1、工商管理學(xué)畢業(yè)論文英文翻譯    工商管理學(xué)畢業(yè)論文英文翻譯    1英文翻譯資料Can Complex Network Metrics Predict the Behavior of NBA Teams?Pedro O.S. Vaz de Melo Federal University of Minas Gerais 31270-901, Belo Horizonte Minas Gerais, Brazil olmodcc.ufmg.br Virgilio A.F. Almeida Federal Univer

2、sity of Minas Gerais 31270-901, Belo Horizonte Minas Gerais, Brazil virgiliodcc.ufmg.br Antonio A.F. Loureiro Federal University of Minas Gerais 31270-901, Belo Horizonte Minas Gerais, Brazil loureirodcc.ufmg.brABSTRACTThe United States National Basketball Association (NBA) is one of the most popula

3、r sports league in the world and is well known for moving a millionary betting market that uses the countless statistical data generated after each game to feed the wagers. This leads to the existence of a rich historical database that motivates us to discover implicit knowledge in it. In this paper

4、, we use complex network statistics to analyze the NBA database in order to create models to represent the behavior of teams in the NBA. Results of complex network-based models are compared with box score statistics, such as points, rebounds and assists per game. We show the box score statistics pla

5、y a significant role for only a small fraction of the players in the league. We then propose new models for predicting a team success based on complex network metrics, such as clustering coefficient and node degree. Complex network-based models present good results when compared to box score statist

6、ics, which underscore the importance of capturing network relationships in a community such as the NBA。Categories and Subject DescriptorsH.2.8 Information Systems: database management? Database Applications, Data mining; G.3 Mathematics of Computing: Probability and Statistics?Statistical computingG

7、eneral Terms2Theory1. INTRODUCTIONThe United States National Basketball Association (NBA) was founded in 1946 and since then is well known for its efficient organization and for its high level athletes. After each game played, a large amount of statistical data are generated describing the performan

8、ce of each player who played in the match. These statistics are used in the United States to move a betting market estimated in tens of billions Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not mad

9、e or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. KDD08, August 24?27, 2008, Las Vegas, Nevada

10、, USA. Copyright 2008 ACM 978-1-60558-193-4/08/08 .$5.00. of dollars. In 2006, the Nevada State Gaming Control Board reported $2.4 billion in legal sports wager 10. Meanwhile, in 1999, the National Gambling Impact Study Commission reported to Congress that more than $380 billion is illegally wagered

11、 on sports in the United States every year 10. The generated statistics are used, for instance, by many Internet sites to aid gamblers, giving them more reliable predictions on the outcome of upcoming games. The statistics are also used to characterize the performance of each player over time, dicta

12、ting their salaries and the duration of their contracts. Kevin Garnett 18 averaged 22.4 Points Per Game (PPG), 12.8 Rebounds Per Game (RPG) and 4.1 Assists Per Game (APG) in the 2006/2007 season, making his salary to be the highest in the 2007/2008 season: $23.75 million. On the other hand, Anderson

13、 Varej ?ao 18, who had 6.0 PPG, 6.0 RPG and 0.6 APG in the 2006/2007 season, asked in the following season for a $60 million contract for six years and had his request neglected. Robert Horry 18, who is at the 7th position in the rank of players who won more NBA championships with seven titles for t

14、hree different teams, has career averages of 7.2 PPG, 4.9 RPG and 2.2 APG and, in the year 2007, of his last title, had a salary of $3.315 million. Two simple questions arise from these observations. First, would Anderson Varej?ao be overpaid in case his request were accepted? Second, is Robert Horr

15、y underpaid, once he wins a title for every team he played? The first question was answered by Henry Abbot, a Senior Writer of ESPN.com, in his blog True Hoop 1. He said PPG, RPG and APG only measure the actions of a player within a second or two when someone shoots the ball. The rest of the time, p

16、oints and rebounds measure nothing. He also said, answering to the first question, that these statistics are against Anderson Varej?ao, who is one of the best players in the NBA in the adjusted plus/minus statistic. The plus/minus statistic keeps track of the net changes in score when a given player

17、 is either on or off the court, and it does not depend on to box scores, such as PPG, APG and RPG 2, 14. This indicates that Anderson Varej?ao could have asked for a $60 million contract. Moreover, in the aid of Anderson Varej?ao,3we point out that after he finally reached an agreement with the Cava

18、liers, the performance of the team went from 9 wins and 11 losses to 15 wins and 7 losses, with Anderson Varej?ao scoring 7.8 PPG, 8.5 RPG and 1.2 APG before his injury. For the second question we could not find an answer. Robert Horry has played 14 seasons, averaging a title per two years played an

19、d per team played. Is he a lucky guy who always play with the best ones or he really makes a difference? One thing we know for sure is, that simple statistics such as PPG, RPG and APG should not be the only metrics used to predict a player and team success. While the statistics are treated separatel

20、y and the players are treated individually, little is known whether there is any relationship between them. We have seen in history, players with insignificant box scores statistics playing significant roles on a team success. A possible way to study the collective behavior of social agents is to ap

21、ply the theory of complex networks 19, 22. A network is a set of vertices, sometimes called nodes, with connections between them, called edges. A complex network is a network characterized by a large number of vertices and edges that follow some pattern, like the formation of clusters or highly conn

22、ected vertices, called hubs 4. While in a simple network, with at most hundreds of vertices, the human eye is an analytic tool of remarkable power, in a complex network, this approach is useless. Thus, to study complex networks it is necessary to use statistical methods in a way to tell us how the n

23、etwork looks like. The goal of this work is to model the NBA as a complex network and develop metrics that predict the behavior of NBA teams. The metrics should take into account the social and work relationship among players and teams and should also be able to predict a team success without relyin

24、g on box score statistics. Before presenting the metrics, we show that the number of players who have made significant impact in the history of the NBA and in their teams is negligible if we draw our conclusions based only on box score statistics. Then, we study the characteristics of the NBA comple

25、x network in the direction of understanding how the relationships among players evolve over time. And then, finally, we present and compare the developed metrics that predict the success of NBA teams. The rest of this paper is organized as follows. Section 2 presents the related work. In Section 3,

26、we show that the box score statistics plays a significant role in only a small fraction of the players in the league. Section 4 describes the NBA as a complex network. The models we develop to predict team behavior are discussed and evaluated in Section 5. Finally, in Section 6, we present the concl

27、usions and future work.2. RELATEDWORKThe growing interest in the study of complex networks has been credited to the availability of a large amount of real data and to the existence of interesting applications in several biological, sociological, technological and communications systems 21. One of th

28、e most popular studies in this area was carried out by Milgram 17 and, from this work, the concepts of “six degrees of separation” and smallworld have emerged. In4other studies, well known complex networks were investigated, such as the Internet 13, World Wide Web 4, online social networking service

29、s 3, scientific collaboration networks 20, food webs 8, electric power grid 22, airline routes 5 and railways 13. The analysis of the relationship that exists among players of a sports league from the point of view of complex networks is already present in the literature. Onody and de Castro 21 anal

30、yzed statistics of the editions from 1971 to 2002 of the Brazilian National Soccer Championship. From the complex network analysis, Onody and de Castro 21 found, among other interesting results, that the connectivity of the players has increased over the years while the clustering coefficient declin

31、ed. The authors suggest that the possible causes for this phenomenon are the increase in the exodus of players to outside of Brazil, the increasing number of trades of players among national teams and, finally, the increase in the players career time. Moreover, it was found that the assortativity de

32、gree is positive and also increases over time, indicating that exchanges between players are, in most cases, between teams of the same size. Finally, the work of 7 presents an statistical analysis to quantify the predictability of all sports competitions in five major sports leagues in the United St

33、ates and England. To characterize the predictability of games, the authors measure the “upset frequency” (i.e., the fraction of times the underdog wins). Basketball has a low upset frequency, which instigated us to look into the basketball league database to find out models to predict the team behav

34、ior.3. MOTIVATIONFor every game played in the NBA, a huge amount of statistics is generated. This leads to the existence of a rich historical database that motivates us to discover implicit knowledge in it. The NBA data we used in this work was obtained from the site Database Basketball 11, which wa

35、s cited by the Magazine Sports Illustrated 9, 11 as the best reference site for basketball. The site makes available all the NBA statistical data in text files, from the year of 1946 to the year of 2006. Among the data, it is available information on 3736 players and 97 teams, season by season or by

36、 career. Our main goal is to move beyond the usual box score statistics presented in this database and discover new knowledge in the plain recorded numbers. The first analysis of the database aims to show why we need to look beyond the box score statistics. In the NBA, players are evaluated accordin

37、g to various box score statistics. The main ones are the points, assists and rebounds a player scores in a game. Figure 1 illustrates the distribution of points, assists and rebounds for the players during their careers in the NBA (with their mid-range and their 99 percentile). We observe that the d

38、istributions follow a power law. This means that the majority of the players who played, or are playing, in the NBA contributed with a small fraction of the points, assists and rebounds registered in the history of game. Moreover, the majority of the points, assists and rebounds were scored by a sma

39、ll fraction of the players. Figure 1 shows that more than 99% of the players have scored less points, assists or rebounds5than the mid-range value. It is important to point out that there are players that did not score a single point, assist or rebound during their careers. They are likely the playe

40、rs who were signed to a team for an experience period and then were released by the team, without playing a single game in the NBA. Thus, these players correspond to points that fall outside the power law curve showed in Figure 1, for they were not considered as NBA players. In terms of box score statistics, we also analyze the average performance of the players per game played. The results presented in Fi