. Median. Q3. Max. WP AACES ADF FSER FSERW. 46.49% 5.4743 2.8143 60.77% 70.31%. 15.10% 3.0696 1.0542 4.47% 4.61%. 0.00% 0.0000 0.1000 43.00% 52.00%. 36.36% 3.3000 2.1000 58.00% 67.00%. 45.83% 4.9000 2.7000 61.00% 70.00%. 56.10% 7.0000 3.4000 64.00% 73.00%. 95.29% 20.6000 11.5000 74.00% 85.00%. SSERW RET1S RET2S. 50.02% 28.50% 48.79%. 3.37% 3.22% 3.47%. 34.00% 13.00% 35.00%. 48.00% 26.00% 47.00%. 50.00% 29.00% 49.00%. 52.00% 31.00% 51.00%. 61.00% 40.00% 58.00%. TBWP BPW BPS AGE CAR. 47.97% 39.02% 59.74% 26.42 8.08. 19.62% 5.58% 5.66% 3.57 3.40. 0.00% 10.00% 14.00% 17.00 0.00. 37.50% 36.00% 57.00% 24.00 6.00. 50.00% 39.00% 60.00% 26.00 8.00. 59.22% 42.00% 63.00% 29.00 10.00. 100.00% 100.00% 79.00% 37.00 20.00. ‧. N=1540. 學. ‧ 國. 立. 政治大. sit. y. Nat. io. er. Table 4.1.2 presents the summary of strong hand per year. As shown in table 4.1.2, right-. al. n. handers have 1,363 times of players within the 10 years while left-handers only have 177. In. C h each year. U n i total there are approximately 150 players engchi. v. Table 4.1.2 Summary of Strong Hand per Year PlayR PlayL 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Times. 1363. 177. 156. 163. 158. 164. 151. 147. 146. 156. 146. 153. Table 4.1.3 lists Pearson correlation between all variables. As Table 4.1.3 indicates, the variables are significantly correlated with WP, and the correlations between these variables are at 1% significant level. Moreover, most of variables are positively correlated with WP, except ADF is negatively correlated.. 17.

(25) Table 4.1.3 Pearson Correlation Coefficient of All Variables Variables WP. WP. AACES. ADF. FSER. FSERW. SSERW. RET1S. RET2S. TBWP. 1 0.2490. ***. 1. ADF. -0.2548. ***. 0.1842. ***. 1. FSER. 0.0991. ***. -0.1336. ***. -0.3369. ***. 1. FSERW. 0.4918. ***. 0.8067. ***. 0.0670. ***. -0.2408. ***. 1. 0.6221. ***. 0.2751. ***. -0.3775. ***. 0.1256. ***. 0.4207. ***. RET1S. 0.4276. ***. -0.3653. ***. -0.1324. ***. 0.0651. *. -0.2232. ***. RET2S. 0.3787. ***. -0.4172. ***. -0.1123. ***. 0.0327. **. -0.2071. ***. 0.1065. ***. 0.5127. ***. 1. TBWP. 0.3846. ***. 0.1164. ***. -0.0907. ***. 0.0365. **. 0.1631. ***. 0.1840. ***. 0.0778. ***. 0.0822. BPW. 0.2928. ***. -0.2323. ***. -0.0861. ***. -0.0145. **. -0.1357. ***. 0.0493. *. 0.4132. ***. 0.4257. ***. 0.4434. ***. 0.4670. ***. -0.0172. ***. 0.0945. *. 0.5245. ***. 0.4352. ***. -0.0676. ***. -0.0941. ***. -0.0813. ***. -0.0526. **. -0.0158. **. 0.0298. **. -0.0658. ***. 0.0227. -0.1037. ***. -0.0359. **. 0.0212. **. SSERW. CAR. 0.0085. -0.0410 -0.0265. -0.0132 0.0408. 0.0243. ***. CAR. 0.1116. n. er. io. sit. y. Nat. Ch. engchi. 18. i n U. v. 1 0.0017 0.0908 -0.0136. ***. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level.. al. AGE. ***. ‧. AGE. BPS. 1 治政 0.1139 1 大. 學. BPS. 立. ‧ 國. AACES. BPW. 0.0063. 1 ***. -0.0426. *. -0.0110 0.0532. **. 1 -0.0049. 1. 0.0143. 0.9076. *. 1.

(26) 4.1.2 Descriptive Statistics of Grand Slam Data In addition, the study also tries to examine whether the Grand Slam Tournaments (GST) have the different results with ATP tours. Due to the limitations of data collection, GST data drops BPS, and combines RET1S and RET2S into RETGW. Table 4.1.4 provides the summary of descriptive statistics of GST. As shown in Table 4.1.4, the mean (median) of WP is 43.15% (50%) with the maximum (minimum) percentage of 100 (0). The maximum percentage is kept by the four champions, with the minimum percentage is kept by players lost in the first round. The mean (median) of AACE, ADF, FSER, FSERW and SSERW are 10.33 (9), 4.18 (3.5), 62.45% (66.26%),. 治政 72.05% (72.17%) and 51.53% (52.26%). The above values大 of the means are slightly higher 立 than ATP tours, which implies that the GSTs are more competitive than ATP tours. ‧ 國. 學. Table 4.1.4 Summary of Descriptive Statistics of Grand Slam Tournaments Median. Q3. Max. 0.00% 0.0000 0.0000. 0.00% 5.6667 2.1429. 50.00% 9.0000 3.5000. 66.67% 14.0000 5.5000. 100.00% 36.6667 20.0000. 5.95% 6.78% 7.14% 6.59% 41.33% 17.53% 3.69 3.73. 45.81% 52.94% 27.50% 14.00% 0.00% 0.00% 19.00 0.00. 58.33% 67.22% 47.11% 30.36% 0.00% 26.32% 25.00 7.00. 62.26% 72.17% 52.26% 34.70% 50.00% 37.09% 28.00 10.00. 66.67% 76.88% 56.76% 38.36% 100.00% 46.15% 30.00 12.00. 78.92% 87.84% 70.83% 70.37% 100.00% 100.00% 36.00 18.00. al. Ch. engchi. y. 31.56% 6.3947 2.6962. sit. 62.45% 72.05% 51.53% 34.29% 42.72% 36.05% 27.77 9.77. Q1. er. FSER FSERW SSERW RETGW TBWP BPW AGE CAR. Min. ‧. 43.15% 10.3291 4.1753. n. WP AACES ADF. Stdev.. io. Mean. Nat. Variables. i Un. v. N=290 Table 4.1.5 provides Pearson Correlation Coefficient of GST. As Table 4.1.5 indicates that most of the variables are significantly and positively correlated with WP, except FSER (is insignificant) and ADF (is negatively correlated).. 19.

(27) Table 4.1.5 Pearson Correlation Coefficient of Grand Slam Tournaments Variables WP. WP. AACE. ADF. FSER. FSERW. AACE. 1 0.22471. ***. 1. ADF. -0.2148. ***. 0.11961. FSER. 0.09401. FSERW. 0.37903. ***. 0.60047. ***. -0.0024. SSERW. 0.28725. ***. 0.15607. ***. -0.3329. RETGW. 0.40977. ***. -0.1592. ***. -0.0028. -0.0311. 立 -0.1238. TBWP. 0.34354. ***. 0.13098. **. -0.028. 0.0467. BPW. 0.22275. ***. -0.1558. ***. AGE. 0.11293. *. -0.0886. 0.16702. ***. ***. 1. BPW. AGE. CAR. 1 治政 0.28432 1 大. 0.02195 ***. -0.0222. 0.08935. -0.0653. -0.1069. *. -0.1419. **. 0.12509. **. 0.12024. **. *** **. -0.1825. 0.10106. *. 0.02741. -0.1394. **. 0.04633 0.03466. ***. -0.0707 0.10057. **. 0.10901. **. 1 0.20259. ***. 1. 0.33113. ***. 0.0147. 1. 0.09804. *. 0.04193. 0.07317. 1. 0.08724. 0.90703. ‧. -0.1314. -0.3308. **. TBWP. 1. ‧ 國. 0.07681. RETG W. 學. CAR. *. SSERW. 0.13853. n. al. er. io. sit. y. Nat. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level.. **. Ch. engchi. 20. i n U. v. 0.04605. ***. 1.

(28) 4.2 Tennis Skills and Winning Percentage In this section, the paper constructs two multiple regression models to test which skills associate with the winning percentage. 4.2.1 Regression Results of ATP and Grand Slam Data Table 4.2.1 presents the regression results between WP and tennis skills by using the data of ATP tours. The adjust R2 is 0.8032 implies the offensive and defensive skills and mental toughness highly associate with WP. The results reveal that coefficients of FSER,. 政治大 The coefficient of AACE and ADF is negative significantly at 10% level associated with WP. 立 SSERW, RET1S, RET2s, TBWP, BPW and BPS all positive significantly associate with WP.. ‧ 國. 學. The coefficients of control variables AGE and CAR are insignificantly associated with WP. Table 4.2.1 VIF column denotes that no coefficient is greater than 10, which implies there is. ‧. no multicollinearity problem.. y. Nat. io. sit. Moreover, the standardized estimate coefficients column of Table 4.2.1suggests which. n. al. er. variable is more relevant to WP. According to Table 4.2.1 FSERW is the most influence. Ch. i Un. v. variable with a 0.408 of standardized estimate coefficient. Coefficients of RET1S, SSERW,. engchi. RET2S and FSER are 0.256, 0.205, 0.164 and 0.095, respectively. TOP and BOTTOM are used to control the rank effect.. 21.

(29) Table 4.2.1 Regression Results of ATP Tours WPATP=α+β1AACE+β2ADF+β3FSER+β4FSERW+β5SSERW+β6RET1S+β7RET2S+β8TBWP 𝑖=14 +β9BPW+β10BPS+β11AGE+β12CAR+∑21 13 𝛽 ∑𝑖=06 𝑌20𝑖 +β22PLAYR+β23TOP+β24BOTTOM+ε. Variables. Expected Direction. Parameter Estimate. Standardized Estimate. T value ***. VIF. INTERCEPT AACE ADF FSER FSERW. ? + + +. -2.104 -0.002 -0.008 0.320 1.336. 0.000 -0.044 -0.053 0.095 0.408. -25.59 * -1.92 *** -3.79 *** 7.11 * 17.13. SSERW RET1S RET2S TBWP BPW BPS AGE CAR PLAYR Y2006 Y2007. + + + + + + ? ? ? ? ?. 0.918 1.203 0.714 0.146 0.297 0.288 -0.001 -0.001 -0.002 -0.003 -0.001. 0.205 0.256 0.164 0.190 0.110 0.108 -0.034 -0.013 -0.004 -0.006 -0.002. 13.38 *** 16.99 *** 10.63 *** 16.12 *** 8.4 *** 7.46 -1.19 -0.45 -0.37 -0.42 -0.1. 1.499 1.393 4.433 1.839 1.333 1.634 1.780 1.870 1.043 1.843 1.837. -0.001 0.001 -0.002 0.007 0.001 0.000 0.004 0.060 -0.022. -0.003 0.002 -0.003 0.014 0.003 0.000 0.008 0.157 -0.070. -0.18 0.1 -0.21 0.94 0.19 -0.01 0.51 *** 10.56 *** -5.22. 1.863 1.810 1.786 1.784 1.834 1.810 1.864 1.729 1.409. Ch. engchi. y. sit. er. ‧ 國 n. al. ‧. io. ? ? ? ? ? ? ? ? ?. 政治大. 學. Nat. Y2008 Y2009 Y2010 Y2011 Y2012 Y2013 Y2014 TOP BOTTOM. 立. ***. i Un. v. 0.000 6.350 6.600 1.082 4.129. N=1540 R2=0.8063 adj.R2=0.8032 F=262.74 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 22.

(30) TBWP, BPW and BPS are 0.190, 0.110 and 0.108, respectively. Independent variables can be grouped into three categories, offensive skill (FSERW, SSERW, FSER and ADF), defensive skill (RET1S and RET2S) and mental toughness (TBWP, BPW and BPS), and the values of standardized estimate are 0.612, 0.421 and 0.407, respectively. Table 4.2.2 suggest that offensive skill has the highest value, but the other two categories also play an important role in tennis competition, and as the results of F-test shown, they are all significantly differ from each other. The result implies that current pro tennis competitions are highly competitive. To win a match a player must equip not only offensive and defensive skills, but also strong mental toughness.. 政治大. Table 4.2.2 Standardized Estimate Value and the Results of F-test of ATP Tours 0.612 0.421 0.407. F Test. Off. & Def. Off. & mental Def. & mental. F Value. 學. Offensive Defensive Mental. 立. Tennis Skills. 19.5 *** 177 *** 111 ***. ‧. ‧ 國. Tennis Skills. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. y. Nat. io. sit. Furthermore, the study uses GST to examine which tennis skills are associated with the. n. al. er. WP again. However, due to limitation of the data, the study replaces RET1S and RET2s as. Ch. i Un. v. RETGW and drops the year dummy. Table 4.2.3 presents the results of the regression, which. engchi. denotes a similar result as Table 4.2.1, most of the coefficients of the independent variables are positive significantly associated with WP, except AACE and FSER. According to the standardize estimate coefficients of the variables, RETGW has the highest value 0.399, while values of FSERW, SSERW, TBWP, BPW and ADF are 0.318, 0.215, 0.205, 0.155 and 0.123, respectively. Although these values are slightly different from ATP tours, the standardize coefficients of offensive, defensive and mental strength are 0.656, 0.399 and 0.360, respectively. These values reveal that all the skills are important to WP. Though the offensive skill is the highest associated with WP, table 4.2.4 shows that defensive skills are as important. 23.

(31) as offensive skills. The results indicate that the competitiveness remains high in higher level tournament. Table 4.2.3 Regression results of Grand Slam Tournaments WPGL=γ+δ1AACE+δ2ADF+δ3FSER+δ4FSERW+δ5SSERW+δ6RETGW+δ7TBWP+δ8BPW+δ9 AGE+δ10CAR+δ11PLAYR+ζ. Variables. Expected Direction. Parameter Estimate. Standardized Estimate. T value. VIF. INTERCEPT. ?. -1.754. 0. -5.64 ***. 0. AACE ADF FSER FSERW SSERW RETGW TBWP BPW AGE CAR PLAYR. + + + + + + + + + ?. 0.004 -0.014 0.155 1.479 0.95 1.908 0.157 0.278 -0.015 0.017 -0.022. 0.088 -0.123 0.029 0.318 0.215 0.399 0.205 0.155 -0.179 0.207 -0.001. 1.59 -2.54 ** 0.64 5.82 *** 4.52 *** 8.5 *** 4.71 *** 3.44 *** -1.79 * 2.03 ** -0.08. 1.755 1.328 1.182 1.699 1.29 1.256 1.082 1.149 5.733 5.894 1.042. er. sit. y. ‧. ‧ 國. 學. al. n. adj.R2=0.4937. io. R2=0.513. Nat. N=290. 立. 政治大. Ch. engchi. i Un. v. F=26.62 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level Table 4.2.4 Standardized Estimate Value and the Results of F-test of Grand Slam Tournaments Tennis Skills. Tennis Skills. F Test. Offensive. 0.656. Off. & Def.. Defensive Mental. 0.399 0.36. Off. & mental Def. & mental. F Value 2.32 27.97 *** 29.88 ***. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 24.

(32) 4.3 Talent Players Perform Better Than Less Talent Players In order to test Hypothesis 2, the study needs to define “ talent players.”. However, it is. hard to define what kind of player can be defined as a talent player. Who has won a junior Grand Slam title might be a good proxy. However, due to lack of related information in Grand Slam web site, the study uses a player who had won his first ATP title within 3 years after turning professional tennis player instead. Therefore, the research defines talent players into 3 groups.. 政治大 within three years after they turned to professional. 立. Group 1, the most talent players, is defined as those players who won their first ATP title. ‧ 國. 學. Group 2, the median talent players, is defined as those who won their first ATP title three years after they turn to professional.. ‧. Group 3, the less talent players, is defined as those who never won an ATP title in their. y. Nat. er. io. sit. professional career until 2014.. Based on the above grouping, the study sets two dummy variables IN3 and NONE,. n. al. Ch. i Un. v. which represent Group1 and Group3, respectively. Table 4.3.1 presents regression results of. engchi. Model 3. As Table 4.3.1 indicates both coefficients of variables are significantly associated with WP. However, the coefficient IN3 (Group 1) is positive, while NONE (Group 3) is negative. The results reject the Hypothesis 2, there is no significant difference between talented players and non-talented players with respect to tennis skills and mental toughness, which suggests that Group 1, who won their first ATP title in 3 years had better performance than other groups; and Group 3, those who never won an ATP title has less winning percentage than other groups.. 25.

(33) Table 4.3.1 The Regression Results of Groups Divided by Talent WPATP=η+θ1IN3+θ2NONE+θ3AACE+θ4ADF+θ5FSER+θ6FSERW+θ7SSERW+θ8 RET1S+θ9 𝑖=14 RET2S+θ10TBWP+θ11BPW+θ12BPS+θ13AGE+θ14CAR+θ25PLAYR+∑24 16 𝜃 ∑𝑖=06 𝑌20𝑖 +θ25TO P+θ26BOTTOM+ι. Variables. Expected Direction. Parameter Estimate. INTERCEPT IN3 NONE AACE. ? + +. -2.0139 0.0223 -0.0127 -0.0027. 0.0000 0.0508 -0.0416 -0.0550. -24.09 *** 3.68 *** -2.94 *** -2.4 **. 0.000 1.512 1.585 4.168. ADF FSER FSERW SSERW RET1S RET2S TBWP BPW BPS AGE. + + + + + + + + ?. -0.0076 0.3169 1.2920 0.8871 1.1471 0.6651 0.1440 0.2976 0.2855 -0.0011. -0.0528 0.0939 0.3944 0.1983 0.2445 0.1531 0.1872 0.1101 0.1071 -0.0251. -3.84 *** 7.09 *** 16.58 *** 12.97 *** 16.1 *** 9.86 *** 16.02 *** 8.49 *** 7.46 *** -0.89. 1.500 1.394 4.492 1.855 1.830 1.915 1.084 1.333 1.635 6.378. CAR PLAYR Y2006 Y2007 Y2008 Y2009 Y2010 Y2011 Y2012 Y2013 Y2014. ? ? ? ? ? ? ? ? ? ? ?. -0.0012 -0.0024 -0.0028 0.0000 -0.0008 0.0018 -0.0004 0.0085 0.0034 0.0030 0.0084. -0.0262 -0.0051 -0.0056 0.0000 -0.0017 0.0035 -0.0007 0.0165 0.0068 0.0058 0.0167. TOP BOTTOM. ? ?. n. R2=0.8094. F=247.14. adj.R2=0.8061. Ch. engchi. 0.0517 -0.0199. y. sit. i Un. 0.1356 -0.0633. v. VIF. -0.9 -0.45 -0.37 0 -0.11 0.23 -0.05 1.09 0.44 0.38 1.07. 6.743 1.044 1.846 1.843 1.868 1.817 1.795 1.797 1.854 1.838 1.917. 8.8 *** -4.64 ***. 1.887 1.479. er. io. N=1540. 政治大. ‧. Nat. al. T value. 學. ‧ 國. 立. Standardized Estimate. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level 26.

(34) Moreover, the study further applies univariate and multiple regression approaches to examine whether any differences among groups in respect to their tennis skills and how these skills affect WP among groups. Table 4.3.2 depicts the means of three groups. Group 1 indicates better performances than other groups, Group 2 perform better than Group 3, and Group 3 reveals the worst performances. Table 4.3.3 presents performances difference statistical results of ANOVA among groups. Except ADF fail to reject the difference assumption, and other independent variables, (offense and defense skills, and mental toughness) all reject null hypothesis of no. 政治大 results strengthen performance difference hypothesis. 立. difference among groups. Table 4.3.4 denotes the pairwise t test between groups and the. FSERW. 60.92%. 5.53. 2.73. 60.66%. 4.85. 2.95. 60.83%. RET1S. io. 30.25%. Group 2. 28.95%. Group 3. 27.50%. al. n. Group 1. RET2S. TBWP. 50.72%. 49.08% 49.30%i v C h47.88% Un e n g c h i44.20%. 27. 52.94%. 70.74%. 50.37%. 68.65%. 48.76%. BPW. 55.74%. SSERW. 74.25%. y. 2.63. sit. Variables. FSER. 7.28. Nat. Group 3. ADF. er. Group 2. AACE. ‧. Group 1. ‧ 國. Variables. 學. Table 4.3.2 Comparison of the Variance Means of 3 Groups. BPS. 40.62%. 63.43%. 39.45%. 60.03%. 38.09%. 58.30%.

(35) Table 4.3.3 ANOVA Statistical Results of Groups. ADF. FSER. FSERW. DF. Model. 471.6948. Error. 1537. 13557.8321. 8.8210. Corrected Total. 1539. 14501.2217. 2. 24.0186. 12.0093. Error. 1537. 1686.2271. 1.0971. Corrected Total. 1539. 1710.2457. 2. 0.0016. 0.0008. Error. 1537. 3.0797. 0.0020. Corrected Total. 1539. 3.0814. Model. Model. Model. 2 1537 立. 10.95. 0.000 ***. 0.41. 0.664. 0.000 ***. 154.78. 0.000 ***. 76.26. 0.000 ***. 0.0696. 0.000 ***. 1.4581. 0.0009. 1539. 1.7517. 2. 0.1438. 0.0719. 1537. 1.4491. 0.0009. Corrected Total. 1539. 1.5929. Model. 2. 0.1392 1.7182. Corrected Total. Ch. 1539. iv 0.0011 n U. 62.26. Error. al. 2. 2.3336. 1.1668. 31.53. 0.000 ***. Error. 1537. 56.8799. 0.0370. Corrected Total. 1539. 59.2135. 2. 0.1235. 0.0617. 20.31. 0.000 ***. Error. 1537. 4.6733. 0.0030. Corrected Total. 1539. 4.7968. 2. 0.4300. 0.2150. 73.43. 0.000 ***. 1537 1539. 4.4999 4.9299. 0.0029. Model. io. Model. Model Error Corrected Total. n. Model. 1537. e n1.8574 gchi. ‧. ‧ 國. 1537. 學. 0.1468. er. 146.31. 0.2937. Nat. BPS. 0.000 ***. 2. Model. Error. BPW. 53.47. 3.2676. Corrected Total. TBWP. 治政 0.5226 0.2613 大 2.7450 0.0018. P Value. 1539. Error. RET2S. F Value. 943.3896. Corrected Total. RET1S. Mean Square. 2. Error SSERW. Sum of Square. y. AACE. Source. sit. Variables. Comparisons significant at the 0.05 level are indicated by ***. 28.

(36) Table 4.3.4 Mean Difference between Groups. ADF. FSER1. FSERW. G1 - G2. 1.7478. 1.2866. 2.2090 ***. G1 - G3. 2.4262. 1.9652. 2.8873 ***. G2 - G3. 0.6785. 0.3590. 0.9980 ***. G1 - G2. -0.0981. -0.2608. G1 - G3. -0.3184. -0.4810. -0.1558 ***. G2 - G3. -0.2203. -0.3330. -0.1077 ***. G1 - G2. NA. NA. NA. G1 - G3. NA. NA. NA. G2 - G3. 治政 0.0350 大 0.0560. NA. NA. NA. G1 - G2. 立. G1 - G3. 0.0164. 0.0255 ***. 0.0371. 0.0466 ***. G2 - G3. 0.0161. 0.0128. G1 - G2. 0.0130. ‧. 0.0195 ***. 0.0082. 0.0177 ***. G1 - G3. 0.0274. 0.0227. y. 0.0322 ***. G2 - G3. 0.0145. 0.0112. 0.0178 ***. io. G1 - G2. al. 0.0164. n. BPS. 0.0626 ***. 0.0418. G1 - G3. G2 - G3. BPW. 0.0495. 0.0305 ***. 0.0257. G1 - G3 TBWP. 0.0416 ***. 0.0209. G1 - G2. Nat. RET2S. 0.0646. 0.0285. 學. RET1S. 0.0210. ‧ 國. G2 - G3 SSERW. 95% Confidence Limits. Ch. 0.0284. e n0.0120 gchi. sit. AACE. Strain Difference Between Comparison Means. er. Variables. i Un. v 0.0232. 0.0216 ***. 0.0084. 0.0156 ***. 0.0112. 0.0336 ***. G1 - G2. 0.0644. 0.0345. 0.0943 ***. G1 - G3. 0.1154. 0.0856. 0.1453 ***. G2 - G3. 0.0510. 0.0303. 0.0717 ***. G1 - G2. 0.0117. 0.0031. 0.0202 ***. G1 - G3. 0.0253. 0.0167. 0.0338 ***. G2 - G3. 0.0136. 0.0077. 0.0195 ***. G1 - G2. 0.0341. 0.0257. 0.0425 ***. G1 - G3. 0.0513. 0.0429. 0.0597 ***. G2 - G3. 0.0173. 0.0114. 0.0231 ***. Comparisons significant at the 0.05 level are indicated by *** 1. FSER has no value due to the result of ANOVA test of it is insignificant. 29.

(37) In addition, the study bases on talent difference to divide the data into 3 subsets to compare the association between tennis skills and mental toughness with winning percentage. According to Table 4.3.5, Group 1 and Group 2 show almost the identical feature that most of coefficients of the skills are positive significantly associated with WP, except AACE. The only difference is that ADF is positive significant correlation in Group 1, insignificant in Group 2 and negative significantly in Group3. FSERW, SSERW, RES1S and RET2S are the highest 4 associated variables, then follow by FSER, TWBP, BPS and BPW. The comparison indicates that serving ace (AACE) is not associated with WP to those players with the highest talent, while to those players with the least talent group the more aces serve the less winning. 治政 percentage is. Furthermore, in Table 4.3.6, the tennis skill 大 variables are combine into 立 offensive, defensive and mental toughness, the orders of Group 1 and Group 2 from high to ‧ 國. 學. low are offensive, defensive and mental toughness, while the difference between offence and. ‧. defense in Group 1 is insignificant. The results suggest that for most talented player, offence. sit. y. Nat. and defense skills are equally important, while offence skill is more important than defense. io. er. skill for median talent players. On the other hand, Group 3 shows different order, which is. al. n. offensive, mental, and defensive. The skills order comparison implies that to win more games. ni C h than other groups. for Group 3 needs more mental toughness U engchi. 30. v.

(38) Table 4.3.5 Regression Results by Talent WPATP=α+β1TBWP+β2AACE+β3ADF+β4FSER+β5FSERW+β6SSERW+β7BPW+β8BPS+β9R 𝑖=14 ET1S+β10RET2S+β11AGE+β12CAR+ + ∑21 13 𝛽 ∑𝑖=06 𝑌20𝑖 +β22PLAYR+ε. Variables. GROUP 1 Standardized T value Estimate. GROUP 2 Standardized T value Estimate. 0.000 -18.300 *** 0.077 1.290 0.065 1.850 * 0.207 6.180 *** 0.285 5.460 ***. SSERW RET1S RET2S. 0.366 0.394 0.317. 9.130 *** 9.430 *** 6.490 ***. TBWP BPW BPS. 0.209 0.153 0.155. 8.170 *** 3.980 *** 4.640 ***. 9.710 *** 14.580 *** 10.270 ***. 0.234 0.302 0.174. 7.550 *** 9.740 *** 5.630 ***. 0.000 -14.660 *** -0.098 -2.060 ** -0.120 -3.620 *** 0.087 2.760 *** 0.476 10.310 ***. 4.650 *** 4.960 ***. 0.273 0.183 0.153. 10.090 *** 6.310 *** 4.960 ***. 政治大 0.210 10.880 *** 0.103 0.125. Group 2 : N=664. Group 3 : N=666. R2=0.7806. R2=0.5426. adj.R2=0.773. adj.R2=0.5269. sit. y. Nat. adj.R2=0.8949. 0.236 0.355 0.270. ‧ 國. R2=0.9054. -23.820 *** -0.280 -1.180 7.960 *** 13.850 ***. ‧. Group 1 : N=210. 立. 0.000 -0.012 -0.027 0.174 0.575. 學. INTERCEPT AACE ADF FSER FSERW. GROUP 3 Standardized T value Estimate. n. al. er. io. F=85.72 F=103.65 F=34.67 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. Ch. engchi. i Un. v. Table 4.3.6 Standardize Estimate Values and F test of 3 Groups from Table 4.3.5 Tennis Skills. Group 1. Group 2 0.923 0.7102 0.5173. Offensive Defensive Mental. 0.985 0.6259 0.438. F Value Off. & Def. Off. & mental Def. & mental. Group 3. F Value 6.05 **. 1.66 31.85 *** 30.9 ***. 116.14 *** 102.83 ***. 0.9278 0.4736 0.6083 F Value 7.45 *** 54.13 *** 29.23 ***. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 31.

(39) 4.4 A Major Win Enhance a Player’s Performance As many researchers mentioned that level of self-confidence can be raised by the performance accomplishment if the experiences are successful (Bandura, 1977, Dewhurst, Anderson, Cotter, Crust and Clough, 2012, Newton, Finch, Harbke, and Podlog ,2013). Therefore in this section the study constructs two regression models to test whether a major win can enhance a player’s performance. The sample used in this section defined as players who won their major title after they turned to professional player. A major win defined as the first ATP title and Grand Slam title, respectively. 4.4.1 ATP Title as a Major Win. 立. 政治大. ‧ 國. 學. To test Hypothesis 3, a dummy variable, FTITLE, a player won his first ATP title year and after, sets as 1, whereas the year prior to that year sets as 0. As shown in Table 4.4.1, the. ‧. coefficient of FTITLE is significantly and positively associated to WP at 5% level. This. Nat. sit. y. indicates that players do improve their game winning percentage after getting their first ATP. n. al. er. io. title. Moreover, Table 4.4.2 indicates that most of the offensive and defensive skills have. i Un. v. significantly improved after winning the first ATP title, except FSER.. Ch. engchi. To further compare the difference before and after winning the first ATP title in respect to tennis skills and mental toughness. The regression model divide two subsets (before and after). The regression results reveal in Table 4.4.3. As shown in Table 4.4.3, coefficients of ACCE and ADF are insignificant for both sets, while coefficients of BPW and BPS (mental toughness) are insignificant in before set, but positive and significant in after set at 1% level. Table 4.4.4 indicates that after winning the first ATP title, mental toughness becomes more important with winning percentage, which explains that players indeed increase their confidence with a major win. On the other hand, table 4.4.4 also indicates that before winning first ATP title, offense and defense skills are equally important. Table 4.4.5 presents the mean 32.

(40) comparison of before and after sets. The comparison indicates that AACE and TBWP are the most improving variables, which means that players serve more serving aces per match and become more confident to win the tie-break games after winning the first ATP title. Table 4.4.1 Regression Results Before and After Winning the First ATP Title WPATP=κ+λ1FTITLE+λ2AACE+λ3ADF+λ4FSER+λ5FSERW+λ6SSERW+λ7RET1S+λ8RET2S +λ9TBWP+λ10BPW+λ11BPS+λ12AGE+λ13CAR+λ14PLAYR+μ. + + ? ? ?. ‧ 國 Nat. io. n. al. -2.681 0.019 0.002 -0.004 0.507 1.471 1.095 1.638 1.135 0.17. 0 0.065 0.056 -0.029 0.167 0.499 0.245 0.362 0.3 0.192. 0.259 0.268 -0.004 0 -0.02. 0.094 0.104 -0.095 -0.005 -0.043. 政治大. Ch. y. BPW BPS AGE CAR PLAYR. 立. T value. sit. ? + + + + + + + +. Standardized Estimate. er. INTERCEPT FTITLE AACE ADF FSER FSERW SSERW RET1S RET2S TBWP. Parameter Estimate. engchi. i Un. v. VIF. -19.57 *** 2.58 ** 1.15 -1.18 6.95 *** 10.85 *** 8.39 *** 11.94 *** 9.37 *** 9.13 ***. 0 1.584 5.822 1.548 1.439 5.25 2.119 2.289 2.549 1.098. 3.66 *** 3.58 *** -1.65 -0.09 -2.06 **. 1.658 2.114 8.303 8.194 1.074. ‧. Expected Direction. 學. Variables. N=444 R2=0.8275 adj.R2=0.8219 F=147 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 33.

(41) Table 4.4.2 ANOVA testing results of Before and After the First ATP Title Variables. Source. DF Sum of Square Mean Square F Value P Value. Between Groups Within Groups Total. 1 442 443. 48.33879 5379.405 5427.7435. 48.33879 12.1706. 3.9718. 0.0469**. ADF. Between Groups Within Groups Total. 1 442 443. 5.721152 349.905 355.6262. 5.721152 0.79164. 7.227. 0.0075**. FSER. Between Groups Within Groups. 1 442. 0.000039 0.83908. 0.000039 0.001898. 0.0205. 0.8861. Total. 443. 0.8391. FSERW. Between Groups Within Groups Total. 1 442 443. 0.036848 0.849837 0.8867. 政治大. 0.036848 19.1647 <.0001*** 0.001923. SSERW. Between Groups Within Groups Total. 1 442 443. 0.038547 0.34727 0.3858. 0.038547 49.0622 <.0001*** 0.000786. RET1S. Between Groups Within Groups Total. 1 442 443. 0.003847 0.373417 0.3773. 0.003847 0.000845. RET2S. Between Groups. 1. 0.018466. 0.018466 15.7083 <.0001***. 442 443. 0.519598 0.5381. 0.001176. 442 443. 0.266435 9.551734 9.8182. n. TBWP. Between Groups Within Groups Total. C1 h. engchi. y. 0.0334**. sit. io. al. 4.5536. er. Nat. Within Groups Total. ‧. ‧ 國. 立. 學. AACE. iv n U 0.266435. 12.3291 0.0005***. 0.02161 8.1993 0.0044***. BPW. Between Groups Within Groups Total. 1 442 443. 0.018756 1.011079 1.0298. 0.018756 0.002288. BPS. Between Groups Within Groups. 1 442. 0.047292 1.118509. 0.047292 18.6883 <.0001*** 0.002531. Total. 443. 1.1658. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 34.

(42) Table 4.4.3 Regression Results of Before and After the First ATP Title WPATP=α+β1TBWP+β2AACE+β3ADF+β4FSER+β5FSERW+β6SSERW+β7BPW+β8BPS+ β9RET1S+β10RET2S+β11AGE+β12CAR +β14PLAYR+ε. INTERCEPT AACE ADF FSER. -5.55 *** 0.94 -0.81 1.63. 0 -0.023 -0.019 0.185. -21.42 *** -0.45 -0.74 7.32 ***. 0.495 0.269 0.497 0.304 0.28 0.1 0.126. 3.24 *** 3.07 *** 5.17 *** 3.17 *** 4.35 *** 1.26 1.4. 0.546 0.257 0.314 0.309 0.167 0.108 0.123. 11.87 *** 8.91 *** 9.9 *** 9.38 *** 7.79 *** 4.01 *** 4.13 ***. 立. ‧ 國. T value. 0 0.151 -0.066 0.123. After N=319. R2=0.5815. R2=0.8734. adj.R2=0.532. adj.R2=0.868. ‧. Before N=125. 政治大. 學. Nat. y. FSERW SSERW RET1S RET2S TBWP BPW BPS. After Standardized Estimate. sit. Variables. Before Standardized T value Estimate. n. al. er. io. F=11.86 F=161.83 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level.. Ch. engchi. 35. i Un. v.

(43) Table 4.4.4 Integrate Coefficients Comparison of Defensive, Offensive and Mental Toughness Before and After Winning the First ATP Title Tennis Skills Before Offensive Defensive Mental. After. 0.972 0.801 0.506. F Test. 0.946 0.623 0.398. Before F Value. After F Value. 0.27 6.24 ** 14.28 ***. Off. & Def. Off. & mental Def. & mental. 8.83 *** 86.79 *** 62.04 ***. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. Table 4.4.5 Comparison of the Mean of Before and After the First ATP Title 2.92 2.67 -8.65%. 立. RET1S. 28.26% 28.92% 2.32%. FSERW. 60.70% 60.63% -0.11%. 70.36% 72.39% 2.88%. 政治大 RET2S TBWP 47.70% 49.14% 3.01%. 46.30% 51.75% 11.76%. BPW. 學. 38.00% 39.45% 3.80%. ‧. Nat. y. Before After Improve. 5.90 6.64 12.43%. FSER. io. sit. Variables. ADF. n. al. er. Before After Improve. AACE. ‧ 國. Variables. Ch. engchi. 36. i Un. v. SSERW 49.25% 51.32% 4.21% BPS 59.30% 61.60% 3.87%.

(44) 4.4.2 Grand Slam Title as a Major Win As mentioned in 4.4.1, players do improve their performance after winning the first ATP title, therefor the study tries to further examine whether players will improve even more after winning the highest level tournament, 4 GST. A dummy variable, FGS, a player won his first ATP title year and after, sets as 1, whereas the year prior to that year sets as 0. Table 4.4.6 presents the regression results after winning the first Grand Slam title. As shown in Table 4.4.6, the coefficient of FGS is statistical significantly but negatively associated with WP, which seems to imply that players won’t be better after getting the first Grand Slam title. The results also suggest that Grand Slam tournaments are indeed the highest competition level in. 治政 tennis, because a player must give his best effort in order to 大win a match in GST. On the other 立 hand, a player, who won a Grand Slam title, suggests that his tennis skills have reached a ‧ 國. 學. high and steady level. Therefore, it is not surprising that after winning the first Grand Slam. ‧. title, a player did not keep improving his tennis skills. However, a player, who had won. sit. y. Nat. Grand Slam title, also had stress to defend his titles, which might have a negative effect on. io. er. his performance. Furthermore, once a player had won a Grand Slam title, then his opponents. al. might study his strategies, habits, strength and weakness, which might clause more challenge. n. iv n C and make his performance worse. The mean shown in Table 4.4.7 reveals before h e ncomparison gchi U and after winning the first GST title and Table 4.4.8 shows the statistical results of ANOVA test before V.S. after winning the first Grand Slam title. The results denote that most of the. variables show no statistically significant difference before and after winning GS title, except for ADF, FSER, SSERW and BPW. However, those variables, showing a significant difference, are getting worse after winning the first Grand Slam title.. 37.

(45) Table 4.4.6 Regression Results for Winning the First Grand Slam Title WPGL=ν+ξ1FGS+ξ2AACE+ξ3ADF+ξ4FSER+ξ5FSERW+ξ6SSERW+ξ7RET1S+ξ8RET2S+ξ9T BWP+ξ10BPW+ξ11BPS+ξ12AGE+ξ13CAR+ξ14PLAYR+ο. Variables. Expected Direction. INTERCEPT FGS AACE ADF FSER. ? ? + +. -2.316 -0.027 0.001 0.011 0.213. 0 -0.092 -0.006 0.083 0.076. -10.96 *** -2.17 ** -0.07 1.53 1.66 *. 0 1.810 7.122 2.935 2.082. FSERW SSERW RET1S RET2S TBWP BPW BPS CAR PLAYR. + + + + + + + ? ?. 0.942 1.327 0.795 0.991 0.237 0.833 0.389 -0.004 -0.009. 0.325 0.318 0.204 0.205 0.24 0.221 0.118 -0.088 -0.021. 3.68 *** 5.2 *** 4.15 *** 4.06 *** 6.63 *** 5.22 *** 2.17 ** -1.97 * -0.54. 7.795 3.718 2.408 2.543 1.306 1.787 2.930 1.984 1.498. ‧ 國. 政治大. VIF. ‧ y. sit. n. al. er. io. adj.R2=0.8254. T value. 學. R2=0.8384. 立. Standardized Estimate. Nat. N=175. Parameter Estimate. i Un. v. F=64.27 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level.. Ch. engchi. Table 4.4.7 Comparison of the Mean of Before and After the First Grand Slam Title Variables Before After Improve Variables Before After Improve. AACE 6.62 6.28 -5.09% RET1S 30.87% 30.41% -1.50%. ADF. FSER. 2.48 3.03 22.53% RET2S. 60.94% 58.80% -3.51% TBWP. 51.81% 51.70% -0.20%. 38. 56.00% 53.45% -4.54%. FSERW 74.11% 73.55% -0.75% BPW 41.35% 41.10% -0.60%. SSERW 53.21% 51.55% -3.13% BPS 63.87% 62.37% -2.34%.

(46) Table 4.4.8 ANOVA Testing Results of Before and After the First Grand Slam Title. FSER. FSERW. 1. 4.947115. 4.947115. Within Groups. 173. 1858.16146. 10.740818. Total. 174. 1863.1086. 1. 13.594309. 13.594309. Within Groups. 173. 204.636777. 1.182872. Total. 174. 218.2311. 1. 0.019972. 0.019972. Within Groups. 173. 0.438914. 0.002537. Total. 174. 0.4589. Between Groups. Between Groups. Between Groups. 173. 立174. Total. 0.012107. Within Groups. 173. 0.193667. 0.001119. Total. 174. 0.2058. 1. 0.000934. 0.000934. Within Groups. 173. 0.235352. 0.00136. Total. 174. 0.2363. 1. 0.000049. BPS. ‧ 國. 0.5498. 0.4594. 10.8147. 0.0012 ***. 0.8144. 0.154194 0.000891 a173 iv l174C n 0.1542 hengchi U 1 0.028232 0.028232. 1.3381. 0.249. 0.1813. 0.6708. 173. 3.650103. Total. 174. 3.6783. 1. 0.000265. 0.000265. Within Groups. 173. 0.25291. 0.001462. Total. 174. 0.2532. 1. 0.009768. 0.009768. Within Groups. 173. 0.317886. 0.001837. Total. 174. 0.3277. Between Groups. 0.0056 ***. 0.0553. Within Groups Between Groups. 7.8719. 0.000049. n. BPW. Between Groups. 0.0009 ***. ‧. io. TBWP. 11.4926. 0.4084. Between Groups Total. 0.4983. 0.6867. Between Groups. Within Groups. P Value. 0.4288 0.012107. Nat. RET2S. 0.4606. 0.001359 0.001359 政0.427456治 0.002471 大. 1. Between Groups. F Value. 學. RET1S. 1. Between Groups Within Groups. SSERW. Mean Square. y. ADF. Sum of Square. DF. sit. AACE. Source. er. Variable. 0.021099. ***Significant at the .001 level, **Significant at the .05 level. 39. 5.316. 0.0223 **.

(47) To further compare the difference before and after winning the first GST title in respect to tennis skills and mental toughness. The regression model divides two subsets (before and after). The regression results depict in Table 4.4.9. The comparison indicates that RET1S has the highest coefficient of standardize estimate in before subset, but RET1S becomes statistically insignificant in after subset. ADF, FSER and BPS, on the contrary, are statistically insignificant in before subset, but they become statistically significant in after subset. The results imply that defensive skills become less important after winning the first GST title. Meanwhile, mental toughness improves more after winning the first GST title. On the other hand, table 4.4.10 shows that before winning the first GST title offence skills are as. 治政 important as defense skills, but after winning the first GST大 title, offense skills become the 立 most important, while defense skills and mental toughness are equally important. ‧ 國. 學. Therefore, the above statistical results reject the Hypothesis 3 there is no significant. ‧. change in tennis skills and mental toughness after a player won his first ATP (Grand Slam). Nat. sit. y. title. However, unlike winning the first ATP title, winning the first GST title shows only. n. al. er. io. mental toughness improvement and some skills even became worse. Ch. engchi. 40. i Un. v.

(48) Table 4.4.9: Regression Results Before and After Winning the First Grand Slam Title WPGL=α+β1TBWP+β2AACE+β3ADF+β4FSER+β5FSERW+β6SSERW+β7BPW+β8BPS+β9R ET1S+β10RET2S+β11AGE+β12CAR +β14PLAYR+ε Before Variables. Standardized Estimate. After Standardized Estimate. T value. INTERCEPT. 0. AACE1. -. -9.65 ***. T value 0. -. -10.15 ***. -0.216. -2.12 **. ADF. 0.091. 1.07. 0.094. 1.67 *. FSER. 0.078. 1.13. 0.116. 2.1 *. 4.17 ***. 0.456. 4.61 ***. ***. 0.267. 3.19 ***. ***. 0.027. 0.43. ***. 0.217. 3.34 ***. 0.323. 7.32 ***. 0.169. 3.3 ***. 0.168. 2.64 ***. FSERW. 0.41. SSERW. 0.347. RET1S. 0.532. 立. 治政4.91 大 7.74. TBWP. 0.197. 3.91 ***. 0.192. 3.15 ***. 0.133. 1.65. Group 2 : N=104. R2=0.8908. R2=0.8755. io. adj.R2=0.8704 adj.R2=0.8591. y. Nat. Group 1 : N=71. sit. BPS. n. al. er. BPW. ‧ 國. 2.95. ‧. 0.192. 學. RET2S. i Un. v. F=43.76 F=53.33 ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 1. Deleted in group 1 due to multicollinearity examined by variance inflation factors. Ch. engchi. Table 4.4.10 Integrate Coefficient Comparison of Defensive, Offensive and Mental Toughness Before and After Winning the First Grand Slam Title Tennis Skills Before. After. F Test. Before F Value. Offensive. 0.926. 0.717. Off. & Def.. 0.01. Defensive. 0.724. 0.244. Off. & mental. 4.08 **. Mental. 0.522. 0.66. Def. & mental. 9.62 ***. After F Value 8.08 *** 5.5 ** 1.13. ***Significant at the .001 level, **Significant at the .01 level, *Significant at the .05 level. 41.