On the Value of Individual Athletes in Team Sports

Transcription

1 No. 102 On the Value of Individual Athletes in Team Sports Falk Scherzer July 2010 An analysis conducted by the Chair of Macroeconomics at HHL Leipzig Graduate School of Management

2 HHL-Arbeitspapier HHL Working Paper No. 102 On the Value of Individual Athletes in Team Sports Falk Scherzer ISSN (Online version) HHL Leipzig Graduate School of Management

3 On the Value of Individual Athletes in Team Sports July 2010 Abstract This paper deals with the valuation of individuals in teams. Historical data for the National Basketball Association(NBA) was used to analyze the individual athletes contribution to team success. The analysis is conducted with data of all players who have played in the NBA since its foundation in A panel analysis is used to measure age effects. After adjusting the data for these effects, a multiple regression is applied to examine the players value assuming constant returns to added value. In a final step, the marginal returns to added value are examined and individual effective talent is calculated. Key words: production function, basketball, talent, team sports, evaluation 1 Introduction This papers deals with the valuation of individuals in teams. To examine this question, historical data for the North American National Basketball Association (NBA) was used to analyze the individual athletes contribution to team success. The discussion about players individual value was especially vital after the National Basketball Association (NBA) published a list of the 50 Greatest Players in NBA History at the 50th anniversary of the league in The players were chosen by a panel consisting of media, former players and coaches, current and former general managers and team executives 1. Panelists were asked for the 50 greatest players of all time without ranking them. However, it is difficult to define greatness and criteria obviously considered in the selection include standard basketball statistics like points scored, rebounds, assists, shots blocked and championships won. But since basketball is a team sport, even the 1 1

4 statistics of great players will deteriorate when they team up with other great players and certain decisive contributions like defense, hustle or clutch plays do not show up in any statistic. Did the Chicago Bulls win a record of 72 of their 82 regular season games just because of Micheal Jordan scoring 30 points per game? How big was the impact of the newly acquired defensive specialist Dennis Rodman who scored a mediocre 5.5 points per game but grabbed a league high of 14.9 rebounds per game. One could argue about this endlessly...or make use of the fact that NBA players usually change teams several times in their career and simply run a multiple regression. The economic analysis of sports has become a vital field of research as documented by the growing number of journals specialized on this topic. Since basketball is a team game and the team constitution varies each season, the impact of single players can be calculated. A data set containing all 3478 players who have played at least one regular season game since the NBA was founded in 1946 until 2008 is used to calculate the individual value of each player and analyze the marginal effect of adding player value to a team. 2 Theoretical Foundation The evaluation of athletes in team sports and the analysis of a production function are an uncommon but interesting field of economic research. Stadelmann and Eichenberger [2008] evaluate the talent of Formula One drivers using a multiple regression. 2 One of the first authors to deal with the topic was Scully [1974] who estimated a production function for Major League Baseball (MLB). Scully uses team statistics as the slugging average and the average strikeout-to-walk ratio as well as overall team quality dummies as input and the winning percentage as output to estimate a linear production function. Other studies like Berri [1999] evaluate individual talent by estimating a team production function based on individual statistics. The contribution of each statistic to team success is estimated and the players value is calculated based on individual statistics. These studies are useful to measure individual contribution to team success but not to asses individual talent of team members. 3 Chatterjee et al. [1994] use team statistics instead of 2 Formula One races are not a typical team sport. The fact that there are always two drivers in one team who use the same material is used to compare teammates. 3 It can regularly be observed that individual player statistics change significantly after players move from a mediocre team to a top contender or vice versa. This should not be interpreted as a change in talent. Individual statistics depend on individual talent but also on the teammates talent, amongst other things. This method could also create a bias towards front court players due to unobserved defensive skills. Good defense causes the opponents shooting percentage to drop and will be measured as an increase in defensive rebounds - but not necessarily by the player who defended the shot but likely by the team s front court 2

5 individual statistics as input to estimate the winning percentage of NBA teams for and try to make mid-season predictions for the play-offs and the season based one these estimates. Gustafson et al. [1999] estimate a joint production function for MLB using individual statistics as inputs and victories as well as attendance as output. Kahane [2005] analyzes the efficiency in the National Hockey League (NHL). A production function which uses player ability as proxied by team payroll as input is estimated using a stochastic frontier analysis. In order to determine the effective talent of individual athletes, the effect of aging on performance has to be considered. In this paper, this will be done by an adjustment of the impact proxies (games played per season) based on an analysis of individual performance over time. This aspect has been studied by Sowell et al. [2005], among others. The authors perform a aging frontier analysis to asses the development of performance over time using data from the Iron Man Triathlon World Championship. Fair [1994] uses a similar technique to analyze the effect of aging using data of men s track and field competitions. As the wages of professional athletes in the major sports are enormous and continue to rise, the valuation of these athletes is of high economic interest. Players are often evaluated based on individual statistics. While most individual statistics certainly are good indicators of a player s value, they leave much room for interpretation in team sports. Individual statistics will depend on a player s position, his team mates abilities, and the team s tactic, for example. The evaluation of individual players value is based on the following function of performance: P = F(talent,effort,training,age) (1) Performance (P) is a function of inherent talent, effort, training and age, where talent, effort, and training are assumed to be constant over time for each individual. It is further assumed that training is equally well for all professional basketball players. The effect of age here contains not only the pure effect of aging but also the gain of experience. This combined effect will be calculated and controlled for. What is left is talent and effort. Since it cannot be assumed that effort is identical for all athletes, the analysis will yield estimators of a combination talent and effort. This combination can be called the effective talent of an players. 3

6 individual athlete. Initially, it is assumed that the strength of a team is a linear function of the values of the team s individual players and that team strength translates into victories: n V ij = ( P kij GP kij ) α +ǫ ij. (2) k=1 Here, V ij is the percentage of regular season games won by team i in season j, P kij is the value of the n players who are on team i in season j, GP kij is the number of games played by player k and α is the elasticity of team success with regard to the combined player value. After initially assuming α to be equal to 1, the value which optimizes the fit of the regression will be determined. This function recognizes the fact that players miss games due to injuries or suspensions and that, unlike other team sports, in basketball, players on every position have equal influence on the game s outcome. The assumption of a linear strength function is a simplification but seems to be appropriate for the case of NBA basketball. Of course, if a team hoarded star players and barely used them, the marginal effect of adding a strong player would be decreasing. This possibility is however dampened by the restrictions for the roster size and the NBA salary cap rules which severely punish teams that spend more than a certain amount of money on salaries. The result is a fairly balanced league. Different assumptions regarding the marginal returns to adding player value to a team are analyzed in Section 7. The number of regular season victories is chosen as the measure of success. This could create a possible bias since not every NBA team plays the same number of games against all opponent teams. Currently, the league is divided into the Eastern and the Western Conference. During the regular season, each team plays four games against each team from its respective conference and two games against each team from the other conference. A bias could stem from possible imbalances between the two conferences. However, even if such imbalances should temporarily exist, they can expected to be considerably small. The inclusion of play-off games as in Berri [1999], would create a bias against players in strong teams who reach the play-offs, since these teams face only opponents with above average strength in the post season. 4 A point which is of more importance in certain sports than in others is average playing time. In a basketball game, players are substituted several times each game and playing time varies. This aspect will 4 The eight teams with the best regular season record in each of the two conferences reach the play-offs. Since the season, the team that prevails in a best-of-seven series advances to the next round. Before 2003, there have been several changes in the number of required victories in the different play-off rounds. Today, a team could play up to 28 additional games in the play-offs. 4

7 remain disregarded in this analysis. The differences in playing time among players of a certain status are fairly small, however. The analysis also implicitly assumes that the average strength of opponent teams is constant over time. Should this assumption not hold true, only a comparison of players that played at about the same time would be possible and the estimates would be the athletes effective talent relative to players of a similar time period. An increase in average team strength could be attributed mainly to improvements in training, however. Assuming this factor to be constant over time also allows us to assume the average team strength to be fairly constant over time without creating a bias in measurement of effective talent. The result will be an estimation of the constant effective talent of individual athletes. Applying the estimated age function to these estimates results in individual values which are not constant over time. 3 Data The data set includes accurate data for all 3800 players who have played at least one minute in the NBA or the American Basketball Association (ABA) - a rival league that existed from 1967 until it merged with NBA in between 1946 and Between 1967 and 1976, several players switched between the two competing leagues. After the merger in 1976, the Denver Nuggets, Indiana Pacers, San Antonio Spurs and New York Nets were integrated into the NBA. Because of differences in the rules 6 in these two leagues, statistics of ABA seasons are not included in the analysis. Of the 3800 players, 322 players have not played in the NBA. The player statistics used are the player s age, the number of games played for a certain team in a certain season and the average points scored with that team. For players who were traded to another team during the regular season, the games for the respective teams are considered. With the data available it is impossible however, to determine the exact date of player trades. The measure of team performance used is the total number of regular season wins. The number of teams in the NBA has continuously increased from eleven in 1946 to 30 in The total number of seasons played by all teams was 1141 in All data was gathered from 6 One of the most important differences was the new three point line. 5

8 4 Age Adjustment Since the aim of this paper is to shed light on the evaluation of individual athletes contribution in team sports, the final multiple regression should yield a time constant effective talent factor for each individual player. The number of games played in a particular season for a particular team is used as a proxy for each player s influence on this teams total number of regular season victories. However, the impact of a player with a certain constant talent and effort will vary over time due to unobservable changes in physical condition and experience. Leaving these changes over time unaccounted for would result in a meaningless regression biased towards players who ended their career early or are still active (See Section 8 for results without age adjustment). It seems reasonable to expect the impact which a 35 year old Jason Kidd has on the number of regular season victories to be smaller than the impact of a 26 year old Jason Kidd, for example. Since this difference is not related to the time constant effective talent, it has to be controlled for in the final multiple regression. To control for the effects of physical deterioration and experience, the players impact factors (i.e. the number of games played in a particular season for a particular team) are weighted according to an estimated career performance function. To estimate this function, a panel regression with cross-section fixed effects is conducted. This career performance function expresses the average performance development of each player over his career, assuming cross-section fixed talent and effort for each player. Here, points per game are used as a proxy for individual performance. Of course, comparing different players only on the basis of this criterion would be misleading but accounting for cross-section fixed effects eliminates individual differences (which are of no interest here). For the career performance function, a polynomial function of the 3rd degree is estimated. In the panel analysis, only the 2514 cross-sections consisting of more than one season are considered. 7 The results are shown in table 1. The estimated polynomial of the 3rd degree has a local maximum at The values for the variable AGE are the ages the individual players reach in the year a season started 8, so many players will be older than the value of AGE at the end of that particular season. This means according to the chosen specification, an average NBA player s prime age is about 26. From this point on, physical deterioration outweighs gains in experience. The 3rd degree polynomial has a value of at the local maximum. This value is regarded as the prime performance value. The ratios of the performance values for the different ages relative to the 7 That means 964 of 3478 players got to play only one season. 8 The NBA season usually starts at the beginning of November and ends in the middle of April. 6

9 Table 1: Age Adjustment Variable Coefficient Std.Error t-statistic Prob. C AGE AGE AGE R Adjusted R Prob (F-statistic) Number of Cross-Sections: 2514 prime performance value are used as weights for the impact proxies (games per season). 9 5 Methodology Since a regression with 3478 explanatory and 1141 observations would be underidentified, not all players could be included. Of the 3478 players who have played at least one game in the NBA between 1946 and 2008, 964 have played only one season. It can be expected that the impact of those players on the total number of regular season victories is negligible. In order to decrease the number of explanatories further, only the 949 players who have played at least 400 regular season games in their career are included in the regression. The number of regular season games has increased over time with the number of teams. In 1946, the regular season included 62 games. The number dropped to 48 the next season but from then increased steadily to reach 80 in 1962 and now stands at 82 since To play 400 games, players had to be in the league for at least 4 seasons. This can be justified since the objective is to find the most valuable players and to determine their impact on team success. It can be expected that the most valuable players played long enough to fulfill this criterion. Problematic are the early years of the league because of the smaller number of regular season games and the time between 1967 and 1976 when several star players switch between the NBA and the ABA. This exclusion of players creates a further problem: Since many players who were active in the early years of the league, the ABA time, or have started their career after 2003 did not or not yet play 9 The weight for games played at the age of 26 is 0.997, for the age of 29, for the age of 32. 7

10 400 career games, there are team seasons with very few players who are actually included in the regression. 10 This problem renders these seasons useless as observations of the dependent variable since their inclusion would result in poor coefficient estimates. In order to receive meaningful results, those observations had to be excluded. In the preferred specification, the 58 team seasons were excluded in which on average less than 3.1 players included in the regression were used per game (cut), leaving us with 1083 observations and 949 independent variables plus a constant. A lower barrier would result in low t-values for the parameters and lower the overall fit. Increasing this barrier would further decrease the degrees of freedom and a lower overall fit. A higher barrier would also mean that more players who are included in the regression lose part of their seasons which decreases the significance of the estimated coefficient for those players. These difficulties also determined the choice of the minimum number of 400 career games. With a less restrictive mark, more players would be included in the regression but due to the very few degrees of freedom, only very few team seasons (i.e. observations) could have been excluded resulting in a meaningless regression. Alternative specifications are discussed in Section 8. The equation to be estimated is of the form y = X β +ǫ (3) where y is the vector of regular season victories for the different teams and years (for i team seasons). X is a i k matrix of the age adjusted numbers of games played by the k 1 players in the i team seasons and a constant. β is the vector of the estimated values of effective talent. The estimation equation takes the following form: 10 There are six team seasons in which no player was used who ever reached the 400 game mark and in 18 team seasons less than two included players were used on average per game. 8

11 ATL70 ATL71... ATL08 BOS47 BOS48... WAS08 = A.Jabbar ATL70 A.Rauf ATL70... Young ATL70 1 A.Jabbar ATL71 A.Rauf ATL71... Young ATL A.Jabbar WAS07 A.Rauf WAS07... Young WAS07 1 A.Jabbar WAS08 A.Rauf WAS08... Young WAS08 1. β 1 β 2... β 949 C + ǫ 1 ǫ 2... ǫ Results assuming Constant Marginal Returns The results of the preferred specification regarding the cut value are shown in table 2. In this regression, age adjustment is applied and only players with at least 400 NBA career games are included. Also, only team seasons, in which at least 3.1 players considered in the regression were used on average are included. In this specification, the overall fit is maximized. Of the 949 calculated parameters, 649 are significant at the 1 percent level, 70 are significant at the 5 percent level and 35 are significant at the 10 percent level. The lower significance of the 195 parameters stems from the necessity to exclude several team seasons. This results in a decrease of the number of games actually considered in the regression for some players with 400 and more career games and in a deterioration in the level of significance for those coefficients. The estimates represent the constant effective talent of the individual athletes. Applying the age adjustment function would yield individual values for certain seasons in the individuals careers. The average effective talent is The individual values can be interpreted as individual values relative other players values. Players with estimated effective talent of more than 0.06 can be regarded as above average (relative to this group of 949 players). The null hypothesis of no heteroscedasticity can not be rejected with the Breusch-Pagan-Godfrey-Test. Of the 30 players with the highest estimated effective talent, twelve are already in the Basketball Hall of Fame 11 and twelve are still active Players can only be inaugurated into the Hall of Fame after their retirement. 12 Still active are Parker, Kirilenko, Marion, Prince, Nowitzki, Miles, Garnett, Haywood, Maggette, Ilgauskas, Iverson and 9

12 The high and insignificant coefficients for George Senesky and Bob Davies are the results of the necessary cutting off of several seasons. These two coefficients are, unlike the majority of coefficients, not robust to changes in the cut level. With a cut level of 3.0 instead of 3.1, none of the two players ranks among the top 30 (see table 8). George Senesky played eight seasons from 1946 until 1954, all with the Philadelphia Warriors. Five of these eight seasons are cut off in the preferred specification and only 180 of his 482 games are considered in the regression. One of the two seasons that are lost by the increase of the cut level from 3.0 to 3.1 is the season of the Philadelphia Warriors in which George Senesky played 69 games. This could be considered a small sample problem due to the required negligence of several seasons. The lack of robustness in the Bob Davies coefficient is caused by a high correlation with other coefficients. Davies played seven seasons of professional basketball ( ), all with the Rochester Royals. The season is the second season which is lost by increasing the cut level from 3.0 to 3.1. In all of the other seasons, Bob Davies played together with Arnie Risen, Bobby Wanzer and Jack Coleman. The only other players considered in the regression who played together with these four are Jack McMahon ( ) and Alex Hannum ( ). After the season, Davies, Risen and Coleman leave the Royals together. This unusual correlation leads to the insignificance of the estimated coefficient. Jack Coleman joined the team only after the cut off season. The inclusion of this season in the specification with the 3.0 cut level diminishes the very high correlation of these four variables. The estimated effective talent of Bob Davies in the 3.0 specification is as compared to in the preferred specification. The estimated effective talent of Jack Coleman increases to in the 3.0 specification as compared to in the preferred specification. These are unusually high changes representing the lack of robustness in these coefficients. As a result of this multiple regression analysis, Tony Parker seems to be the NBA player with the greatest effective talent in NBA history. The insignificant estimates for George Senesky and Bob Davies are results of the above mentioned data problems. Is this result plausible? Parker, a French, turned 27 in He entered the league in 2001 and spent all his first seven NBA seasons with the San Antonio Spurs. The Spurs have been one of the most successful teams in the NBA since In the 18 seasons from to they won at least 57 percent of their regular season games except for the dismal season. In the seven seasons with Parker on their roster they won at least 68 percent of their regular season games each season and three championships in 2003, 2005 and Turkoglu. 10

13 Table 2: Regression Results (400G; cut 3.1; α = 1) Rank Name β Standard Error 1 Senesky,George Davies,Bob (HOF) Parker,Tony Russell,Bill (HOF) Olajuwon,Hakeem (HOF) Kirilenko,Andrei Schayes,Dolph (HOF) Marion,Shawn Abdul-Jabbar,Kareem (HOF) Thomas,Isiah (HOF) Bradley,Bill (HOF) Prince,Tayshaun Nowitzki,Dirk Miles,Darius Garnett,Kevin Catchings,Harvey Thompson,Lasalle Macauley,Ed (HOF) Barkley,Charles (HOF) Haywood,Brendan Maggette,Corey Ilgauskas,Zydrunas Mullin,Chris Unseld,Wes (HOF) Gale,Mike Iverson,Allen Pollard,Jim (HOF) Turkoglu,Hidayet Jones,Bobby Sharman,Bill (HOF) R Adjusted R *** : significant at 1 percent level (649 of 949) ** : significant at 5 percent level (70 of 949) * : significant at 10 percent level (35 of 949) 1 HOF indicates that the player is a member of the Basketball Hall of Fame 11

14 7 Analysis of non-constant Returns to Value The results in Section 6 assumed constant returns to value added to a team. In this section, different values for the elasticity of team success with regard to the combined player value (see equation 2 in Section 2) and the impact on the overall fit of the regression are examined. The elasticity that maximizes the overall fit for the preferred regression specification (cut level 3.1) is For values smaller or larger than 0.75, the overall fit is constantly decreasing. Furthermore, regarding only team seasons where at least 3.1 players considered in the regression where used (cut level 3.1) is also maximizing the overall fit when an elasticity of 0.75 is assumed. Table 3: Regression Characteristics with different Elasticities cut 3.1 cut 3.0 cut 3.3 α R adj.r *** ** * *** : coefficients significant at 1 percent level ** : coefficients significant at 5 percent level * : coefficients significant at 10 percent level The regression results for a cut level of 3.1 and an elasticity of team success with regard to the combined player value of 0.75 are reported in table 4. The value of adjusted R 2 increases by Even though this value seems to be small, it indicates that this specification describes the translation of combined player value into victories better than the model with constant returns to value. 13 The precision of examination is

15 Table 4: Regression Results (400G; cut 3.1; α = 0.75) Rank Name β Standard Error 1 Senesky,George Davies,Bob (HOF) Parker,Tony Russell,Bill (HOF) Olajuwon,Hakeem (HOF) Schayes,Dolph (HOF) Kirilenko,Andrei Thomas,Isiah (HOF) Marion,Shawn Nowitzki,Dirk Abdul-Jabbar,Kareem (HOF) Prince,Tayshaun Garnett,Kevin Thompson,Lasalle Mullin,Chris Bradley,Bill (HOF) Miles,Darius Macauley,Ed (HOF) Pollard,Jim (HOF) Sharman,Bill (HOF) Catchings,Harvey Kersey,Jerome Iverson,Allen Unseld,Wes (HOF) Gale,Mike Barkley,Charles (HOF) Dawkins,Darryl Robertson,Oscar (HOF) Smith,Phil Jones,Bobby R Adjusted R *** : significant at 1 percent level (650 of 949) ** : significant at 5 percent level (60 of 949) * : significant at 10 percent level (39 of 949) 1 HOF indicates that the player is a member of the Basketball Hall of Fame 13

16 8 Robustness The results of the multiple regression including only players who played at least 400 regular season games and excluding all team seasons in which less than 3.1 of these players have played per game on average (cut) is relatively robust to changes in the exact specification. The applied age adjustment increases the overall fit. As can be seen in table 5, the difference in the adjusted R 2 is In the panel regression which yielded the career performance function, only those players were considered who played at least two regular seasons in the NBA. Table 6 shows the estimation results when all players are included in the estimation. 14 The estimated function is much flatter, the overall fit is lower and the estimator for the intercept term is not significant at the 5 percent level. Table 7 shows the results for the estimation of the career performance function including only players who have played at least three seasons in the NBA. 15 The estimated function differs only slightly from the one estimated with the preferred specification (table 1) but the overall fit is slightly lower. Tables 8, 9 and 10 give an overview of the estimation results for different specifications concerning the cut level. Decreasing the cut value from 3.1 to 3.0 would increase the number of degrees of freedom from 133 to 135 but lower the adjusted R 2 by An increase of the cut value from 3.1 to 3.2 does not result in any changes. An increase to 3.3 would reduce the degrees of freedom from 133 to 132. In this specification, 649 (70, 35) of the 949 parameter estimates are significant at the 1 (5, 10) percent level as compared to 667 (61, 31) in the preferred specification which includes one more team season and adjusted R 2 decreases by A further increase of the cut level to 4 (which is equivalent to a decrease of the number of degrees of freedom to 98) leads to even less significant coefficient estimates and a lower overall fit (see table 10). The ranking varies since the differences between the estimated coefficients of players with similar effective talent are very small. The actual estimates do not vary much in the different cut-specifications. The high and insignificant coefficients for George Senesky and Bob Davies, who rank at the top two positions in the preferred specification are the results of the necessary cutting off of several seasons. These two coefficients are, unlike the majority of coefficients, not robust to changes in the cut level. With a cut level of 3.0 instead of 3.1, none of the two players ranks among the top 30 (see table 8. In the case of George Senesky, it is simply a short sample problem since changing the cut level from 3.0 to 3.1 decreases the number of Senesky s games considered in the regression from 249 to only 180. In the case of Bob Davies, the high, insignificant and non-robust coefficient results from an unusually high correlation between his career and 14 The number of cross-sections increases by 964; the number of players who left the league after one season. 15 The number of cross-sections decreases by 432 as compared to the preferred specification. 14

17 the careers of Arnie Risen, Bobby Wanzer and Jack Coleman. Increasing the cut level to 3.1 would add one season in which Davies has not played together with Coleman and therefore decease this correlation. Regardless of these obstacles, the cut level of 3.1 is the preferred specification since it yields the highest overall fit. 15

18 Table 5: Regression Results without Age Adjustment (400G; cut 3.1; α = 0.75) Rank Name β Standard Error 1 Wanzer,Bobby (HOF) Senesky,George Marion,Shawn Ilgauskas,Zydrunas Prince,Tayshaun Gasol,Pau Thomas,Isiah (HOF) Collins,Jason Miles,Darius Ellis,Joe Peterson,Morris Bradley,Bill (HOF) Schayes,Dolph (HOF) Jones,Bobby Parker,Tony Blount,Mark West,Doug McGrady,Tracy Anderson,Derek Nowitzki,Dirk McMillan,Nate Smith,Phil Stockton,John Catledge,Terry Lewis,Rashard Miller,Brad Unseld,Wes (HOF) Macauley,Ed (HOF) Williams,Monty Maggette,Corey R Adjusted R *** : significant at 1 percent level (730 of 949) ** : significant at 5 percent level (37 of 949) * : significant at 10 percent level (29 of 949) 1 HOF indicates that the player is a member of the Basketball Hall of Fame 16

19 Table 6: Age Adjustment (Data from all Players) Variable Coefficient Std.Error t-statistic Prob. C AGE AGE AGE R Adjusted R Prob (F-statistic) Number of Cross-Sections: 3478 Table 7: Age Adjustment (Data from Players who playeda min. of 3 Seasons) Variable Coefficient Std.Error t-statistic Prob. C AGE AGE AGE R Adjusted R Prob (F-statistic) Number of Cross-Sections:

20 Table 8: Regression Results (400G; cut 3.0; α = 0.75) Rank Name β Standard Error 1 Parker,Tony Olajuwon,Hakeem (HOF) Kirilenko,Andrei Thomas,Isiah (HOF) Schayes,Dolph (HOF) Marion,Shawn Abdul-Jabbar,Kareem (HOF) Nowitzki,Dirk Thompson,Lasalle Prince,Tayshaun Davies,Bob (HOF) Hagan,Cliff (HOF) Garnett,Kevin Mullin,Chris Miles,Darius Russell,Bill (HOF) Kersey,Jerome Pollard,Jim (HOF) Iverson,Allen Dawkins,Darryl Robertson,Oscar (HOF) Gale,Mike Catchings,Harvey Unseld,Wes (HOF) Barkley,Charles (HOF) Dunn,T.r Issel,Dan (HOF) Turkoglu,Hidayet Smith,Phil R Adjusted R *** : significant at 1 percent level (667 of 949) ** : significant at 5 percent level (61 of 949) * : significant at 10 percent level (31 of 949) 1 HOF indicates that the player is a member of the Basketball Hall of Fame 18

21 Table 9: Regression Results (400G; cut 3.3; α = 0.75) Rank Name β Standard Error 1 Senesky,George Davies,Bob (HOF) Parker,Tony Russell,Bill (HOF) Olajuwon,Hakeem (HOF) Kirilenko,Andrei Schayes,Dolph (HOF) Thomas,Isiah (HOF) Marion,Shawn Abdul-jabbar,Kareem (HOF) Nowitzki,Dirk Prince,Tayshaun Garnett,Kevin Thompson,Lasalle Bradley,Bill (HOF) Mullin,Chris Macauley,Ed (HOF) Pollard,Jim (HOF) Miles,Darius Sharman,Bill (HOF) Catchings,Harvey Iverson,Allen Kersey,Jerome Unseld,Wes (HOF) Barkley,Charles (HOF) Gale,Mike Dawkins,Darryl Jones,Bobby Smith,Phil Robertson,Oscar (HOF) R Adjusted R *** : significant at 1 percent level (643 of 949) ** : significant at 5 percent level (64 of 949) * : significant at 10 percent level (42 of 949) 1 HOF indicates that the player is a member of the Basketball Hall of Fame 19

22 Table 10: Regression Results (400G; cut 4; α = 0.75) Rank Name β StandardError 1 Wanzer,Bobby (HOF) Russell,Bill (HOF) Kirilenko,Andrei Senesky,George Parker,Tony Greer,Hal (HOF) Olajuwon,Hakeem (HOF) Phillip,Andy (HOF) Macauley,Ed (HOF) Sharman,Bill (HOF) Thomas,Isiah (HOF) Thompson,Lasalle Prince,Tayshaun Jones,Bobby Mullin,Chris Pettit,Bob (HOF) Garnett,Kevin Yardley,George (HOF) Marion,Shawn Nowitzki,Dirk Catchings,Harvey Rollins,Tree Kersey,Jerome Pollard,Jim (HOF) Bird,Larry (HOF) Bridges,Bill Unseld,Wes (HOF) Iverson,Allen Lanier,Bob (HOF) Smith,Phil R Adjusted R *** : significant at 1 percent level (516 of 949) ** : significant at 5 percent level (77 of 949) * : significant at 10 percent level (40 of 949) 1 HOF indicates that the player is a member of the Basketball Hall of Fame 20

23 9 Criticism Some problematic points have already been mentioned above. Since the number of players who have played at least one NBA game far exceeds the number of team seasons, it was necessary to exclude all players who have played less than 400 career games. Even though the impact on regular season victories of most of those players can be expected to be sufficiently small, problems arise with the early seasons, the ABA era and the seasons from 2004 on. In the early years, the number of regular season games was smaller and several star players simply did not reach the mark of 400 games because they were already relatively old when the league was founded. In the ABA era ( ), several very talented players spent significant parts of their careers in the ABA and therefore did not record 400 NBA games. Finally, none of the players who entered the league after the 2004 season is included in the analysis since in the four seasons from 2004 to 2008 only 328 games have been played per team. These exclusions made it necessary to skip 58 team seasons in the preferred specification because only a few number of players included in the regression where used by those teams. Another limitation is the complete negligence of coaches. A savvy head coach certainly has a significant impact on the number of regular season victories but the inclusion would have increased the number of dependent variables by several hundred and made a sensible regression impossible. The multiple regression takes into account that players sometimes change teams during a season. What it does not take into account, however, is the success of the player s old and new team before and after the trade. Trades during a season are common but their number is small relative to the total number of players. The assumption that individual values linearly add up to team strength is in this context not completely unrealistic but simplifying. Therefore, decreasing marginal returns to added player value are assumed in the preferred specification. Another possible shortcoming is the way the age adjustment is conducted. The method applied assumes that a player s performance is a function of his age (and talent, effort and training; see equation 1 in Section 2). The method, which yields quite reasonable results, could be improved by considering the age at which a player has entered the league. On the one hand, athletes who start their professional career at the age of 18 can be expected to be much more experienced at the age of 23 compared to others who played college basketball for several seasons. On the other hand, since the number of games per season on college is less than half the number of NBA regular season games, players who enter the league early might face physical problems earlier than those who enter at a higher age. The career performance could 21

24 be expressed using the two variables ( age, years as pro ). The effect of years as pro is expected to be strictly increasing. The effect of age on performance is expected to depend on years as pro since many players improve their physical condition in the first couple of years as professional athletes. From than on, their body deteriorates due to natural aging and the high physical loading. The career performance function estimated in Section 3, which estimates the combined effects of age and experience neglects the fact that not all players enter the professional league at the same age and therefore differ in their experience at a certain age. Other basketball specific shortcomings are the differences in playing time per game and play-off performance which are completely disregarded in this analysis. 10 Conclusion The focus of this work is on the value of individual athletes in a team sport. To analyze this value, the effects of aging and gathering experience where jointly estimated and applied to adjust data of 949 professional basketball players which was then used in a multiple regression to determine what could be called individual effective talent (which is constant over time). In this first step, constant marginal returns to adding player value to a team were assumed. The regression results improve when this function is altered in a way that recognizes the possibility, that the marginal value of a strong player is smaller in a strong team than in a weak one. This is done by simply weighting the values of the dependent variable accordingly. From the analysis in Section 7 it follows that the specification with a value of elasticity of success of 0.75 yields the highest overall fit for the multiple regression. The player with the highest effective talent in the history of NBA basketball (given the limitations regarding players included mentioned in Section 9) seems to be the French Tony Parker. A possible extension to this paper could be a panel analysis of the effect of team success on franchise revenue. Total franchise revenue can be expected to include a fixed component and variable components such as ticket and merchandise sales, TV earnings for nation wide televised games and revenues generated by playoff appearances. The revenue function will thus be a strictly increasing function of team success. Assuming that players are remunerated according to their performance (which is a function of effective talent, age and training), the team payroll is a convex and strictly increasing function of team success. 22

25 Depending on the characteristics of the revenue function, a situation with two equilibria is possible where certain franchises choose to form mediocre teams and others try to build teams as strong as possible. This phenomenon can be observed in the US professional leagues where franchises are not threatened by regulation. Of course, the techniques applied in this paper can not be used to assess the effective talent of young players who have played only a small number of games. For this purpose, the method used by Berri [1999] provides acceptable estimates of individual effective talent. Considering the age performance function calculated in section 4, these estimates can be used to determine the impact of a certain player on franchise revenue over the time of his contract. 23

26 References D.J. Berri. Who is most valuable? Measuring the player s production of wins in the National Basketball Association. Managerial and Decision Economics, pages , S. Chatterjee, M.R. Campbell, and F. Wiseman. Take that jam! An analysis of winning percentage for NBA teams. Managerial and Decision Economics, pages , R.C. Fair. How fast do old men slow down? The Review of Economics and Statistics, pages , E. Gustafson, L. Hadley, and J. Ruggiero. Alternative econometric models of production in major league baseball. Sports Economics: Current Research (Westport: CT, Praeger), L.H. Kahane. Production efficiency and discriminatory hiring practices in the National Hockey League: A stochastic frontier approach. Review of Industrial Organization, 27(1):47 71, G.W. Scully. Pay and performance in major league baseball. The American Economic Review, pages , C.B. Sowell, W. Mounts, et al. Ability, Age, and Performance: Conclusions From the Ironman Triathlon World Championship. Journal of Sports Economics, 6(1):78, D. Stadelmann and R. Eichenberger. Wer ist der beste Formel 1 Fahrer? Eine okonometrische Talentbewertung. Perspektiven der Wirtschaftspolitik, 9(4): ,

27 Table 11: Results 25 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 11 Abdul-jabbar,Kareem (HOF) Abdul-rauf,Mahmo Abdur-rahim,Shareef Adams,Alvan Adams,Don Adams,Michael Aguirre,Mark Ainge,Danny Allen,Lucius Allen,Ray Alston,Rafer Anderson,Cadillac Anderson,Derek Anderson,Kenny Anderson,Nick Anderson,Richard Anderson,Ron Anderson,Shandon Anderson,Willie Anthony,Greg Archibald,Nate (HOF) Arenas,Gilbert Arizin,Paul (HOF) Armstrong,B.j Armstrong,Darrell Arroyo,Carlos Artest,Ron Askew,Vincent Askins,Keith Atkins,Chucky Attles,Alvin Augmon,Stacey Austin,Isaac Awtrey,Dennis Bagley,John Bailey,James Bailey,Thurl Baker,Vin Ballard,Greg Banks,Gene Bantom,Mike Barkley,Charles (HOF) Barnes,Jim Barnett,Dick Barnett,Jim Barnhill,John Barros,Dana Barry,Brent Barry,Jon Barry,Rick (HOF) *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

28 Table 11: Results 26 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 879 Battie,Tony Battier,Shane Battle,John Baylor,Elgin (HOF) Beard,Butch Beaty,Zelmo Bell,Raja Bellamy,Walt (HOF) Benjamin,Benoit Benoit,David Benson,Kent Best,Travis Bianchi,Al Bibby,Henry Bibby,Mike Billups,Chauncey Bing,Dave (HOF) Bird,Larry (HOF) Birdsong,Otis Blackman,Rolando Blaylock,Mookie Blount,Corie Blount,Mark Bockhorn,Arlen Boerwinkle,Tom Bogues,Muggsy Bol,Manute Boozer,Bob Bowen,Bruce Bowen,Ryan Bowie,Anthony Bowie,Sam Boykins,Earl Bradley,Bill (HOF) Bradley,Dudley Bradley,Shawn Brand,Elton Brandon,Terrell Bratz,Mike Braun,Carl Breuer,Randy Brewer,Jim Brewer,Ron Brickowski,Frank Bridgeman,Junior Bridges,Bill Bristow,Allan Brooks,Scott Brown,Chucky Brown,Dee *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

29 Table 11: Results 27 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 454 Brown,Fred Brown,John Brown,Kwame Brown,Mike Brown,P.J Brown,Randy Brown,Roger A Bryant,Emmette Bryant,Joe Bryant,Kobe Bryant,Mark Buckner,Greg Buckner,Quinn Buechler,Jud Bullard,Matt Burleson,Tom Buse,Don Butler,Caron Caffey,Jason Cage,Michael Caldwell,Joe Calhoun,Corky Camby,Marcus Campbell,Elden Campbell,Tony Carr,Antoine Carr,Austin Carr,Kenny Carr,M.l Carroll,Joe Barry Carter,Anthony Carter,Fred Carter,Vince Cartwright,Bill Cassell,Sam Catchings,Harvey Catledge,Terry Cato,Kelvin Causwell,Duane Ceballos,Cedric Chamberlain,Wilt (HOF) Chambers,Tom Chandler,Tyson Chaney,Don Chapman,Rex Chappell,Len Cheaney,Calbert Cheeks,Maurice Chenier,Phil Chilcutt,Pete *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

30 Table 11: Results 28 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 52 Childs,Chris Chones,Jim Christie,Doug Clark,Archie Cleamons,Jim Clemens,John Clifton,Nat Coleman,Derrick Coleman,Jack Coles,Bimbo Collins,Doug Collins,Jarron Collins,Jason Colter,Steve Conlin,Ed Conner,Lester Cook,Darwin Cook,Jeff Cooper,Chuck Cooper,Michael Cooper,Wayne Corbin,Tyrone Corzine,Dave Costello,Larry Counts,Mel Cousy,Bob (HOF) Cowens,Dave (HOF) Crawford,Jamal Criss,Charlie Croshere,Austin Crotty,John Cummings,Pat Cummings,Terry Cunningham,Billy (HOF) Cureton,Earl Curry,Dell Curry,Eddy Curry,Michael Dailey,Quintin Dalembert,Samuel Dampier,Erick Dandridge,Bob Daniels,Antonio Daniels,Mel Dantley,Adrian (HOF) Daugherty,Brad Davies,Bob (HOF) Davis,Antonio Davis,Baron Davis,Brad *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

31 Table 11: Results 29 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 132 Davis,Charlie Davis,Dale Davis,Hubert Davis,Jim Davis,Johnny Davis,Ricky Davis,Terry Davis,Walter Dawkins,Darryl Dawkins,Johnny Day,Todd Debusschere,Dave (HOF) Declercq,Andrew Dehere,Terry Del Negro,Vinny Dele,Bison Delk,Tony Dierking,Connie Dietrick,Coby Diop,Desagana Dischinger,Terry Divac,Vlade Doleac,Michael Donaldson,James Dooling,Keyon Douglas,Leon Douglas,Sherman Dreiling,Greg Drew,John Drew,Larry Drexler,Clyde (HOF) Duckworth,Kevin Dudley,Chris Dukes,Walter Dumars,Joe (HOF) Duncan,Tim Dunleavy,Mike Dunleavy,Mike Dunn,T.r Eackles,Ledell Eaton,Mark Edwards,Blue Edwards,James Edwards,Kevin Egan,Johnny Ehlo,Craig Eisley,Howard Elie,Mario Elliott,Sean Ellis,Dale *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

32 Table 11: Results 30 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 233 Ellis,Joe Ellis,Laphonso Ellis,Leroy Ellison,Pervis Elmore,Len Embry,Wayne English,Alex (HOF) Erickson,Keith Erving,Julius (HOF) Evans,Mike Evans,Reggie Ewing,Patrick (HOF) Farmer,Mike Felix,Ray Ferrell,Duane Ferry,Bob Ferry,Danny Finkel,Hank Finley,Michael Fisher,Derek Fleming,Vern Floyd,Sleepy Ford,Chris Ford,Don Ford,Phil Fortson,Danny Foster,Fred Foster,Greg Foster,Jeff Foust,Larry Fox,Jim Fox,Rick Foyle,Adonal Francis,Steve Frazier,Walt (HOF) Free,World Fulks,Joe (HOF) Gale,Mike Gallatin,Harry (HOF) Gambee,Dave Gamble,Kevin Garland,Winston Garmaker,Dick Garnett,Kevin Garrity,Pat Gasol,Pau Gatling,Chris Gattison,Kenny Geiger,Matt George,Devean *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

33 Table 11: Results 31 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 768 George,Jack Gervin,George (HOF) Gianelli,John Gill,Kendall Gilliam,Armen Gilliam,Herm Gilmore,Artis Ginobili,Emmanuel Glenn,Mike Gminski,Mike Gola,Tom (HOF) Gondrezick,Glen Gooden,Drew Goodrich,Gail (HOF) Graboski,Joe Grant,Brian Grant,Gary Grant,Harvey Grant,Horace Grayer,Jeff Green,A.c Green,Johnny Green,Rickey Green,Si Green,Sidney Greenwood,David Greer,Hal (HOF) Grevey,Kevin Griffin,Adrian Griffin,Paul Griffith,Darrell Gross,Bob Grunfeld,Ernie Guerin,Richie Gugliotta,Tom Guokas,Matt Hagan,Cliff (HOF) Hairston,Happy Ham,Darvin Hamilton,Richard Hammonds,Tom Hannum,Alex (HOF) Hansen,Bob Hanzlik,Bill Hardaway,Anfernee Hardaway,Tim Harper,Derek Harper,Ron Harpring,Matt Harrington,Al *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

34 Table 11: Results 32 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 245 Harrington,Othella Harris,Lucious Harrison,Bob Haskins,Clem Hassell,Trenton Hastings,Scott Havlicek,John (HOF) Hawes,Steve Hawkins,Connie (HOF) Hawkins,Hersey Hawkins,Tom Hayes,Elvin (HOF) Haywood,Brendan Hazzard,Walt Heard,Garfield Heinsohn,Tom (HOF) Henderson,Alan Henderson,Gerald Henderson,Tom Herrera,Carl Hetzel,Fred Higgins,Rod Hill,Armond Hill,Grant Hill,Tyrone Hillman,Darnell Hinson,Roy Hitch,Lew Hodges,Craig Hoiberg,Fred Hollins,Lionel Hornacek,Jeff Horry,Robert House,Eddie Houston,Allan Howard,Juwan Howell,Bailey (HOF) Hubbard,Phil Hudson,Lou Hudson,Troy Hughes,Larry Humphries,Jay Hundley,Rod Hunter,Lindsey Huston,Geoff Hutchins,Mel Iavaroni,Marc Ilgauskas,Zydrunas Imhoff,Darrall Issel,Dan (HOF) *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

35 Table 11: Results 33 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 23 Iverson,Allen Jackson,Bobby Jackson,Jaren Jackson,Jim Jackson,Lucious Jackson,Mark Jackson,Phil Jackson,Stephen James,Mike Jamison,Antawn Jefferson,Richard Johnson,Anthony Johnson,Avery Johnson,Buck Johnson,Charlie Johnson,Clemon Johnson,Dennis Johnson,Eddie Johnson,Eddie A Johnson,Ervin Johnson,Frank Johnson,George L Johnson,George T Johnson,Gus Johnson,Joe Johnson,John Johnson,Kevin Johnson,Larry Johnson,Magic (HOF) Johnson,Marques Johnson,Mickey Johnson,Ollie Johnson,Steve Johnson,Vinnie Johnston,Neil (HOF) Jones,Bobby Jones,Caldwell Jones,Charles Jones,Damon Jones,Dwight Jones,Eddie Jones,Jumaine Jones,K.c. (HOF) Jones,Popeye Jones,Sam (HOF) Jones,Wali Jordan,Eddie Jordan,Michael Jordon,Phil Kauffman,Bob *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

36 Table 11: Results 34 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 235 Keefe,Adam Keller,Billy Kelley,Rich Kemp,Shawn Kenon,Larry Kerr,Johnny Kerr,Steve Kersey,Jerome Kidd,Jason King,Albert King,Bernard King,George King,Jim King,Reggie King,Stacey Kirilenko,Andrei Kite,Greg Kittles,Kerry Kleine,Joe Knight,Billy Knight,Brevin Kojis,Don Komives,Howard Koncak,Jon Krebs,Jim Krystkowiak,Larry Kuberski,Steve Kukoc,Toni Kunnert,Kevin Kupchak,Mitch Lacey,Sam Laettner,Christian Lafrentz,Raef Laimbeer,Bill Lambert,John Landsberger,Mark Lang,Andrew Lanier,Bob (HOF) Larusso,Rudy Leavell,Allen Leckner,Eric Lee,Clyde Lee,Ron Lenard,Voshon Leonard,Bob Lever,Lafayette Levingston,Cliff Lewis,Freddie Lewis,Rashard Lewis,Reggie *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

37 Table 11: Results 35 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 252 Lister,Alton Lloyd,Earl Lohaus,Brad Long,Grant Long,John Longley,Luc Loscutoff,Jim Loughery,Kevin Love,Bob Lovellette,Clyde (HOF) Lucas,Jerry (HOF) Lucas,John Lucas,Maurice Lue,Tyronn Lynch,George Macauley,Ed (HOF) Macy,Kyle Madsen,Mark Maggette,Corey Magloire,Jamaal Mahorn,Rick Majerle,Dan Malone,Jeff Malone,Karl Malone,Moses (HOF) Manning,Danny Maravich,Pete (HOF) Marbury,Stephon Marin,Jack Marion,Shawn Marshall,Donyell Martin,Darrick Martin,Kenyon Martin,Slater (HOF) Mashburn,Jamal Mason,Anthony Mason,Desmond Massenburg,Tony Matthews,Wes Maxwell,Cedric Maxwell,Vernon Mayberry,Lee McAdoo,Bob (HOF) McCarty,Walter McCloud,George McCormick,Tim McCray,Rodney McDaniel,Xavier McDyess,Antonio McElroy,Jim *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

38 Table 11: Results 36 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 763 McGee,Mike McGinnis,George McGlocklin,Jon McGrady,Tracy McGuire,Dick (HOF) McHale,Kevin (HOF) McIlvaine,Jim McInnis,Jeff McKey,Derrick McKie,Aaron McKinney,Billy McLemore,Mccoy McMahon,Jack McMillan,Nate McMillen,Tom McMillian,Jim Meminger,Dean Mengelt,John Mercer,Ron Meriweather,Joe Meschery,Tom Mihm,Chris Mikan,George (HOF) Mikkelsen,Vern (HOF) Miles,Darius Miles,Eddie Miller,Andre Miller,Brad Miller,Mike Miller,Oliver Miller,Reggie Mills,Chris Mills,Terry Ming,Yao Mitchell,Mike Mitchell,Sam Mix,Steve Mobley,Cuttino Mohammed,Nazr Mokeski,Paul Moncrief,Sidney Money,Eric Monroe,Earl (HOF) Montross,Eric Moore,Johnny Moore,Mikki Moore,Otto Morris,Chris Mourning,Alonzo Mueller,Erwin *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

39 Table 11: Results 37 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 15 Mullin,Chris Mullins,Jeff Murdock,Eric Murphy,Calvin (HOF) Murphy,Troy Murray,Lamond Murray,Tracy Mutombo,Dikembe Najera,Eduardo Nance,Larry Nash,Steve Nater,Swen Natt,Calvin Naulls,Willie Neal,Lloyd Nealy,Ed Nelson,Don Nesterovic,Radoslav Netolicky,Bob Neumann,Paul Newlin,Mike Newman,Johnny Nichols,Jack Nimphius,Kurt Nixon,Norm Noble,Chuck Norman,Ken Norris,Moochie Norwood,Willie Nowitzki,Dirk O Koren,Mike O neal,jermaine O neal,shaquille Oakley,Charles Odom,Lamar Ohl,Don Okur,Mehmet Olajuwon,Hakeem (HOF) Olberding,Mark Ollie,Kevin Olowokandi,Michael Orr,Louis Ostertag,Greg Outlaw,Bo Overton,Doug Owens,Billy Owens,Tom Pack,Robert Padgett,Scott Palacio,Milt *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

40 Table 11: Results 38 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 159 Parish,Robert (HOF) Parker,Sonny Parker,Tony Parks,Cherokee Patterson,Ruben Paultz,Billy Paxson,Jim Paxson,John Payton,Gary Peeler,Anthony Perdue,Will Perkins,Sam Perry,Curtis Perry,Elliot Perry,Tim Person,Chuck Person,Wesley Petersen,Jim Peterson,Morris Petrie,Geoff Pettit,Bob (HOF) Phillip,Andy (HOF) Phills,Bobby Piatkowski,Eric Pierce,Paul Pierce,Ricky Pinckney,Ed Piontek,Dave Pippen,Scottie Pollard,Jim (HOF) Pollard,Scot Polynice,Olden Poquette,Ben Porter,Howard Porter,Kevin Porter,Terry Posey,James Potapenko,Vitaly Pressey,Paul Price,Brent Price,Jim Price,Mark Prince,Tayshaun Przybilla,Joel Radmanovic,Vladimir Rambis,Kurt Ramsey,Frank (HOF) Randolph,Zachary Ransey,Kelvin Rasmussen,Blair *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

41 Table 11: Results 39 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 829 Ratliff,Theo Ray,Clifford Redd,Michael Reed,Hub Reed,Willis (HOF) Reid,Don Reid,J.r Reid,Robert Restani,Kevin Reynolds,Jerry Rice,Glen Richardson,Clint Richardson,Jason Richardson,Micheal Ray Richardson,Pooh Richardson,Quentin Richmond,Mitch Rider,Isaiah Riordan,Mike Risen,Arnie (HOF) Rivers,Doc Roberson,Rick Roberts,Fred Robertson,Alvin Robertson,Oscar (HOF) Robey,Rick Robinson,Clifford R Robinson,Clifford T Robinson,David Robinson,Flynn Robinson,Glenn Robinson,Truck Robinzine,Bill Robisch,Dave Rodgers,Guy Rodman,Dennis Rogers,Rodney Rollins,Tree Rooks,Sean Rose,Jalen Rose,Malik Roundfield,Dan Rowe,Curtis Royal,Donald Ruffin,Michael Rule,Bob Russell,Bill (HOF) Russell,Bryon Russell,Campy Russell,Cazzie *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

42 Table 11: Results 40 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 207 Sabonis,Arvydas Salley,John Salmons,John Sampson,Ralph Sanders,Mike Sanders,Thomas Sauldsberry,Woody Schayes,Danny Schayes,Dolph (HOF) Schlueter,Dale Schrempf,Detlef Scott,Alvin Scott,Byron Scott,Charlie Scott,Dennis Scott,Ray Sealy,Malik Sears,Ken Seikaly,Rony Selvy,Frank Senesky,George Seymour,Paul Share,Charlie Sharman,Bill (HOF) Shaw,Brian Shelton,Lonnie Short,Purvis Shue,Gene Sichting,Jerry Siegfried,Larry Sikma,Jack Silas,James Silas,Paul Simmons,Connie Simmons,Lionel Skiles,Scott Skinner,Brian Sloan,Jerry Smith,Adrian Smith,Bingo Smith,Charles Smith,Derek Smith,Don Smith,Elmore Smith,Greg Smith,Joe Smith,Kenny Smith,Larry Smith,Michael Smith,Phil *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

43 Table 11: Results 41 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 423 Smith,Randy Smith,Steve Smith,Tony Smits,Rik Snow,Eric Snyder,Dick Sobers,Ricky Sparrow,Rory Spencer,Felton Sprewell,Latrell Stackhouse,Jerry Stallworth,Dave Starks,John Steele,Larry Stevenson,Deshawn Stipanovich,Steve Stith,Bryant Stockton,John Stojakovic,Peja Stoudamire,Damon Strickland,Erick Strickland,Rod Strong,Derek Sundvold,Jon Sura,Bob Swift,Stromile Szczerbiak,Wally Taylor,Maurice Teagle,Terry Terry,Jason Theus,Reggie Thomas,Isiah (HOF) Thomas,Kenny Thomas,Kurt Thomas,Tim Thompson,David (HOF) Thompson,Lasalle Thompson,Mychal Thorn,Rod Thorpe,Otis Threatt,Sedale Thurmond,Nate (HOF) Tisdale,Wayman Tomjanovich,Rudy Toney,Andrew Traylor,Robert Trent,Gary Tresvant,John Tripucka,Kelly Tucker,Trent *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

44 Table 11: Results 42 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 31 Turkoglu,Hidayet Turner,Elston Turner,Jeff Twyman,Jack (HOF) Tyler,Terry Unseld,Wes (HOF) Valentine,Darnell Van Arsdale,Dick Van Arsdale,Tom Van Exel,Nick Vanbredakolff,Jan Vandeweghe,Kiki Vanhorn,Keith Vanlier,Norm Vaughn,Jacque Vaught,Loy Vincent,Jay Voskuhl,Jake Vranes,Danny Walk,Neal Walker,Antoine Walker,Chet Walker,Darrell Walker,Foots Walker,Jimmy Walker,Kenny Walker,Samaki Walker,Wally Wallace,Ben Wallace,Rasheed Walton,Bill (HOF) Wanzer,Bobby (HOF) Ward,Charlie Warner,Cornell Washington,Jim Washington,Kermit Watson,Earl Watts,Slick Weatherspoon,Clarence Weatherspoon,Nick Webb,Spud Webber,Chris Webster,Marvin Wedman,Scott Weiss,Bob Wells,Bonzi Wennington,Bill Wesley,David Wesley,Walt West,Doug *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

45 Table 11: Results 43 cut 3.1 cut 3.0 cut 3.3 Rank Name β St.Err. β St. Err. β St. Err. 362 West,Jerry (HOF) West,Mark Westphal,Paul White,Jojo Whitehead,Jerome Whitney,Chris Wicks,Sidney Wilkens,Lenny (HOF) Wilkerson,Bob Wilkes,Jamaal Wilkins,Dominique (HOF) Wilkins,Gerald Wilkins,Jeff Williams,Aaron Williams,Alvin Williams,Buck Williams,Eric Williams,Gus Williams,Herb Williams,Hotrod Williams,Jason Williams,Jayson Williams,Jerome Williams,John Williams,Michael Williams,Monty Williams,Nate Williams,Ray Williams,Reggie Williams,Ron Williams,Scott Williams,Walt Williamson,Corliss Willis,Kevin Willoughby,Bill Wilson,George Winfield,Lee Wingate,David Winters,Brian Wittman,Randy Wolf,Joe Wood,Al Wood,David Woodson,Mike Woolridge,Orlando Worthy,James (HOF) Wright,Lorenzen Yardley,George (HOF) Young,Danny C *** : significant at 1 percent level ** : significant at 5 percent level * : significant at 10 percent level

46 HHL-Arbeitspapiere / HHL Working Papers 102 Scherzer, Falk (2010) On the Value of Individual Athletes in Team Sports 101 Wulf, Torsten; Brands, Christian; Meißner, Philip (2010) A Scenario-based Approach to Strategic Planning: Tool Description 360 Stakeholder Feedback 100 Viellechner, Oliver; Wulf, Torsten (2010) Incumbent Inertia upon Disruptive Change in the Airline Industry: Causal Factors for Routine Rigidity and Top Management Moderators 99 Wulf, Torsten; Meißner, Philip; Bernewitz, Friedrich Frhr. von (2010) Future Scenarios for German Photovoltaic Industry 98 Wulf, Torsten; Meißner, Philip; Stubner, Stephan (2010) A Scenario-based Approach to Strategic Planning Integrating Planning and Process Perspective of Strategy 97 Wulf, Torsten; Stubner, Stephan; Blarr, W. Henning; Lindow, Corinna (2010) Erfolgreich bleiben in der Krise 96 Wulf, Torsten; Stubner, Stephan (2010) Unternehmernachfolge in Familienunternehmen Ein Untersuchungsmodell zur Analyse von Problemfeldern bei der Übergabe der Führungsrolle 95 Zülch, Henning; Pronobis, Paul (2010) The Predictive Power of Comprehensive Income and Its Individual Components under IFRS 94 Zülch, Henning; Hoffmann, Sebastian (2010) Lobbying on Accounting Standard Setting in a Parliamentary Environment A Qualitative Approach 93 Hausladen, Iris; Porzig, Nicole; Reichert, Melanie (2010) Nachhaltige Handels- und Logistikstrukturen für die Bereitstellung regionaler Produkte: Situation und Perspektiven 92 La Mura, Pierfrancesco; Rapp, Marc Steffen; Schwetzler, Bernard; Wilms, Andreas (2009) The Certification Hypothesis of Fairness Opinions 91 La Mura, Pierfrancesco (2009) Expected Utility of Final Wealth and the Rabin Anomaly 90 Thürbach, Kai (2009) Fallstudie sekretaria - Vom New Economy-Internet-Startup zum Old Economy-Verlagsunternehmen

47 89 Wulf, Torsten; Stubner, Stephan; Blarr, W. Henning (2010) Ambidexterity and the Concept of Fit in Strategic Management Which Better Predicts Success? 88 Wulf, Torsten; Stubner, Stephan; Miksche, Jutta; Roleder, Kati (2010) Performance over the CEO Lifecycle A Differentiated Analysis of Short and Long Tenured CEOs 87 Wulf, Torsten; Stubner, Stephan; Landau, Christian; Gietl, Robert (2010) Private Equity and Family Business Can Private Equity Investors Add to the Success of Formerly Owned Family Firms? 86 Wulf, Torsten; Stubner, Stephan (2008) Executive Succession and Firm Performance the Role of Position-specific Skills 85 Wulf, Torsten; Stubner, Stephan (2008) Unternehmernachfolge in Familienunternehmen Untersuchungsmodell zur Analyse von Problemfeldern bei der Übergabe der Führungsrolle 84 Wulf, Torsten; Stubner, Stephan (2008) Executive Departure Following Acquisitions in Germany an Empirical Analysis of Its Antecedents and Consequences 83 Zülch, Henning; Gebhardt, Ronny (2008) Politische Ökonomie der Rechnungslegung - Empirische Ergebnisse und kritische Würdigung des Forschungsansatzes 82 Zülch, Henning; Löw, Edgar; Burghardt, Stephan (2008) Zur Bedeutung von IFRS-Abschlüssen bei der Kreditvergabe von Banken an mittelständische Unternehmen 81 Suchanek, Andreas (2007) Die Relevanz der Unternehmensethik im Rahmen der Betriebswirtschaftslehre 80 Kirchgeorg, Manfred; Jung, Kathrin (2007) User Behavior in Second Life: an Empirical Study Analysis and Its Implications for Marketing Practice 79 Freundt, Tjark (2007) Neurobiologische Erklärungsbeiträge zur Struktur und Dynamik des Markenwissens 78 Wuttke, Martina (2007) Analyse der Markteintrittsstrategien chinesischer Unternehmen in Mitteldeutschland am Beispiel von chinesischen Unternehmen im MaxicoM in Leipzig 77 La Mura, Pierfrancesco; Swiatczak, Lukasz (2007) Markovian Entanglement Networks 76 Suchanek, Andreas (2007) Corporate Responsibility in der pharmazeutischen Industrie 75 Möslein, Kathrin; Huff, Anne Sigismund (2006) Management Education and Research in Germany

48 74 Kirchgeorg, Manfred; Günther, Elmar (2006) Employer Brands zur Unternehmensprofilierung im Personalmarkt : eine Analyse der Wahrnehmung von Unternehmensmarken auf der Grundlage einer deutschlandweiten Befragung von High Potentials 73 Vilks, Arnis (2006) Logic, Game Theory, and the Real World 72 La Mura, Pierfrancesco; Olschewski, Guido (2006) Non-Dictatorial Social Choice through Delegation 71 Kirchgeorg, Manfred; Springer, Christiane (2006) UNIPLAN Live Trends 2006 : Steuerung des Kommunikationsmix im Kundenbeziehungszyklus ; eine branchenübergreifende Befragung von Marketingentscheidern unter besonderer Berücksichtigung der Live Communication. 2., erw. Aufl. 70 Reichwald, Ralf; Möslein, Kathrin (2005) Führung und Führungssysteme 69 Suchanek, Andreas (2005) Is Profit Maximization the Social Responsibility of Business? Milton Friedman and Business Ethics 68 La Mura, Pierfrancesco (2005) Decision Theory in the Presence of Uncertainty and Risk 67 Kirchgeorg, Manfred; Springer, Christiane (2005), UNIPLAN LiveTrends 2004/2005 : Effizienz und Effektivität in der Live Communication ; eine Analyse auf Grundlage einer branchen-übergreifenden Befragung von Marketingentscheidern in Deutschland 66 Kirchgeorg, Manfred; Fiedler, Lars (2004) Clustermonitoring als Kontroll- und Steuerungsinstrument für Clusterentwicklungsprozesse - empirische Analysen von Industrieclustern in Ostdeutschland 65 Schwetzler, Bernhard (2004) Mittelverwendungsannahme, Bewertungsmodell und Unternehmensbewertung bei Rückstellungen 64 La Mura, Pierfrancesco; Herfert, Matthias (2004) Estimation of Consumer Preferences via Ordinal Decision-Theoretic Entropy 63 Wriggers, Stefan (2004) Kritische Würdigung der Means-End-Theorie im Rahmen einer Anwendung auf M-Commerce-Dienste 62 Kirchgeorg, Manfred (2003) Markenpolitik für Natur- und Umweltschutzorganisationen 61 La Mura, Pierfrancesco (2003) Correlated Equilibria of Classical Strategic Games with Quantum Signals 60 Schwetzler, Bernhard; Reimund, Carsten (2003) Conglomerate Discount and Cash Distortion: New Evidence from Germany

49 59 Winkler, Karsten (2003) Wettbewerbsinformationssysteme: Begriff, Anforderungen, Herausforderungen 58 Winkler, Karsten (2003) Getting Started with DIAsDEM Workbench 2.0: A Case-Based Tutorial 57 Lindstädt, Hagen (2002) Das modifizierte Hurwicz-Kriterium für untere und obere Wahrscheinlichkeiten - ein Spezialfall des Choquet-Erwartungsnutzens 56 Schwetzler, Bernhard; Piehler, Maik (2002) Unternehmensbewertung bei Wachstum, Risiko und Besteuerung Anmerkungen zum Steuerparadoxon 55 Althammer, Wilhelm; Dröge, Susanne (2002) International Trade and the Environment: The Real Conflicts 54 Kesting, Peter (2002) Ansätze zur Erklärung des Prozesses der Formulierung von Entscheidungsproblemen 53 Reimund, Carsten (2002) Internal Capital Markets, Bank Borrowing and Investment: Evidence from German Corporate Groups 52 Fischer, Thomas M.; Vielmeyer, Uwe (2002) Vom Shareholder Value zum Stakeholder Value? Möglichkeiten und Grenzen der Messung von stakeholderbezogenen Wertbeiträgen 51 Fischer, Thomas M.; Schmöller, Petra; Vielmeyer, Uwe (2002) Customer Options Möglichkeiten und Grenzen der Bewertung von kundenbezogenen Erfolgspotenzialen mit Realoptionen 50 Grobe, Eva (2003) Corporate Attractiveness : eine Analyse der Wahrnehmung von Unternehmensmarken aus der Sicht von High Potentials 49 Kirchgeorg, Manfred; Lorbeer, Alexander (2002) Anforderungen von High Potentials an Unternehmen eine Analyse auf der Grundlage einer bundesweiten Befragung von High Potentials und Personalentscheidern 48 Kirchgeorg, Manfred; Grobe, Eva; Lorbeer, Alexander (2003) Einstellung von Talenten gegenüber Arbeitgebern und regionalen Standorten : eine Analyse auf der Grundlage einer Befragung von Talenten aus der Region Mitteldeutschland (not published) 47 Fischer, Thomas M.; Schmöller, Petra (2001) Kunden-Controlling Management Summary einer empirischen Untersuchung in der Elektroindustrie 46 Althammer, Wilhelm; Rafflenbeul, Christian (2001) Kommunale Beschäftigungspolitik: das Beispiel des Leipziger Betriebs für Beschäftigungsförderung

50 45 Hutzschenreuter, Thomas (2001) Managementkapazitäten und Unternehmensentwicklung 44 Lindstädt, Hagen (2001) On the Shape of Information Processing Functions 43 Hutzschenreuter, Thomas; Wulf,Torsten (2001) Ansatzpunkte einer situativen Theorie der Unternehmensentwicklung 42 Lindstädt, Hagen (2001) Die Versteigerung der deutschen UMTS-Lizenzen eine ökonomische Analyse des Bietverhaltens 41 Lindstädt, Hagen (2001) Decisions of the Board 40 Kesting, Peter (2001) Entscheidung und Handlung 39 Kesting, Peter (2001) Was sind Handlungsmöglichkeiten? Fundierung eines ökonomischen Grundbegriffs 38 Kirchgeorg, Manfred; Kreller, Peggy (2000) Etablierung von Marken im Regionenmarketing eine vergleichende Analyse der Regionennamen "Mitteldeutschland" und "Ruhrgebiet" auf der Grundlage einer repräsentativen Studie 37 Kesting, Peter (2000) Lehren aus dem deutschen Konvergenzprozess eine Kritik des Eisernen Gesetzes der Konvergenz und seines theoretischen Fundaments 36 Hutzschenreuter, Thomas; Enders, Albrecht (2000) Möglichkeiten zur Gestaltung internet-basierter Studienangebote im Markt für Managementbildung 35 Schwetzler, Bernhard (2000) Der Einfluss von Wachstum, Risiko und Risikoauflösung auf den Unternehmenswert 34 No longer available. There will be no reissue. 33 Löhnig, Claudia (1999) Wirtschaftliche Integration im Ostseeraum vor dem Hintergrund der Osterweiterung der Europäischen Union: eine Potentialanalyse 32 Fischer, Thomas M. (1999) Die Anwendung von Balanced Scorecards in Handelsunternehmen 31 Schwetzler, Bernhard; Darijtschuk, Niklas (1999) Unternehmensbewertung, Finanzierungspolitiken und optimale Kapitalstruktur 30 Meffert, Heribert (1999) Marketingwissenschaft im Wandel Anmerkungen zur Paradigmendiskussion

51 29 Schwetzler, Bernhard (1999) Stochastische Verknüpfung und implizite bzw. maximal zulässige Risikozuschläge bei der Unternehmensbewertung 28 Fischer, Thomas M.; Decken, Tim von der (1999) Kundenprofitabilitätsrechnung in Dienstleistungsgeschäften Konzeption und Umsetzung am Beispiel des Car Rental Business 27 Fischer, Thomas M. (2000) Economic Value Added (EVA ) - Informationen aus der externen Rechnungslegung zur internen Unternehmenssteuerung? (rev. edition, July 2000) 26 Hungenberg, Harald; Wulf, Torsten (1999) The Transition Process in East Germany 25 Vilks, Arnis (1999) Knowledge of the Game, Relative Rationality, and Backwards Induction without Counterfactuals 24 Darijtschuk, Niklas (1998) Dividendenpolitik 23 Kreller, Peggy (1998) Empirische Untersuchung zur Einkaufsstättenwahl von Konsumenten am Beispiel der Stadt Leipzig 22 Löhnig, Claudia (1998) Industrial Production Structures and Convergence: Some Findings from European Integration 21 Schwetzler, Bernhard (1998) Unternehmensbewertung unter Unsicherheit Sicherheitsäquivalentoder Risikozuschlagsmethode 20 Fischer, Thomas M.; Schmitz, Jochen A. (1998) Kapitalmarktorientierte Steuerung von Projekten im Zielkostenmanagement 19 Fischer, Thomas M.; Schmitz, Jochen A. (1998) Control Measures for Kaizen Costing - Formulation and Practical Use of the Half-Life Model 18 Schwetzler, Bernhard; Ragotzky, Serge (1998) Preisfindung und Vertragsbindungen bei MBO-Privatisierungen in Sachsen 17 Schwetzler, Bernhard (1998) Shareholder-Value-Konzept, Managementanreize und Stock Option Plans 16 Fischer, Thomas M. (1998) Prozeßkostencontrolling Gestaltungsoptionen in der öffentlichen Verwaltung 15 Hungenberg, Harald (1998) Kooperation und Konflikt aus Sicht der Unternehmensverfassung

52 14 Schwetzler, Bernhard; Darijtschuk, Niklas (1998) Unternehmensbewertung mit Hilfe der DCF-Methode eine Anmerkung zum Zirkularitätsproblem 13 Hutzschenreuter, Thomas; Sonntag, Alexander (1998) Erklärungsansätze der Diversifikation von Unternehmen 12 Fischer, Thomas M. (1997) Koordination im Qualitätsmanagement Analyse und Evaluation im Kontext der Transaktionskostentheorie 11 Schwetzler, Bernhard; Mahn, Stephan (1997) IPO s: Optimale Preisstrategien für Emissionsbanken mit Hilfe von Anbot-Modellen 10 Hungenberg, Harald; Hutzschenreuter, Thomas; Wulf, Torsten (1997) Ressourcenorientierung und Organisation 9 Vilks, Arnis (1997) Knowledge of the Game, Rationality and Backwards Induction (Revised edition HHL Working Paper No. 25) 8 Kesting, Peter (1997) Visionen, Revolutionen und klassische Situationen Schumpeters Theorie der wissenschaftlichen Entwicklung 7 Hungenberg, Harald; Hutzschenreuter, Thomas; Wulf, Torsten (1997) Investitionsmanagement in internationalen Konzernen - Lösungsansätze vor dem Hintergrund der Agency-Theorie 6 Hungenberg, Harald; Hutzschenreuter, Thomas (1997) Postreform - Umgestaltung des Post- und Telekommunikationssektors in Deutschland 5 Schwetzler, Bernhard (1996) Die Kapitalkosten von Rückstellungen zur Anwendung des Shareholder- Value-Konzeptes in Deutschland 4 Hungenberg, Harald (1996) Strategische Allianzen im Telekommunikationsmarkt 3 Vilks, Arnis (1996) Rationality of Choice and Rationality of Reasoning (rev. Edition, September 1996) 2 Schwetzler, Bernhard (1996) Verluste trotz steigender Kurse? - Probleme der Performancemessung bei Zinsänderungen 1 Meffert, Heribert (1996) Stand und Perspektiven des Umweltmanagement in der betriebswirtschaftlichen Forschung und Lehre

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