jonathan jebson dissertation

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Washington University in St. Louis

Olin Business School

DETERMING THE MARGINAL VALUE OF

PROFESSIONAL ATHLETES IN THE NATIONAL

BASKETBALL ASSOCIATION

Author

Jonathan Jebson

May 2013



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Abstract

This paper researches the marginal revenue products of athletes who played in the

National Basketball Association between 2006 and 2012. Two regressions, one to predict

team wins in a given season and another to predict annual team revenues, are generated to

calculate values for individual players. Data from Forbes, the U.S. Census Bureau, and

Basketball-Reference.com are used in the regressions. Results from the research indicate that

differences between player value and compensation exist due to labor market rigidities

created by the NBA. These rigidities are necessary to create parity in the league, to

maintain/elevate fan interest, and to help the NBA maximize profits. Without these rigidities,

individual players would see compensation levels closer to their marginal revenue products

but the league would suffer overall.



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I declare that this dissertation is the result of my own work and includes nothing which is the

outcome of work done in collaboration. It is not substantially the same as any which I have

submitted for a degree, diploma, or other qualification at any other university. Additionally,

no part of this dissertation has already been, or is currently being, submitted for any such

degree, diploma, or other qualification.

Jonathan Jebson

London, UK

17 May 2013



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Table of Contents

Introduction……………………………………………………………………………………4

Literature Review…………………………………………………………………………….11

Calculating Marginal Revenue Products of Professional Athletes………………......11

Competitive Imbalance in the National Basketball Association..................................15

Generating Revenue in the National Basketball Association……………..………....17

Generating Wins in the National Basketball Association…………..………………..19

Data Employed……………………………………………………………………………….25

Methodology…………………………………………………………………………..……..29

Statistical Models………………………………………………………………………….....38

Statistical Findings………………………………………………………………………..….44

The Case for Good Centers……………………………………......………………....44

The Case for Shooting Efficiency……………………………………......…………..46

The Case for LeBron James……………………......………………………………...49

The Case for Tyson Chandler …………………......…………………………………50

Conclusion…………………………………...……………………………………………….52

Works Cited……………………………………………………..…………………...……....54



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Indroduction

―LeBron James is getting hosed.‖ – Economist Kevin Grier.

―LeBron James, you deserve a raise. A massive one. Just know that you won‘t get

it.‖ – ESPN Columnist Bill Simmons1.

How could a professional athlete — an adult making a living by playing a game — be

paid over $30 million dollars a year and still be underpaid? Despite restrictions on athlete

pay — like salary caps and payroll limits — heightened league popularity has led to increased

compensation for professional athletes since league formation in the early 20th

Century. However, many people, like Professor Grier from the University of Oklahoma, will

controversially say that top athletes are underpaid. He argues that the amount of money

LeBron James brings in to the Miami Heat is significantly more than what he is

compensated2. This paper attempts to mathematically calculate to what extent, if any, the

best athletes in the National Basketball Association (NBA) are getting overpaid or underpaid.

Debates about the salaries of professional athletes have existed almost since leagues

were inaugurated. Major League Baseball (MLB) legend Babe Ruth earned more than

President Herbert Hoover did during the United States‘ Great Depression of the 1930s. Ruth

famously defended his $80,000 a year salary (equivalent to just over $1,000,000 today) by

saying, ―Why not? I had a better year than President Hoover did.‖3 Today, even middling

professional athletes are compensated considerably more than President Obama‘s $400,000 a

year salary. In fact, the minimum yearly salary in 2013 for rookie American Football payers

in the National Football League (NFL) is $405,0004.

1 Simmons, Bill. "The Best Bargains of the NBA." Grantland . ESPN, 1 Mar. 2013. Web. 13 Apr. 2013.

2 "Episode 427: Lebron James in Overpaid." Planet Money. National Public Radio. N.d. National Public Radio, 4 Jan. 2013.Web. 13 Apr. 2013.

3 "President Herbert Hoover Baseball Related Quotations." Baseball Almanac. N.p., n.d. Web. 15 Apr. 2013.

4 Bryan, Dave. "2011-2014 NFL Minimum Base Salaries." Steelers Depot . N.p., 23 July 2011. Web. 15 Apr. 2013.



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In 1962, fans were shocked to see star NBA player Wilt Chamberlain turn down an

offer that would have made him the highest paid player at the time. More recently, NBA

player Latrell Sprewell turned down an offer of $10 million a year calling it ―insulting‖ and

famously saying, ―Why would I want to help them win a title? They‘re not doing anything

for me. I‘m at risk. I have a lot of risk here. I got my family to feed.‖5 Tales like these

serve to demonstrate how out of control professional athlete salaries have seemingly become.

Marginal revenue product of labor is defined as the additional revenue a firm creates

from adding one additional unit of labor. In theory, workers will be hired up to the point

where their marginal revenue products equal wage rates, because beyond this point, it is sub-

optimal for a firm to pay a worker more than the revenues he or she will generate. Though

difficult to calculate, marginal revenue products of professional athletes can be defined as the

additional revenue a franchise generates from a specific player. LeBron James has a

wonderfully high marginal revenue product, as demonstrated by Cleveland‘s sky-rocketing

revenues after drafting him in 2003.

However, because most professional athletes participate in team sports, individual

marginal revenue products can be extremely difficult to calculate. Statistical models cannot

account for player externalities that very clearly exist in team sports. A player like Bill

Russell who has an attitude of ‗do anything to help the team win, my statistics come second‘

or the San Antonio Spurs‘ ‗find the extra pass‘ culture may lead to synergies on the

court. Opposite types of players, like Kobe Bryant and Wilt Chamberlain, might be more

interested in individual statistics than winning games, creating a potential for antagonism.

There are many traditional arguments against high athlete compensation. First and

foremost, fans argue that athletes merely play a game and don‘t truly contribute to

5 "Sprewell to Timberwolves: New Deal or Trade Me." Associated Press. The Boston Globe. N.p., 2 Nov. 2004. Web. 15

Apr. 2013.



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(contribution) and player compensation (reward). The NBA‘s labor market is especially

advantageous to economists. Due to the few number of players, each player‘s marginal

contribution is readily available to be calculated and analyzed. Furthermore, professional

sports leagues are often the only true employers of professional athletes in their specific

fields, eliminating the potential for competing employers.

Kahn points at the rise and fall of rival leagues as the reason for the introduction of

the ‗reserve clause‘ in Major League Baseball in 1876. This clause, Kahn argues, maintained

the quality of play in the MLB and protected it from competition from other leagues by

binding players to the teams by which they were originally acquired. Players were unable to

sell their talents on the free market and were restricted to negotiations with only their

owner. Empirically, this caused a significant drop in player salaries. The researcher outlines

a long plot about rising and falling competitors to Major League Baseball and their effects on

player salaries. Kahn asserts that the removal of the reserve clause in 1976 caused average

real salary of professional baseball players to increase by 10%. The next season, the first

under a true collective bargaining agreement, led to an increase of 38%. In the NBA, true

free agency started in 1976 as well. Real salaries as a percentage of team revenue increased

between the 1976 and 1983 seasons until the 1984 introduction of a salary cap, yet another

rigidity in the labor markets of professional sports leagues. To end the first focus of his

paper, Kahn attempts to determine the degree of monopsonistic exploitation of professional

athletes. He finds that before 1976, baseball players received 20% of their marginal revenue

products and star players received only 15%. After the introduction of free agency, the

marginal revenue products of players jumped to around 40%. He concludes that the removal

of the reserve clause has been a step in the right direction to perfect competition for labor in

professional sports leagues — under which players would be paid extremely closely to their

marginal revenue products.



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Kahn then studies the Coase theorem, which states that under no transaction costs, if

trade in an externality is a possibility, efficient outcomes will be reached through bargaining

regardless of initial property rights. In sports, the Coase theorem implies that changes in

draft or free agency rules should not have an effect on the distribution of talent throughout

the league. Under the reserve clause, Kahn argues that a player whose marginal revenue

product is $500,000 to Cleveland and $1,000,000 to Miami will end up in Miami because any

offer from Miami greater than $500,000 but less than $1,000,000 will economically benefit

each team. Under free agency, the same result will happen because Miami will offer the

player a larger contract and the player will choose to move on his own. If owners are sports

enthusiasts that don‘t profit-maximize and solely want to win (like English Premier League

Manchester City‘s new owner, Shiekh Mansour bin Zayed Al Nahyan), the same results will

occur because owners will overpay for top players under either free agency or the reserve

clause.

But, observers can clearly see that the Coase theor em doesn‘t fully apply to sports

leagues. The rise of NBA ‗big threes‘ (Bryant/Nash/Howard in Los Angeles,

Wade/Bosh/James in Miami, and Garnett/Pierce/Allen in Boston) is sufficient evidence to

demonstrate that players are not evenly distributed across franchises. The Coase theorem

operates under the assumptions of perfect information, no wealth effects, and no transactions

costs. In the NBA, transaction costs lead to limited movements of players. NBA

Commissioner David Stern, for example, blocked a trade that would have sent All-Star Chris

Paul to the Los Angeles Lakers from the league-owned New Orleans Hornets. Stern sought

to keep a balance of power in the league but conspiracy theorists point to the fact that he was

in concurrent negotiations to sell the franchise to the private sector and didn‘t want to

devalue the team by shipping away its best player. Kahn says that blocked trades and salary

caps (which make it difficult for teams with high payrolls to continue to acquire top talent)



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are transaction costs that break down the Coase theorem. Another breakdown occurs from

the fact that wealth effects are not zero in trades involving professional athletes. Players are

willing to take pay cuts to be in favorable locations or to be on the best team. In 2010, Chris

Bosh and LeBron James, two NBA superstars, took pay cuts to join Dwyane Wade in Miami

(a desirable location with no individual state income tax) and create a team full of

superstars. Teams in desirable locations, according to Kahn, have comparative advantages

over teams in less-preferred areas.

The Coase theorem, according to Kahn, gets put to the test in professional leagues

when major rule changes are put in place. In 1936, following increasing numbers of bidding

wars for college players, the National Football League instituted a player draft, with the worst

teams drafting first. Numerous studies have found that the introduction of the draft did not

affect the standard deviation of winning percentages the following season. Similar findings,

all of which are consistent with the Coase theorem, have been discovered in the National

Basketball Association. In Major League Baseball, there are two examples, both of which

can be justified through other explanations, where rule changes have had effects on

competitive balance. Kahn concludes that while there is evidence that the Coase theorem

holds in sports, empirical and statistical examples that disprove the theorem exist and need to

be looked at7.

Without a doubt, a divide exists between what athlete‘s feel they should be paid and

what the general population thinks they should be paid. Like in any labor market, if there

was perfect competition, professional athletes would be paid extremely close to the revenues

they bring in to the team. However, labor market rigidities break down true perfect

competition. Blocked trades, salary caps, and payroll caps are league rules to create parity in

7 Kahn, Lawrence M. "The Sports Business as a Labor Market Laboratory." Journal of Economic Perspectives 14.3 (2000):

75-94. Print.



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professional sports leagues. Unwavering franchise loyalty, though becoming increasingly

uncommon, hinders the free movement of players on the market. This research attempts to

calculate the marginal revenue products of elite NBA players.

Literature Review

The purpose of this literature review is to examine current works and explore the

topic of marginal revenue products in sports. Many scholarly articles and undergraduate

dissertations have studied professional sports leagues through statistical analysis. The

articles in this literature review can be placed into four categories — calculating marginal

revenue products, researching competitive balance in the National Basketball Association,

predicting revenues of NBA teams, and predicting the number of wins NBA teams will

generate.

CALCULATING MARGINAL REVENUE PRODUCTS OF PROFESSIONAL ATHLETES

Scully (1974) is oft-cited and one of the first academic papers written on the

subject. In it, he researches the effects of the ‗reserve clause‘ in Major League

Baseball. This clause, he argues, creates labor market rigidities because it gives owners the

exclusive rights to renegotiate contracts with their players. Under the reserve clause, even

when the contract was terminated, players were constrained to renegotiations with only their

owner and couldn‘t sell their services on the free market. This MLB monopsony led to

significant owner exploitation of the players. Scully wrote this paper in the aftermath of the

1972 MLB players‘ strike, in which the reserve clause was a top point of contention. He

finds that significant exploitation of the players existed in the league; by his models, average

players received only 20% their marginal revenue product over their careers.



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Scully (1974) also lays the foundation for creating statistical models to calculate

marginal revenue products, a task difficult to accomplish in the labor market for professional

athletes. Logically, he hypothesizes that increased player performance leads to more wins,

and more wins lead to increased team revenues. His challenge then, was to create models to

predict two things: to what extent player performance affects wins, and to what extent wins

affect team revenues. This is an especially arduous task given the nuances of baseball — one

pitcher playing in one of every five games and realistically not being expected to generate

offense, for example. To deal with this, Scully doesn‘t use individual player statistics in his

model for predicting percentage of wins.

In his model to predict the percent of games teams will win, Scully uses team

strikeout-to-walk ratio, team slugging average, a dummy variable if the team is in the

National League, and two variables to take intangibles into account: CONT, which captures

increased performance from a team vying for a playoff spot, and OUT, which captures

demoralization of teams that have been eliminated from playoff contention. His model for

team revenues has six independent variables: percentage of games the team wins, the size of

the city, team attendance, if the team is in the National League, if the team has a poor

stadium in a bad part of the city, and the percentage of players on the team that are African-

American (due to the fact that racism still existed in professional baseball during that time

period.

In his attempt to determine the degree of monopsonistic exploitation of players in

Major League Baseball, he places players into three categories: mediocre, average, or

star. Each category has a different percentage of team at-bats and length of playing

career. Scully determines that over the length of their careers, average players receive

compensation equal to 20% of their net marginal revenue products. Star players receive only



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15% of their net marginal revenue products. The monopsonistic exploitation of professional

baseball players, he concludes, is of significant magnitude8.

Berri (1999) uses statistical models to predict which NBA players are truly the ‗most

valuable‘. He says that the idea of measuring the productivity of an individual participating

in a team sport is of enormous value to coaches, general managers, and owners. He points to

media subjectivity in determining post-season awards and sets out to calculate player

marginal revenue products by creating an econometric model to link player productivity to

team wins. His data comes from four NBA seasons, beginning in 1994/1995 and ending in

1997/1998.

Berri theorizes that the primary determinants of wins in the NBA are points scored

(PTS) and points surrendered (DPTS). Unsurprisingly, he finds that these two factors explain

95% of the variation in team wins. Theoretically, the value of a specific player should

merely be a function of how many points he scores and how many points he

surrenders. However, Berri says that this is severely misleading. Because basketball is a

team sport and each player contributes in different ways, statistics like rebounding, assists,

steals, and turnovers need to be factored into the model.

He breaks down both win percentage and points surrendered into two linear

equations. His independent variables are standard basketball statistics: free throws made,

offensive/defensive rebounds, turnovers, and assist-to-turnover ratio, for example. Both

equations have r-squared values above 0.96, meaning that the productivity of NBA players

can theoretically be predicted with relatively high accuracy. His next step is to merge these

two equations into one equation that links both factors to wins. This enables Berri to find the

8 Scully, Gerald W. "Pay and Performance in Major League Baseball." The American Economic Review 64.6 (1974): 915-

30. Print.



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marginal value of each individual statistic. He does this by taking the first-order derivative of

his win percentage equation.

Once he discovers the impact each statistic has on the number of wins a team

produces, Berri is able to calculate the number of wins each specific player generates. His

first step is to calculate per-minute production of a player, which is equal to the marginal

value of each statistic multiplied by the accumulation of the statistic. He then divides this

product by the total number of minutes the player plays. Next, Berri examines team

statistics. To calculate a team‘s per minute tempo factor, he adds the products of team field

goal attempts and team free throw attempts by their respective marginal values. He then

divides this by total minutes played. To calculate a team‘s per minute defense factor, Berri

multiplies the marginal value of a team defense statistic by the accumulation of the statistic,

then divides this by total minutes played. To account for variances in each position (centers

recording the most rebounds, for example), he adds to his equation the average per-minute

production at each position. Lastly, he divides the total number of games won (1189) by the

total number of minutes played to find the average per minute production of wins in the

league. His final equation asserts:

Production of wins = (per minute player production + per minute team tempo factor +

per minute team defensive factor - average per minute production at position + average

player‘s per minute production) x total minutes played.

Berri uses his model to determine that Karl Malone was more productive than

Michael Jordan in the 1997/1998 NBA season, despite the fact that Jordan was crowned

‗Most Valuable Player‘. He also concludes that Dennis Rodman produced more regular

season wins than either Jordan or Malone. Berri‘s model is surprisingly accurate; his



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predicted wins and actual wins for the majority of NBA franchises are not far off. He points

out that his model, while accurate, does not determine why a player achieves the productivity

he does. However, he sufficiently calculates how productive individual NBA players are, in

terms of wins generated9.

COMPETITIVE IMBALANCE IN THE NATIONAL BASKETBALL ASSOCIATION

Berri, Brook, Frick, Fenn, and Vincente-Mayoral (2005) study the causes of

competitive imbalance throughout professional sports leagues. They state that professional

sports teams, unlike most industries, see decreased revenues when competition is

eliminated. Gate receipts and spending at the stadium depend on the uncertainty of the

outcome of games — fans want some suspense to be entertained. Therefore, leagues profit-

maximize when there is a high level of competitive balance. Because of this, leagues enact

previously-mentioned rules like the reserve clause, the rookie draft, revenue sharing, and

payroll caps to increase competitive balance. The researchers hypothesize that because there

is a short supply of tall people throughout the world, the NBA suffers from competitive

imbalance the most.

They measure the dispersion of wins by looking at the actual performance of teams

compared to the performance of teams if the league had perfect levels of competitive

balance. The higher the difference between the two, the more competitive imbalance

exists. In their initial study of 17 leagues throughout the world, the National Basketball

Association and the now-defunct American Basketball Association topped the list of leagues

with the most competitive imbalance by a wide margin.

9 Berri, David J. "Who Is 'Most Valuable'? Measuring the Player's Production of Wins in the National Basketball

Association." Managerial and Decision Economics 20.8 (1999): 411-27. Print.



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Berri, Brook, Frick, Fenn, and Vincente-Mayoral ascertain that human beings have

biomedical limits on athletic ability. For example, today‘s world-class sprinters can run 100

meters in about 9.6 seconds but because of the limitations of the human body, will never be

able to break 5 seconds. Upon formation of leagues in team sports, a few athletes will

perform close to the limits of the human body. The vast majority, however, will be far below

this line, creating a large distribution of talent. As popularity of the sport rises and more

athletes grow up with sport-specific training, the distribution of talent will narrow and

competitive balance will rise. Football leagues, the researchers find, have the most

competitive balance. This is unsurprising when one remembers that football is the most

popular sport on the planet. They state that basketball is arguably one of the most popular

sports in the world — so why is it so competitively imbalanced? The simple answer can be

found in the height of professional basketball players, a significant unwritten barrier to entry

into professional basketball leagues.

In the United States, the average height of a young adult male is about five feet nine

inches. For the years 1994-2004 in the NBA, only four athletes were average in

height. Nearly 98% of all young adult males in America are six feet three inches or shorter —

only 20% of NBA players fall into this category. Almost one in three NBA players is six feet

ten inches or taller. While dedicated training can improve likelihood of joining a

professional team in other sports, no amount of training can significantly increase

height. The population that NBA teams can realistically select players from is drastically

restricted, creating competitive imbalance.

To test the hypothesis that short NBA players have less variation in performance than

tall players, Berri, Brook, Frick, Fenn, and Vincente-Mayoral measure player productivity on

a per-minute basis by using points scored, total rebounds, steals, field goals attempted, free

throws attempted, and turnovers. Shorter players, they find, offer significantly less deviation



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in performance than taller players. This suggests that there is a short supply of quality tall

basketball players in the NBA because of the overall short supply of tall people in the

world. This suggests that the short supply of tall human beings in the world is the reason for

competitive imbalance in professional basketball leagues10.

GENERATING REVENUE IN THE NATIONAL BASEKTBALL ASSOCIATION

Berri, Schmidt, and Brook (2004) build off previous studies that found that despite

the National Basketball Association‘s rookie draft, free agency, revenue sharing, and payroll

caps, the league has the lowest level of competitive balance of any professional sports league

in the world. Berri, Schmidt, and Brook aren‘t interested in finding out why the NBA is

competitively imbalanced; they seek to discover how the imbalance affects consumer

demand. They cite Rascher (1999), who discovered that Major League Baseball attendance

(and therefore, revenue) is maximized when the probability of the home team winning the

game is 0.611. It is assumed that fans want a bit of suspense during matches but,

understandably, don‘t want to watch the home team lose that often. Berri, Schmidt, and

Brook hypothesize that bottom-tier NBA teams — teams in small markets — can counter this

by utilizing star players to promote fan interest and increase consumer demand (gate

revenues).

They assume that team performance, franchise, and market characteristics drive

demand and their independent variables fall under these three categories. Variables such as

wins, wins from the prior season, playoff wins, championships, and All-Star votes received

10 Berri, David J., Stacey L. Brook, Bernd Frick, Aju J. Fenn, and Roberto Vicente-Mayoral. "The Short Supply of Tall

People: Competitive Imbalance and the National Basketball Association." Journal of Economic Issues 39.4

(2005): 1029-041. Print.

11 Rascher, Daniel. (1999). A test of the optimal positive production network externality in Major League Baseball. In J.

Fizel, E. Gustafson, & L. Hadley (Eds.), Sports Economics: Current Research (pp. 27-45). New York: Praeger.



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contribute to team characteristics. Variables regarding the stadium capacity and age, if the

team was an expansion team, roster stability, and ratio of white players make up the franchise

characteristics. Population of the city, per-capita income, number of competing teams, and

competitive balance make up the market characteristics for franchises. Their data comes

from four NBA seasons in the early 1990s.

Berri, Schmidt, and Brook take into account team performance and star players in

their independent variables. Because they‘re interested in consumer demand, they use All-

Star Game votes as the measure of fan preference for star players. For each franchise, they

total the votes received by employed players for the variable. While this is a great method to

determine fan interest, it doesn‘t take into account cases like Yao Ming who is an 8-time

NBA All-Star due to his votes from citizens of China, many of whom have never attended an

NBA game and thus, have not directly increased gate revenue. However, these people have

impacted TV revenues by increasing the value of the NBA‘s Chinese television rights. The

researchers hypothesize that roster stability (turnover of a team) has an effect on gate

revenues. They predict that it has a negative relationship — that less turnover leads to more

consumer demand. Berri, Schmidt, and Brook find that, perhaps unsurprisingly, team

performance (wins) is the most important factor in explaining NBA team revenues. Only

their multiplicative model, not their traditional linear regression, finds star power to be

significant in generating gate revenue. This suggests that small market teams might not

optimize consumer demand by overspending on star players12.

12 Berri, D. J., M. B. Schmidt, and S. L. Brook. "Stars at the Gate: The Impact of Star Power on NBA Gate Revenues."

Journal of Sports Economics 5.1 (2004): 33-50. Print.



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GENERATING WINS IN THE NATIONAL BASKETBALL ASSOCIATION

Onwuegbuzie (2000) determines which factors contribute to the variance of winning

percentages among NBA teams. In his research question, he notices that descriptive statistics

(averages, percentages, and totals), not inferential statistics, are the numbers that tend to be

used by NBA teams. He resolves the issue that no research up until that point specifically

looks at which factors directly associated with player skill level directly impact team winning

percentages. In his model, he uses team winning percentage as his dependent variable and 16

independent variables taken off the NBA website.

He finds that field goal percentage is three times more important than three-point

percentage in explaining the variance in NBA team success. Onwuegbuzie concludes that,

with 95% certainty, every increase in field goal conversion rate by 1% increases winning

percentage between 6% and 10%. Each percentage point increase in opposing teams‘ three-

point conversion rate decreases winning percentage between 2.5% and 6%. Over 80% of the

total variance in his model is explained by field goal percentage and opposing average three-

point percentage. This means that NBA team success can be predicted with a relatively high

degree of accuracy.

Onwuegbuzie claims that, since field goal percentage explains three times the

variance in team success more than opposing teams‘ three-point percentage does, defensive

achievements might be less important than offensive ones. This contrasts with other sports,

like American Football, in which statistical analyses have confirmed the old adage ‗defense

wins championships‘. He stresses the importance of overall offensive efficiency with not

only starting players but bench players as well. He suggests that, defensively, teams might be



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better off forcing opponents to take shots from spots further away from the basket but inside

the three-point arc — sub-optimal places on the court13.

Quinn, Bursik, Borick, and Raethz (2003) disprove the traditional owner argument

that new stadiums will lead to more wins. They notice that team performance is often

cyclical and seek out to determine to what extent new stadiums contribute to those

cycles. They assume firms are profit-maximizing (unlike Sheikh Al Nahyan‘s ownership of

Manchester City) and, in the case of the NBA, constrained by payroll caps and minimum

required operating profits. They study winning percentage across the four major American

sports leagues at five different points in time – seven years before the venue opened, three

years before it opened, the year it opened, three years after it opened, and seven years after it

opened. The researchers find regression toward the mean in all of the leagues — meaning that

poor-performing teams tend to improve over time. For the National Football League, the

National Basketball League, and the National Hockey League, Quinn, Bursik, Borick, and

Raethz are unable to conclude that a new venue leads to team success. In Major League

Baseball, they are able to reject their null hypothesis, which states that there is no change in

winning percentages between the 7- or 3-year time periods before and after a team built a

new arena14.

Siegfried and Zimbalist (2002) continue Quinn, Bursik, Borick, and Raethz‘s work

and go on to disprove a second myth — that building new stadiums stimulates economic

development in cities. They assert that this political argument is made because referendums

on using public moneys to fund stadiums are often decided by a close margin. Therefore

13 Onwuegbuzie, Anthony J. "Factors Associated with Success Among NBA Teams." The Sport Journal 3.2 (2000): n. pag.

The Sport Journal . Web. 6 Mar. 2013.

14 Quinn, Kevin G., Paul B. Bursik, Christopher P. Borick, and Lisa Raethz. "Do New Digs Mean More Wins?: The

Relationship between a New Venue and a Professional Sports Team's Competitive Success." Journal of Sports

Economics 4.3 (2003): 167-82. Print.



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arguments from politicians that the stadium will increase the number of jobs can often be

enough to swing a couple votes and effectively, the decision.

The researchers find that because non-essential spending is relatively inflexible, a

new arena often only leads to a rearrangement of leisure dollars spent within a

community. A citizen might choose to golf one fewer round and use that money to instead

buy an NBA ticket at the new arena. This doesn‘t create wealth, it merely shifts it. If outside

money is brought to an arena, it comes at the expense of other leisure areas, a ―beggar -my-

neighbor‖ policy. Estimates suggest that around 5-20% of attendance at live professional

sports games in the United States comes from citizens outside the local area. More often than

not, these people come to the city for other reasons (work, visiting family, vacation) and

merely use a portion of their vacation budget on a ticket to a match in a new arena. Because

this money would have been spent in the local economy anyway, new arenas somewhat

cannibalize ‗sales‘ in the local economy. Furthermore, in sports franchises‘ organizational

structures, high proportions of revenues go to player, owner, and executive salaries. The

economists argue that these individuals have high marginal tax and savings rates. So, with

taxes to the federal government and savings to global financial markets, little is left for the

local economy15.

Nutting (2010) concludes that despite large differences in travel distance among NBA

teams over the course the 16 studied seasons (Miami traveled 53% more than Chicago), this

variable does not have an effect on generating team wins. He gathers data from NBA teams‘

41 home and 41 away games per season for the 16 seasons. Distances are calculated from

arena zip codes and he doesn‘t take into account what time a game started or whether it went

to overtime. Home teams win more than 60% of games, average over 100 points per game,

15 Siegfried, John, and Andrew Zimbalist. "A Note on the Local Economic Impact of Sports Expenditures." Journal of

Sports Economics 4.4 (2002): 361-66. Print.



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and average 0.3 more days off than visiting teams. They also average about 300 fewer miles

traveled since their last game.

The researcher finds minimal evidence that increased travel distances reduces

production of wins. Game frequency‘s effect on win production is amplified in the second

half of the season. Time zone changes are significantly correlated with win percentage only

in the second half of the season (as a team moves west, it produces fewer wins). This

suggests that travel and game frequency costs accrue over the length of the NBA season. He

finds no significant correlation between team location and game frequency, likely due to the

ease and speed of travel for NBA teams16.

McGoldrick and Voeks (2000) study the differences between the National Basketball

Association and the Women‘s National Basketball Association. Empirical differences

between the leagues — like the lack of dunking in the WNBA — are often pointed out, but no

rigorous statistical analysis comparing the two leagues had been achieved prior to this

research. Their data comes from the 2000-2001 seasons and is adjusted to compensate for

rule differences between the leagues and to prevent double counting of games.

Their initial findings are that WNBA teams attempt significantly larger numbers of

three-pointers. They also have more personal fouls, steals, and turnovers. NBA teams score

more points and have a higher percentage of three-pointers made. The WNBA has a

significantly higher ratio of personal fouls and it is more lopsided in this statistic. NBA

games have significantly more blocked shots while WNBA games have a larger ratio of

defensive rebounds. Between the two leagues, there is a statistical difference when using an

absolute measure of performance (total points scored) but no statistical difference when using

a relative measure (ratio of final scores).

16 Nutting, Andrew W. "Travel Costs in the NBA Production Function." Journal of Sports Economics 11.5 (2010): 533-48.

Print.



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After looking at the descriptive statistics, the researchers set up an empirical model

using a dichotomous variable (win/loss) as the dependent variable and various relative

measures of team performance as the 10 independent variables. They use a logit model to

estimate the impact various characteristics of play have on the probability of winning. The

majority of independent variables are not statistically different between leagues. However, in

the NBA, steals and offensive rebounds significantly affect the outcome of games, both of

which are insignificant in the WNBA. Increasing blocked shots in the WNBA has a

statistically significant and positive impact on WNBA win generation, but no significant

impact in the NBA.

In both leagues, the ratio of 2-point shot percentages has the largest marginal impact

on winning games. A 1% increase in the mean 2-point shot ratio leads to a 4.7% increase in

the probability of winning a WNBA game and a 7.1% increase in the probability of winning

an NBA game. The second biggest variables in terms of marginal impact are defensive

rebounds for the NBA and turnovers for the WNBA.

Their next model, a stochastic frontier model, estimates the contribution of different

characteristics of play to the ratio of final points. They use this to measure teams‘ degree of

efficiency — which teams achieved their potential maximum relative score. A high efficiency

score meant that a team either maximized its points given the characteristics of its play or it

kept its opponent‘s scoring to a minimum. The results of this were generally consistent with

the results of the logit model. But, this model shows that there is a significantly less-efficient

pattern of play in the WNBA relative to the NBA. The NBA also displays more disparity in

efficiency scores, indicating less parity in the league17.

17 McGoldrick, Kimmarie, and Lisa Voeks. "―We Got Game!‖: An Analysis of Win/Loss Probability and Efficiency

Differences Between the NBA and WNBA." Journal of Sports Economics 6.1 (2005): 5-23. Print.



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Lastly, Staw and Hoang (1995) research if sunk cost effects exist in the NBA —

namely if, when controlling for player performance, draft order has an effect on minutes

played, future earnings, and likeliness to be traded. They state that a top draft pick doesn‘t

necessarily guarantee acquiring top talent (the Detroit Pistons, for example, drafted Darko

Milicic in 2003, passing up Carmelo Anthony, Chris Bosh, and Dwyane Wade, three future

All-Stars). However, a high draft pick does guarantee high costs — rookie contracts for

highly-drafted NBA players have increased significantly over the past ten years. In a perfect

world, they argue, NBA teams should play their most productive players (this also fits with

aforementioned papers that determine that wins are the most important variable in generating

revenue). Theoretically, after controlling for performance on the court, draft order should

have no impact in likelihood to be traded. The independent variables in their model to

predict playing time fall into the categories of scoring, toughness, or quickness.

Predictably, Staw and Hoang find that a player‘s scoring is the primary variable

driving increased playing time. A bit surprising, perhaps, is the fact that according to their

findings, draft order is a significant predictor of minutes played. Even more startling are

their findings in regard to NBA hazard rates. They find that draft number has a positive,

significant effect on the hazard rate for a player being traded. A player who is drafted in the

second round is 72% more likely to be traded than a player drafted in the first round. These

findings suggest that sunk cost effects exist among NBA franchises and teams might consider

draft order too much in determining future relations with players 18.

18 Staw, Barry M., and Ha Hoang. "Sunk Costs in the NBA: Why Draft Order Affects Playing Time and Survival in

Professional Basketball." Administrative Science Quarterly 40.3 (1995): 474-94. Print.



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Data Employed

All of the data used in the multi-linear regression to predict NBA team wins comes

from a website named Basketball-Reference.com. This site is a free resource with well-

organized data and all the necessary basketball statistics to run the regression. The variables

from this website are all at the team level, and they include: Wins (out of an 82 game season),

Field Goals Made, Field Goals Attempted, Field Goal Percentage, 3-Point Shots Made, 3-

Point Shots Attempted, Free Throws Made, Free Throws Attempted, Offensive Rebounds,

Defensive Rebounds, Assists, Steals, Blocks, Turnovers, and Personal Fouls. The data is

gathered from six NBA seasons, starting in 2006/2007 and going through the 2011/2012

season. Descriptive statistics are as follows:

Table 1 The data necessary for the regression to predict NBA team revenues comes from

multiple places. Forbes publishes annual revenue data for each franchise. The data on the



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size of each city is taken from the U.S. Census Bureau. The rest of the data in this regression

comes from Basketball-Reference.com. The variables used were: Team Revenue, Wins,

Previous Season Wins, Playoff Wins, Previous Season Playoff Wins, Championships in Past

20 Years, Number of All-Star Starters, Age of Stadium, Stadium Capacity, and Size of

City. Data is gathered from six NBA seasons, starting in 2006/2007 and going through

2011/2012. Descriptive statistics are as follows:

Table 2 The rest of the gathered data are statistics on every NBA player that played between

2006 and 2012. This data is not used in a regression, only to generate values for each

specific player in terms of wins and dollars generated. This data is taken from Basketball-

Reference.com and also comes from the same six seasons. The variables generated are Field



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Goals Made, Field Goals Attempted, 3-Point Shots Made, Free Throws Made, Free Throws

Attempted, Offensive Rebounds, Defensive Rebounds, Assists, Steals, Turnovers, and Total

Points For. Descriptive statistics for this data are as follows:

Table 3 I see no potential issue with the quality of the data in my models. NBA statistics are

current and are kept very accurately. There are many sites that keep track and publish NBA

data. I picked Basketball-Reference.com over other sources (like NBA.com, ESPN.com,

SI.com, Yahoo! Sports, 82games.com, and Hoopdata.com) because of how comprehensive

the data was. The website is provides well-organized data. It also is simple to download the

necessary data so I could easily analyze it. Forbes, where I gathered my information on NBA

team revenues, is a reputable business magazine with accurate data, so I do not foresee any



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problems with this portion of the data. Lastly, the U.S. Census Bureau will have extremely

accurate information regarding the size of various metropolitan areas in the United States.

I manipulated and organized my data in certain ways to generate the most accurate

regressions. First, I removed all data regarding the Seattle SuperSonics/Oklahoma City

Thunder before running my regressions. In 2008, this franchise moved from Seattle to

Oklahoma City. Thus, analysis of the team would be skewed by issues regarding a team

moving halfway across the country. For example, team revenues in its first year in

Oklahoma City are driven by factors from both locations. Second, in my data regarding

every NBA players‘ individual statistics, I threw out data on all the players that were traded

in a given season. In determining player value through statistics, it would be too difficult to

determine which statistics went to which team. Furthermore, this data is altered by the

externalities of a player switching franchises mid-season.

Methodology

The variables in the model to predict NBA team wins were fairly straightforward to

come up with. General basketball statistics are readily available and are believed to be good

predictors of team success. Specifically, if conventional wisdom about the game of

basketball holds true, each variable generated should have a statistically significant positive

or negative effect on NBA win generation:

Field Goals Made (FGM): Increasing the number of field goals made is the best way to

generate more wins. Each field goal is worth two points and, according to Basketball-

Reference.com, the typical NBA team produces between 90 and 100 points per game. FGM

should have a positive coefficient in the regression for wins.

Field Goals Attempted (FGA): As a team takes more field goals, it should generate more

points in the long run. The average NBA team attempts about 80 field goals per



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game. Shooting increased amounts of field goals should generate more points over the length

of the game--leading to more wins. Furthermore, increased field goal attempts is a sign that a

team is controlling more of the ball, leading to fewer opportunities for the opposing team to

generate points. Therefore, FGA should have a positive coefficient.

Field Goal Percentage (FG%): Increasing a team‘s percentage of field goal shots made will

lead to more points. NBA teams made approximately 45.7% of their field goals over the time

period studied. Efficient teams with higher field goal percentages should score more

frequently, leading to more wins. Theoretically, FG% will have a positive coefficient.

Three-Point Shots Made (3PM): In the National Basketball Association, there is an arc on

the floor with a radius away from the basket of 23 feet 9 inches (7.24 meters). Shots made

behind this line are worth three points as opposed to two points for shots inside the

arc. Because these shots are 50% more valuable than made field goals, this variable should

have a positive coefficient that is larger than FGM.

Three-Point Shots Attempted (3PA): Teams that attempt more three-point shots should

score more points and win more games. NBA teams over this time period made about 36%

of these valuable shots. Because the expected value of three-point shots is higher than that of

field goals, NBA teams have started shooting more and more three-pointers. Furthermore,

missed three point shots lead to a higher frequency of offensive rebounds than missed field

goals, because the ball bounces further off the rim leading to more randomness in where it

lands. This gives the offensive team another chance to score points. Though the impact of

these additional rebounds should be accounted for in the offensive rebound variable below,

3PA should still have a positive coefficient.

Free Throws Made (FTM): Free throws (also known as foul shots) are unopposed shots

from a distance of 15 feet (4.57 meters). These shots occur after fouls and are worth one

point apiece. Over the studied time period, NBA teams made approximately 76% of their



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free throws. Top players like Steve Nash, Kobe Bryant, and Ray Allen routinely make over

90% of their free throws. Because it has the lowest expected value of the three ways to

generate points in the NBA, FTM should have the lowest positive coefficient.

Free Throws Attempted (FTA): The more a team gets fouled, the more unopposed free

throws it gets to attempt. NBA teams averaged about 26 free throws attempted per game

over the six seasons. Increased free throws attempted is a sign that a team is controlling the

flow of the game, because they are more likely to occur when the team is shooting from

advantageous positions that force the defense to commit fouls in order to stop them. These

shots are the easiest way to quickly generate points in an NBA game because they are

unopposed and the clock is stopped. FTA should have a positive coefficient.

Offensive Rebounds (ORB): Offensive rebounds might be the most underrated statistic in

generating more wins in the NBA. Teams grab offensive rebounds on about 30% of all shot

attempts. These rebounds are a retention of possession for the offensive team--more or less,

a low-percentage pass. Offensive rebounds serve to physically wear down defenses because

the benefitting team has the option to set up another offensive play. Often times, offensive

rebounds are claimed at such an opportune spot on the floor that the offensive player can

attempt a field goal within seconds of obtaining the ball. This leads to high-percentage shots

and more points generated. NBA teams generated about 10 offensive rebounds per game

over the six studied seasons. ORB should have a positive coefficient in this regression.

Defensive Rebounds (DRB): Defensive rebounds are just the opposite of offensive

rebounds--they serve as a way for the defensive team to reclaim the ball and start their

offense. Because total rebounds are a zero-sum variable, increased defensive rebounds leads

to fewer offensive rebounds for the opposing team. NBA teams over this time period had

about 30 defensive rebounds per game. They prevent defenses from getting worn down and



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provide more opportunities for teams to generate points on offense. DRB should have a

positive coefficient in wins generated.

Assists (AST): Assists are slightly different than any of my other variables because they

don‘t specifically generate or prevent points. Instead, they somewhat capture the intangibles

of a team. Increased assists are a sign of a better ―team‖ mentality. They show that a team is

capable of completing good passes and finding open players in opportune locations. Only the

pass directly before the made basket can count as an assist, so there cannot be multiple assists

per basket. The average NBA team over these six seasons generated about 20 assists per

game. AST should have a positive coefficient.

Steals (STL): Steals are the best way for a defensive team to quickly gain possession of the

ball. They occur when a team generates a turnover through its aggressive defensive

play. Because they are relatively uncommon (teams only generate about 7 steals per game)

they are extremely valuable. Steals lead to more opportunities for a team to generate points

on offense. The variable STL should have a positive coefficient on team wins.

Blocks (BLK): Blocks are similar to steals in that they are a way for a defensive team to gain

possession of the ball before the opposing team has a chance to attempt a shot. Blocks are

even more uncommon (only about 5 generated per team in each game) but often, blocked

shots are deflected out of bounds or back to the opposing team. While it is tough to

statistically analyze the psychological intimidation caused by a powerful blocked shot that

sends the ball 20 feet out of bounds, blocked shots that end up back in the shooting teams‘

hands aren‘t very valuable to the defensive team. The variable BLK should have a positive

coefficient.

Turnovers (TOV): Turnovers occur in basketball when a team gives up possession of the

ball to the opposing team. They happen most often through steals, errant passes, or players

dribbling out of bounds. Turnovers are extremely detrimental for NBA teams. They provide



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opposing teams more opportunities to score and generate points. TOV should have a

negative coefficient on team wins.

Personal Fouls (PF): Personal fouls are breaches of the rules that involve illegal contact with

an opposing player. Most personal fouls in the NBA lead to free throw shots for the

opposing team. If a player accumulates six personal fouls in one game, he is

ejected. Personal fouls are a detriment to NBA teams because they lead to ejected players

and unopposed shots for the opposing team. PF should have a negative coefficient.

There are many other statistics that could have been used in the model to predict NBA

team wins. Advanced statistics like Strength of Schedule, Offensive and Defensive

Efficiencies, Free Throws Per Field Goal Attempt are extremely interesting to look at and

analyze but were too detailed to include in my regression. This regression is kept to the

simplest and most traditional NBA statistics--stats that are the building blocks for more

advanced statistics. Including the advanced statistics could have led to multicollinearity

problems in my regression. While, due to the nature of basketball statistics, I do have some

multicollinearity in my regressions, it would have been made much worse if I included

advanced statistics. Travel distance was not included following Nutting‘s 2010 research.

Predicting what variables drive team revenues is slightly more difficult to do. There

are many factors that go into the business side of sports franchises that are difficult to

measure. However, statistics regarding stadiums, size of the cities, and team success are

good predictors of how much revenue individual NBA teams will generate. Specifically, the

following variables should have a statistically significant and positive or negative coefficient

on team revenues:

Wins: Simply put, fans want to attend games in which the home teams are

successful. Rascher (1999) finds that leagues profit-maximize when the probably of the

home team winning an individual game is 0.6. Individual teams are likely to bring in large



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amounts of money when their success rate is much higher. Beyond ticket sales, fans are

more likely to buy jerseys, hats, shirts, and other memorabilia to support successful

teams. Wildly successful teams, like the New York Yankees, sell merchandise to all four

corners of the globe. Teams that win games should see an increase in revenues--this

coefficient should have a positive coefficient in the regression.

Wins (-1): This variable represents lagged wins--wins the team generated in the previous

season. Often times, ―bandwagon fans‖ only start supporting a team when it becomes

successful. They‘ll start spending money on season tickets, memorabilia, and jerseys

following a successful season. However, this money might not r each the franchise‘s bottom

line until the next year. Therefore, previous year wins could have an impact on

revenues. Wins (-1) should have a positive coefficient.

Playoff Wins: In the NBA, 16 teams (eight from each conference) are selected to participate

in the end-of-season playoffs. The format is four series that are seven games each. Playoff

wins, therefore, are on a scale of zero to sixteen--to claim the NBA Championship, a team

must generate 16 wins. Playoff wins might be a stronger indicator of team revenues than

regular season wins because there are many fans who only pay close attention when the

playoffs begin. Because of the nature of the NBA regular season (82 games per team

stretched over six months), it can be easier for fans to start watching and spending money

when the two-month-long playoffs start. Playoff wins are also an indicator of team success,

and it can be hypothesized that fans spend more money on successful teams. Playoff Wins

should be a variable with a positive coefficient in this regression

Playoff Wins (-1): Similar to Wins (-1), this variable represents lagged playoff wins. This

variable will also pick up those ―fair weather fans‖ who only start supporting a franchise

when it becomes successful. Furthermore, the variable will account for the time difference in



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when fans spend money and when it reaches the franchise‘s bottom line. Playoff Wins (-1)

should have a positive coefficient.

Championships 20: Berri, Schmidt, and Brook (2004) first use this variable as a way to

weigh team championships. This variable accounts for all championships a team has claimed

in the previous 20 seasons. Winning the title the previous year gives a value of 20, winning it

two seasons previous is a value of 19, all the way down to winning it 20 seasons before, for a

value of 1. The variable is intended to pick up old championships but not weigh them as

strongly. Teams see surges in revenues in the immediate years following

championships. While the spending certainly dies down over time, older championships still

need to be taken into account. The variable Championships 20 should have a large positive

effect on team revenues.

Number of All-Star Starters: Midway through each season, the NBA holds an All-Star

game featuring the best players from that year. The game is informal and entertaining, more

of a show for the fans than a competitive game. Being selected to play in the game is a

tremendous honor, but being a starter is an even bigger reward. Fans vote on which players

they want to start the game, making it an excellent measure of consumer demand in the

NBA. It can be hypothesized that fans will give more money to franchises that employ

players they want to see play through jersey sales and ticket revenue. Number of All-Star

Starters should have a positive coefficient in this regression.

Stadium Age: Even though Quinn, Bursik, Borick, and Raethz (2003) find that the age of

stadiums doesn‘t lead to more team success, it can be argued that it leads to more

revenues. Fringe fans will be more likely to buy tickets to watch games at brand new, ―state-

of-the-art‖ arenas. While there is something to be said for watching a game in a historical

venue, new venues will theoretically generate more revenues for franchises. As stadiums get

older, fans might be less inclined to attend games. Furthermore, modern stadiums are built to



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maximize profits. They feature numerous luxury suites and various amenities to make the

viewing experience as comfortable as possible for fans. Stadium Age should have a negative

coefficient in this regression.

Stadium Capacity: NBA arenas come in all different shapes and sizes. The largest stadium

(Detroit Pistons) seats about 5,000 more fans than the smallest (New Orleans). Increased

stadium capacity creates the potential for more ticket sales and more fans inside the

arena. These additional fans can lead to more spending on jerseys, hats, and shirts, as well as

food and drinks. Evidence of this revenue potential are the countless news stories where

owners look for ways to fit more fans inside stadiums, and if they can‘t do that, just go out

and build new stadiums. Stadium Capacity should have a positive coefficient.

Size of City: It can be theorized that teams in larger cities will generate more revenues. Most

of this money will come from larger TV contracts. In the NBA, teams equally share moneys

from national TV contracts (amounting to roughly $30 million per season for each

team). However, the league allows each team to negotiate TV rights in its local metropolitan

area. The size of the city can make an incredible difference on the size of this

contract. Small market teams (Memphis, Portland, Sacramento, for example) have local TV

contracts worth about $8 million per season. The Los Angeles Lakers recently signed a deal

which is rumored to be valued at over $50 million per season. Simply put, city population

has a tremendous impact on franchise revenues. Size of City should have a positive

coefficient in the regression.

Thinking of predictors for individual franchise revenues was slightly more difficult

than team wins. After the most recent NBA lockout, revenue sharing became more

prominent throughout the league. Revenue sharing is a way to solve competitive imbalance,

something the NBA desperately needs, especially after Berri, Brook, Frick, Fenn, and

Vincente-Mayoral found in 2005 that the NBA has the lowest level of competitive balance of



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any sports league throughout the world. The new revenue sharing model is set to be fully

phased in by the 2013/2014 season. Small market teams can receive up to $16 million every

season from wealthier teams through the program. This shifting of moneys makes it hard to

generate variables that drive team revenues. Adding a dummy variable if a team was directly

competing with another franchise in the city could have been useful, but likely would not

hold enough statistical weight due to basketball being a team sport. Following Berri,

Schmidt, and Brook (2004), adding dummy variables for franchises that employ specific

superstars (like LeBron James, Kobe Bryant, Tim Duncan, or Kevin Garnett) could be

beneficial but this data is captured in the variable Number of All-Star Starters

Statistical Models

Both team wins and team revenues were best modeled through multi-linear

regressions using the variables previously listed. In the model to predict team revenues, I

began with nine independent variables: Wins, Wins (-1), Playoff Wins, Playoff Wins (-1),

Championships 20, Number of All-Star Starters, Stadium Age, Stadium Capacity, and Size of

City. I used Forbes‘ data for team revenues for the years 2006-2011 as my dependent

variable.

It was somewhat difficult to account for the timing of wins and revenues. Forbes‘

information is for the given calendar year. However, NBA seasons begin in September and

end in June. I had to take this into account when I aligned my data to run the

regressions. For example, in my data, 2011 Team Revenues aligns with 2011/2012 Wins and

Playoff Wins, 2010/2011 Wins (-1) and Playoff Wins (-1). I then worked backwards to make

sure the other six seasons matched up in the same manner.

My initial regression with nine independent variables had an r-squared of 0.676 and

six variables statistically significant to the 5%. To lower the standard error and reduce



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multicollinearity issues, I started a process of backwards elimination of independent

variables. I first eliminated Wins because it had the highest p-value. I assumed that this was

the case because current season wins haven‘t had enough time to affect a franchise‘s bottom

line, making the variable not significant.

The next regression had eight independent variables predicting the same dependent

variable, Team Revenues. This model had an r-squared of 0.676 and seven out of eight

statistically significant variables. Through backwards elimination, I removed Playoff Wins

because of its high p-value. This can be interpreted in a similar way to Wins — revenues from

these two variables simply do not have enough time to affect Team Revenues.

After removing Playoff Wins, I ran the regression once more. This final regression

had the lowest standard error (17.885) and an r-squared of 0.676. All seven of the variables

were statistically significant to the 5% and five variables to the 1%. Results from this

regression are as follows:

*Significant to the 1% Table 4

Table 5



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Most of the coefficients in this regression came out as I predicted. Wins (-1), Playoff

Wins (-1), Championships 20, Number of All-Star Starters, Stadium Capacity, and Size of

City all had coefficient signs that I expected. I found that stadium age was significant to the

1% but in the opposite direction of what I predicted; increased age of the stadium led to

increased revenues. This can be explained by stadiums like Madison Square Garden and the

Staples Center — two older stadiums with tremendous history inside of them. Fans might be

more willing to spend money to watch games played in these historically-rich venues.

I was also shocked at the size of some of the coefficients, especially given that the

average team generated revenues of $120 million per year of this time period. Teams see an

increase in revenues of over $8 million if they won the NBA Championship the previous

season. Increasing stadium size by 10,000 increases revenues nearly $34 million. Most

shocking was the coefficient for Number of All-Star Starters. Having a player start in the

All-Star Game increases a franchise‘s revenues by over $8 million (a 6.5% increase on

average!). Often times, the player sees none of that money, despite the fact that being an All-

Star Starter is largely an individual achievement.

The multi-linear regression to predict NBA Wins began with 14 independent

variables and ended up, through backwards elimination, with 11. The initial variables I

included were Field Goals Made, Field Goals Attempted, Field Goal Percentage, 3-Point

Shots Made, 3-Point Shots Attempted, Free Throws Made, Free Throws Attempted,

Offensive Rebounds, Defensive Rebounds, Assists, Steals, Blocks, Turnovers, and Personal

Fouls. The regression featuring all of these variables had a standard error of 4.772 and an r-

squared of 0.873. Nine of the fourteen variables were significant to the 5% and seven to the

1%. Through backwards elimination, I eliminated Field Goal Percentage, Blocks, and 3-

Point Shots Attempted before coming to my final regression. This regression had a standard



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error of 4.7434 and an r-squared of 0.872. Every variable was significant to the 5% and all

but one to the 1%. Results from this regression are as follows:

*Significant to the 1% Table 6

Table 7 Like in the regression to predict team revenues, most of these coefficients came out as

predicted. I was a bit irked by two coefficients: for Field Goal Attempts and Free Throw

Attempts. Both of these were negative, meaning that as attempts increase total team wins

will decrease. Intuitively, this doesn‘t make sense because more attempts give the team more

chances to score points. Field Goals Made and Free Throws Made are also included in the

regression, however, and each Field Goal Made increases Field Goal Attempts by one (and

same for Free Throws Made). The interaction between these two variables is likely what is

causing the negative coefficients on FGA and FTA.

It also helps to think about the alternative possibilities a player has when trying to

interpret these negative coefficients. For Field Goal Attempts, it might be the case that NBA



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players take shots from sub-optimal places on the court. These shots are less likely to go in

and generate points and wins. Players might be better off waiting for an open shot from an

opportune location. For Free Throw Attempts, the negative coefficient might also be

explained by the low expected value of this shot. NBA players probably miss more free

throws than they should and the shot is only worth one point. This variable suggests that

NBA teams might be better off avoiding free throw shots (or practicing them more often to

increase the expected value of each shot) because the alternative to free throws is most likely

a field goal attempt, which has a higher expected value based on the probability a player

makes each of these differently-scored shots.

As predicted, rebounds have a much larger impact on the outcome of games than the

average fan might think. According to the model, every increase in offensive rebounds by 16

leads to one more win. An increase in defensive rebounds by 16 also leads to an increase in

wins by one. Turnovers and steals also have large impacts. An increase in turnovers by 18

leads to one fewer win and an increase in steals by 17 leads to one more win. Considering

that my model for team revenues found that every increase in wins by one leads to about

$300,000 for the team, NBA franchises that want to profit-maximize should invest in players

that can either avoid turnovers or generate steals and rebounds.

This model does an excellent job at predicting team wins:



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Table 8 For the 2008/2009 season, the average difference between actual wins and predicted

wins through my model was less than three. Overall for the six seasons, the average

difference was 3.6 games. The model does an excellent job predicting the number of wins

most teams will generate. There are only a couple teams that significantly over-performed in

2008/2009 (Chicago and San Antonio) and a lot of teams that severely underperformed

(Detroit, Houston, Minnesota, and Washington).

I took the results from both of these models to predict individual players‘ impacts on

NBA teams over the six seasons. I gathered every players‘ season total statistics and plugged

that data into my regression predicting NBA Wins. This allowed me to compute how many

wins an individual player contributed to his franchise in a given year. Running this number



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through my regression for NBA Revenue, I computed how much revenue, ceteris paribus, an

individual player generated in a given season. Average wins and revenue generated per NBA

player per season over the six seasons from 2006/2007 to 2011/2012 are as follows:

Table 9

Statistical Findings

THE CASE FOR GOOD CENTERS

One of the most interesting findings of my data is the importance of centers in the

NBA. Center is the position name for the post player--typically, the tallest player on the

team. A typical NBA center is around seven feet tall. Centers position themselves close to

the basket to defend and score points.

On average, NBA centers produce 23 wins per season and generate $7.2 million in

revenues. This is roughly 45% more than the average player produces. Over 70% of centers

accounted for more than 16.02 wins, the NBA average over this time period. Of the top 23

seasons in terms of total wins generated by an individual player, 21 were from centers. Only

one season from a center resulted in a negative impact on the team (evidenced by a negative

number of total wins generated): Andrea Bargnani‘s 2010/2011 campaign. This can be

explained by his relatively low levels of rebound production and the fact that this was his first

season as a starter.

Why are centers such valuable players? One of the main reasons is because of their

rebounding. The nature of the position is being close to the basket and this is where the

majority of missed shots land. Furthermore, centers are the traditionally the tallest players on



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the court, making them the most likely to be able to claim rebounds at high points. Because

of their size and positioning, centers claim the vast majority of both offensive and defensive

rebounds, two vitally important statistics in generating wins in the NBA. Recall that,

according to the regression predicting NBA team wins, an increase in offensive or defensive

rebounds by 16 generates an additional win. Given this variable, it makes sense that centers

are extremely valuable in terms of wins generated.

Centers are also valuable because of their efficiencies. In my regression to predict

team wins, variables representing field goals made and field goals attempted were both

included. Because all made field goals are also included in attempted field goals, an addition

to FGA that doesn‘t increase FGM implies a missed shot. Because of this, FGA has a

negative coefficient. Centers miss relatively fewer field goals than the average NBA

player. The average NBA player made 44% of his field goals over this time period. The

average center made nearly 49% of his field goals. Three out of four centers had a better

field goal percentage than the NBA average. Again, this is the case because of the typical

positioning of centers. They are stationed close to the basket the majority of the

time. Centers are most likely to generate dunks, layups, and short-range field goals — all of

which are high-percentage shots. Most centers aren‘t taking long-range jump shots like

inefficient NBA players such as Jason Kidd, Kemba Walker, and Baron Davis do. The fact

that centers take relatively large quantities of high-percentage shots increases their respective

values tremendously.

The last reason centers are extremely valuable players is because they produce

relatively few numbers of turnovers. Recall that the coefficient for turnovers was negative in

the regression for NBA Wins. This implies that each turnover is detrimental — an increase in

turnovers makes a team statistically less likely to generate high quantities of wins. Centers

generate fewer turnovers than any other position. Two-thirds of centers produced fewer



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turnovers than the NBA average over this time period. This possibly occurs because of the

physical nature of an average center. Centers are typically some of the strongest players on

the team, making them able to protect and keep the ball away from the opposing team.

Another potential explanation is that centers possess the ball for less time during the game

than other positions — such as guards — giving them fewer opportunities to turn the ball over.

Based on my statistics, NBA centers should be paid significantly more than players in

any other position. However, in the typical NBA season, only two or three of the top ten

best-paid players across the league are centers. The difference in wins generated by centers

and their relatively low compensation can be accounted for by the overall business of

basketball. On-the-court performance is only one factor that is taken into consideration

during contract negotiations between NBA general managers and players. Marketability of

players is arguably more important to NBA owners than player performance on the

court. With some exceptions, centers are not the most marketable players. An average center

typically doesn‘t sign shoe deals while being the face of his franchise. He doesn‘t play

‗sexy‘ basketball by completing acrobatic dunks and picture-perfect jump shots; he grinds out

statistics through physical, rough play. He isn‘t as big of a headline-grabber. Because of

this, centers‘ compensation levels are likely lower than their on the court statistics indicate

they should be.

THE CASE FOR SHOOTING EFFICIENCY

Shooting efficiency (Field Goals Made divided by Field Goals Attempted) is one of

the most important predictors of wins generated by an individual player. To take a closer

look at the field goal efficiencies of individual NBA players, I reduced the dataset to only

players that attempted more than the average number of field goals in a season. In terms of

highest numbers of field goals attempted by an individual player in a season, fourteen of the



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fifteen players had field goal percentages above average. Only three of those players (Vince

Carter, Monta Ellis, and Gilbert Arenas) were non-superstars. The rest were traditional

superstars — Kobe Bryant, Dwyane Wade, LeBron James, Dirk Nowitzki, Derrick Rose, and

Allen Iverson. All of the traditional superstars had field goal percentages above the league

average. Upon initial review of my data, players like Kobe Bryant, Dwyane Wade, and

LeBron James might be shooting too many field goals. Because FGA has a negative

coefficient (due to its relationship with FGM), shooting too many field goals can be

detrimental to the success of the team over the course of a season. However the high number

of attempted field goals from James, Bryant, and Wade is completely justified because they

make a higher percentage of their field goals than average.

Inefficient field goal shooting does not necessarily guarantee a player will be a

detriment to his franchise. The two least-efficient seasons, Quentin Richardson in 2007/2008

and Jason Kidd in 2010/2011, both resulted in positive numbers of individual wins

generated. Both players attempted more field goals than the NBA average, made less than

37% of the shots they attempted, and generated more wins than overall average and position

average. Richardson generated $5.2 million in revenue for the New York Knicks, and Kidd

generated $7.7 million for the Dallas Mavericks. These two players made up for their

inefficient shooting in different ways. That season, Jason Kidd had three times as many

steals and successful three point shots as the average NBA player. He grabbed twice as many

defensive rebounds, despite being a point guard. Most impressive, Kidd was a full two

standard deviations above the NBA mean in terms of assists. He generated nearly six times

as many assists as the average NBA player. Richardson made up for his lack of field goal

efficiency through three-point shots and rebounding. That season, he made twice as many

three-point shots as the average NBA player. He generated 56% more defensive rebounds

and turned the ball over fewer times that average.



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While inefficient field goal shooting doesn‘t guarantee a player will be a detriment to

his franchise, it is certainly a good indicator. The coefficients of the regression for NBA

team wins show that, ceteris paribus, an increase in FGM by 20 generates one additional win

and increase in FGA by 18 generates one fewer win. Missed field goals, as indicated by low

field goal shooting percentages, increase FGA without affecting FGM. Of individual

players‘ 20 most inefficient seasons in terms of field goal percentage, 17 produced fewer than

the average amount of wins for any player. Twelve of those twenty players generated fewer

wins than the average for their respective positions. Two of the players generated negative

numbers of wins — a sign that they were a significant detriment to their teams. On the other

end of the spectrum, in the 20 most efficient field goal shooting seasons, only one player

generated wins below average. That player was Shaquille O‘Neal in 2006/2007, who made

nearly 60% of his field goals but had an atrocious free throw percentage and generated

relatively low amounts of assists and steals.

If NBA salaries were solely based off on-the-court performance, inefficient players

like Kemba Walker, Brandon Jennings, and Adam Morrison would be compensated

significantly less than average. Efficient players like Nene, Tyson Chandler, and Dwight

Howard would be rewarded handsomely. One argument for why players are paid the way

that they are is that the majority of inefficient shooters in the reduced dataset are point guards

and shooting guards. Players in these positions might not be expected to generate points in

the most efficient way possible. It can be argued that the main job of the point guard is to

pass the ball to teammates in advantageous positions so they can generate the

points. Shooting guards can be expected to make higher percentage of three-point shots and

generate points through that fashion. Point guards and shooting guards tend to be more

marketable players — the types of players who are headline grabbers, are shoe deal signers,

and are the faces of franchises. The majority of efficient shooters are less-marketable



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centers. The juxtaposition between field goal efficiency and the marketability of the players

that typically achieve it helps to explain the differences in compensation.

THE CASE FOR LEBRON JAMES

LeBron James, is the best basketball player in the world right now. In the 2011/2012

season, he was above average in every statistic except for personal fouls. He generated

nearly four times as many free throws and three times as many assists and steals as the

average player. He also made an extremely high 53% of his shots from the field, nearly ten

percentage points above average. That season, James‘ salary was $17,545,000. This season,

he is making 56% of his shots from the field while playing 80% of the game and defending

the opposing teams‘ best player every game.

However, over the six studied seasons, LeBron James generated fewer wins than

average in each and every one. He outperformed his position in terms of wins generated in

only one season. On average, he generated $2.7 million for his franchise each year. But, in

all six seasons, he generated less revenue than the average NBA player did. James‘ on-the-

court performance over the six seasons accounts for a total of $16.5 million of added

revenues for his franchises (Cleveland and Miami). But, he was compensated roughly this

amount in each of those seasons.

LeBron James‘ compensation can be justified in a myriad of ways. In regards to his

performance on the court, he started in the NBA All-Star game in each of the six seasons,

generating $8.33 million in additional revenues for his franchise each time. His teams win an

average of 50 games per season, each of which generate an additional $300,000 in

revenues. LeBron James‘ presence makes a franchise significantly more likely to generate

playoff wins ($1.2 million each) and NBA championships ($36.2 million over the five years

following).



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Off the court, LeBron James‘ compensation can be justified through his extreme

marketability. He‘s one of most famous players in the NBA and has sponsorship deals with

Nike, McDonalds, Coca-Cola, State Farm, and Dunkin‘ Donuts. The Miami Heat‘s cable

ratings jumped 33% after LeBron James and Chris Bosh‘s additions to the roster. In 2009

(James‘ last year in Cleveland), Miami‘s franchise value was $364 million and Cleveland‘s

was $476 million. In 2013, after James left Cleveland and joined Miami, Miami‘s franchise

value is $625 million and Cleveland‘s is $434 million. Despite playing in the 22nd largest

city in the NBA, LeBron James‘ jersey sold more than any other NBA player‘s in 2011 and

Miami was number four on the 2011/2012 list of most popular NBA team

merchandise. James‘ presence in Miami helped his franchise negotiate a new local TV

contract that will generate over four times as much revenue as the old contract. While

LeBron‘s specific individual offensive statistics might point to the fact that he is

overcompensated, other factors seem to be behind his massive salary.

THE CASE FOR TYSON CHANDLER

Tyson Chandler might be one of the most valuable players in the NBA. Two of the

top three seasons (and four of the top 23) in terms of wins generated by an individual player

belong to him. In all six of the studied seasons, Chandler generated wins and revenues well

above both overall average and position average. His teams win an average of 40 wins per

season and he even played a significant role in Dallas‘ 2011 NBA Championship.

Tyson Chandler‘s superb win production can be attributed to his physique and

position. Chandler is seven feet one inch tall and weighs approximately 240 pounds. His

height and size allow him to claim large numbers of rebounds — over the six seasons, he

averaged nearly four times as many offensive rebounds and three times as many defensive

rebounds as the average NBA player. He doesn‘t attempt many field goals (only two of the



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six seasons were above the league average) but makes over 60% of them, fifteen percentage

points above the NBA average. Despite his incredible on the court performance, Tyson

Chandler is not one of the top-compensated players in the league. His compensation over the

six studied seasons is as follows:

Table 10 Over those same six seasons, Tyson Chandler generated a total of $81.3 million for

his franchises (the New Orleans Hornets, the Dallas Mavericks and the New York

Knicks). He was compensated a total of $68.4 million (84%) and was, on average, the 41st

best-paid player in the league over that time span. Tyson Chandler is one of the most

underpaid and underrated players in the NBA today. Not only does he generate large

numbers of wins, he played a major role in Dallas‘ 2011 NBA Championship (worth a

predicted total of $36.2 million in 2012-2017). His low compensation can be attributed to his

affinity for jumping from franchise to franchise (four different teams over the six seasons)

and his lack of marketability. He isn‘t the face of his team and doesn‘t have any major

sponsorships. Simply put, despite being underpaid through relatively low compensation,

Tyson Chandler may be one of the most valuable players in the NBA today.

Conclusion

This research can be of tremendous importance to franchises in the National

Basketball Association. The regressions provide the framework for teams looking to generate

large numbers of wins and revenues. To produce wins, NBA teams should seek to rebound



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the ball as much as possible. Franchises should also pursue high-percentage shots from

optimal places on the court to increase their field goal efficiencies. Lastly, they should look

to avoid turnovers and steals, as these statistics are extremely detrimental to team success.

To increase revenues, unsurprisingly, teams need to win games and championships.

However, arena and city sizes also play integral roles. Franchises should do whatever they

can to get their players in the All-Star game so they can enjoy the additional associated

revenues. Teams should understand that playoff games are more lucrative than regular

season games and know that profit-maximizing NBA teams might be better off playing

partially-injured players to make a late push to earn a playoff berth. Lastly, teams should

think twice before building new arenas to increase revenues. For players, this research is also

of importance. Agents can use the regressions to estimate their players‘ value. This can aide

in negotiations so players are paid closer to their marginal revenue products.

Without a doubt, there is additional research that can be done in the field of marginal

revenue products of professional athletes. Any further research that finds additional variables

to increase the r-squared values of each regression would provide a more accurate assessment

of player value. Furthermore, it would be interesting to study how different league rules

affect player compensation. Many professional football leagues throughout the world do not

have as strict of rules on salaries and team payrolls. Theoretically, research in this field

should find that professional football players are paid much closer to their marginal revenue

products. Specifically with the NBA, further research will want to look at how revenue

sharing in the league will affect competitive balance and player compensation.

Professional athletes in the NBA never will (nor should they) receive compensation

equal to their marginal revenue products. As pointed out by Berri, Brook, Frick, Fenn, and

Vicente-Mayoral, the NBA already has the most competitive imbalance of any professional

sports league in the world Eliminating mechanisms that create parity, solely to equate player



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salaries with marginal revenue products, would be a disaster. If that happened, top players

would benefit through increased compensation but league interest would deteriorate because

franchises like the Boston Celtics, the Miami Heat, and the Los Angeles Lakers would win

the championship every season. That wouldn‘t be good for fans, owners, or the league

overall.

The initial quotes which state LeBron James is severely underpaid probably hold

some warrant. However, LeBron James isn‘t the only player who can complain; many

players see large differences between their on-the-court values and their compensation levels.

At the end of the day, the National Basketball Association is a profit-maximizing

organization. Though labor market rigidities like salary caps, payroll limits, and blocked

trades may seem unfair to players that receive lower levels of compensation, they benefit the

league as a whole. And, for a sport that has the highest levels of competitive imbalance of

any sport throughout the world, these rigidities may be a major reason the National

Basketball Association has stayed in business for nearly 70 years.



52 | P a g e

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