Crime and Punishment in the National Basketball Association
This chapter investigates the overlap between National Basketball Association (NBA) referees, the league’s on-court rule enforcers, and the impact of player violence and aggression on individual salary, team wins, and team revenue. The authors’ meta-analysis highlights emerging research on the role of referees in regulating the sport and describes systematic referee bias in connection with race, league profits, and social pressure in the literature. More narrowly, and in contrast to several high-profile media reports, the authors unearth little to no evidence of NBA referees being biased against specific players, coaches, or team owners. With personal fouls as a proxy for player-level aggression, the analysis finds that players who commit more fouls earn lower salaries and hurt their respective team’s chances of winning. Using the high-profile example of Shaquille O’Neal, the authors also demonstrate how O’Neal’s inability to make free throws had a detrimental impact on how many wins he helped produce for his team and a negative effect on his team’s revenue. Such results reveal the overlapping tension between the NBA’s player discipline protocol, efforts toward referee consistency, and certain marketing and public relation goals the league may have.
My major concern about it is that it’s wrong.
David Stern (AP 2007a)
Predictably, the NBA has launched a PR offensive defending its officials’ work and saying its own study, which looked at individual refs who made a call rather than the results of a three-man crew, showed no bias by the officials.
In addition to the NBA’s response and internal counter-study, criticism of the Price–Wolfers research similarly rained down from others. NBA player Chris Duhon said “I don’t think there’s any prejudice or racial stereotype” (AP 2007b). LeBron James simply said “It’s stupid” (AP 2007b). Noted journalists wrote in similar tones. Bob Ryan of the Boston Globe described the study as “offline” and a “needless distraction” (Ryan 2007). Houston Chronicle columnist Jonathan Feigen posited that “it is easy to see that the study was full of holes and so lacking in perspective that it seemed as if the analysis was done by two accountants who had no idea what they were talking about” (Feigen 2007). David Aldridge of the Philadelphia Inquirer opined that the study “has many gray areas” (Aldridge 2007). The NBA’s own statistical consultant and an academic economist also interjected. Fluhr (2007) stated: “The conclusions drawn in the Price/Wolfers paper…are based on flawed statistics and logic.” Zimbalist (2007) concurred: “Wolfers/Price not only use an incomplete database, but they provide insufficient justification for the modeling they present.”
Much like during this referee scandal, the NBA conducted an internal investigation, and then pronounced the matter settled in their favor without taking the step of letting the public see what the people in the league office know. The only problem was that the NBA was evidently not working with the best facts available, and in the final analysis was almost certainly wrong all along. That notion is supported by countless economists who have vouched for Wolfers’ work, and even, apparently, the NBA’s own secretive internal study, which was eventually handed over to Wolfers and media outlets” (Abbott 2008).
I believe [Price and Wolfers have] the better points. [Their] study focused on the interactions of the race of the referee and the race of the player. The NBA was more concerned with the number of fouls called on black players and comparisons with the number of fouls called on white players. It is remarkable how [Price and Wolfers were] able to use the NBA’s own data set and show that it supported what [they] said at the beginning (Munson 2007).
There was also some early treatment of the NBA’s counter-study. Bialik (2007b) questioned the NBA’s research on the basis that it: (1) confirmed Price and Wolfers in the context of one narrow subset of players and (2) omitted players who were not called for any fouls. Regarding the former point, Bialik (2007a) quoted University of California-Irvine professor Hal Stern as saying that the NBA’s study “can’t be said to disprove the Price–Wolfers analysis.” Pertaining to the latter issue, Columbia University professor Andrew Gelman described the NBA’s study as “suspect” given its omission of players with no fouls (Bialik 2007a).
When the New York Times published the preliminary results of research about referees and race…the top brass at the NBA were livid. Stern and others at the NBA lashed out in spectacular fashion. Three years later, emotions have mellowed. The NBA’s position, meanwhile, is looking weaker than ever. The NBA created a credibility contest, and lost.
The visceral response to the Price–Wolfers research, more so than any other in recent memory, highlighted the sometimes tenuous relationship between independent academic research and league policy/public relations objectives. The same tension is revealed in the competing, and occasionally mutually exclusive, goals of the NBA front office. The league looks to maximize profit while also maintaining a socially acceptable level of on-court violence and aggression. More specifically, the entire episode provides an insightful look into how the league’s referees regulate the game and an anecdotal example of how rules are enforced and punishment is meted out. Detecting referee-specific bias, like the analysis of the optimal levels of violence and aggression in sporting contests, is an empirical challenge (Persico 2009). In the remainder of this chapter, we address both topics, answering the following questions: (1) If NBA referees are biased, how is such bias manifested? (2) Does aggressive play and on-court violence, as measured by personal fouls, contribute to player salary, team wins, and league revenue?
Are NBA Referees Biased?
NBA referees are regulators. Basketball officials are responsible for enforcing the game’s rules. On-court crime and punishment is specifically within the referees’ jurisdiction. Alker et al. (1973) posit that consistent referees are superior referees. Bias, whether overt or subliminal, would almost certainly cause inconsistent officiating. All current NBA referees are employed by the league and are members of the National Basketball Referees Association (NBRA), a government-recognized labor union. The NBA–NBRA collective bargaining agreement grants the commissioner broad powers to direct the action of his employee referees. More generally, the commissioner has near-plenary power in connection with player discipline for both on-court and off-court conduct that is detrimental or prejudicial to the league (Kim and Parlow 2009; Showalter 2007; Bard and Kurlantzick 2002).
The NBA has, at times, outwardly directed or subtly nudged its referees. In 2006, the NBA enacted a “Respect for the Game” rule aimed at reducing excessive levels of complaining by players through the imposition of more technical fouls by the referees. Enforcement of the rule was relaxed from 2007 to 2010 likely due to the lingering referee gambling scandal. However, the rule was renewed for the 2010–2011 season (Zillgitt 2010). Such league-generated directives toward its referees are consistent with broader mandates unrelated to on-court officials. Examples include the NBA’s rookie wage scale, player dress code, age eligibility rule, and attempted genetic testing of players, all examples that have, according to McCann (2006), “usurped player autonomy” (p. 821).
Given that egregious violent behavior during sporting contests has occasionally resulted in criminal prosecutions (Standen 2009), the NBA certainly has a vested interest in using its referees in such a way to maintain order and prevent injury. The credibility of the league’s product is also at stake. For example, Russia’s top-tier basketball league disbanded in 2010 after governing body representatives were recorded instructing referees to fix the outcome of the country’s championships (Schwirtz 2010). Outright game-fixing by referees, whether ordered by the league or not, would, undoubtedly, adversely impact the game’s competitive purity, uncertainty of outcome, and fairness of on-court punishment. Less certain is the impact of referee bias, or even the perception of any such bias, on the integrity of the sporting contest. In the subsections that follow, we provide an overview of rapidly emerging research analyzing referee-level bias and explain how such findings may impact aggressive play.
A number of papers have investigated across-the-board bias by basketball referees. The primary finding of Price and Wolfers (2010) is easily summarized: “[M]ore personal fouls are awarded against players when they are officiated by an opposite-race officiating crew than when they are officiated by an own-race refereeing crew” (p. 1859). The authors conclude that such biases are large enough to affect game outcomes. The Price–Wolfers NBA referee research line spawned two spin-off papers. In the first, the authors determine that a profitable gambling strategy could have been employed by exploiting own-race referee bias (Larson et al. 2008). In the other sequel, the authors, in the course of reconciling their own results with those in the NBA’s counter-study, explain that the NBA’s own data, albeit in a limited way, support their original findings (Price and Wolfers 2011).
Other researchers with their analytical lens pointed toward basketball referees have made similar findings consistent with bias on the part of officials. Thu et al. (2002) found evidence that college basketball referees call more fouls on teams that are leading, but such “close bias” disappears when games are not televised nationally. Anderson and Pierce (2009) pinpointed the same “close bias” in the college ranks, which the authors find incentivizes teams to play more aggressively, causing the level of physicality to increase. Moskowitz and Wertheim (2011) found basketball officials, as well as referees in other sports, to suffer from omission bias (so-called “whistle swallowing”) in noncalls. Lehman and Reifman (1987) determined NBA referees to be influenced by crowd reactions when calling fouls on star players but not nonstars.
Price et al. (2011) focused on “profitable biases” among NBA referees that could help boost league ticket sales, television-related revenue, and consumer demand. By measuring “discretionary” turnovers such as traveling and offensive fouls with “nondiscretionary” turnovers such as steals or out-of-bounds calls, the authors found that referees favor teams: (1) playing at home; (2) behind in a game; and (3) trailing in a playoff series. Price et al.’s evidence of lengthier playoff series is consistent with the analogous results of Zimmer and Kuethe (2009) and Hassett (2008).
As a result of the NBA referee gambling scandal (Donaghy 2009; Griffin 2011), the NBA commissioned an investigation of its own officials (Pedowitz 2008). The resulting Pedowitz Report made three bias-related findings. First, it acknowledged that the integrity of the game is threatened by referee bias (p. 57). Second, the report revealed that a non-de minimis number of team representatives believe bias sometimes influences referee calls (p. 56). Third, it confirmed that the NBA is taking action to “help identify patterns consistent with referee bias for/against certain players or teams” (p. 114). Nevertheless, even after the Pedowitz Report’s release, the perception of referee bias remained (Aldridge 2009; Adande 2008; Stein 2008).
Macrolevel referee bias has also been identified outside of basketball. In soccer (or football as it is generally know outside of North America), both crowd noise (Nevill et al. 2002) and social pressure (Garicano et al. 2005; Dohmen 2008) have been found to impact referee decision-making. Like Price and Wolfers (2010), Parsons et al. (2011) found evidence of racial bias by baseball umpires, although such bias dissipated in games featuring a technologically advanced monitoring system. A home-ice advantage was pinpointed in hockey (Brimberg and Hurley 2009). Judges in Olympic diving (Emerson et al. 2009) and gymnastics (Morgan and Rotthoff 2010) were also found to be biased. Finally, nationalistic bias has been found in rugby (Page and Page 2010) and figure skating (Zitzewitz 2006; Fenwick and Chatterjee 1981).
A number of papers have looked at the issue of referee bias with a narrower focus. Shmanske (2008) analyzed over 1,000 NBA games during the 2007–2008 season and found no evidence of referee-related corruption with regard to game outcomes or point spread gambling. However, he did isolate one referee (Dick Bavetta) who significantly favored the home team on the basis of scoring, free throws awarded, foul calling, and game ejections (p. 133). Rodenberg and Lim (2009) did not find any systematic bias by specific referees against Dallas Mavericks owner Mark Cuban when looking at 654 regular season and playoff games over the course of seven seasons, although trace evidence was pinpointed in a smaller subsample of the team’s playoff games. Similarly, Rodenberg (2011) did not find any bias on the part of two officials (Derrick Stafford and Steve Javie) involved in high-profile altercations with Miami Heat coach and general manager Pat Riley. Finally, Winston (2009) analyzed the interaction between long-time NBA referee Joey Crawford and Tim Duncan of the San Antonio Spurs and found Crawford to have no significant adverse effect on the performance of the Spurs. Such an inquiry was ripe following an on-court dispute between the two that resulted in Crawford’s multimonth suspension by Commissioner Stern.
Are NBA referees biased? It depends on how one defines “biased.” Specifically, it depends on the type and scope of bias being investigated. A number of research papers have pinpointed various macrolevel biases that are subconscious or unconscious in nature. Such findings, rooted in implicit associations and social cognition (Bertrand et al. 2005), seem to be at odds with NBA President Joel Litvin, who opined: “I do believe, and I think it is the case, that [NBA referees] are, in fact, immune to the things that you and I would say are just human nature” (Bachman 2009). In contrast, research investigating referee bias at the narrower owner/coach/player level has not revealed any bias of a systematic nature that coincides with several high-profile anecdotal examples of alleged nefarious conduct by referees.
How Does Aggressive Play Contribute to Outcomes?
The discussion of referee bias suggests that personal fouls are “important.” Such a suggestion leads us to ask how personal fouls impact player salary, as well as team revenue and team wins. The factors that determine an NBA player’s salary have been investigated for more than two decades. See Berri (2006) for a review of the literature. A recent investigation was offered by Berri et al. (2007), a model later updated by Berri and Schmidt (2010). Their results reveal that an NBA’s free agent salary is driven by points scored, points-per-shot (i.e., shooting efficiency from the field), rebounds, blocked shots, assists, and personal fouls. As Berri and Schmidt (2010) report, free agent salaries are most responsive to total points scored. In addition to scoring, we see players are paid for increases in shooting efficiency from the field, rebounds, blocked shots, and assists. Free throw percentage, steals, and turnovers were not found to impact a player’s salary. Beyond these factors, personal fouls also matter. Players who commit more fouls will see their salaries fall. Part of this is due to the nature of the game. Once a player commits six fouls in a game, he is removed from the contest. So, additional fouls can impact how much time a player can see on the court.
The issue of playing time, though, is not the only concern. Personal fouls also impact the efficiency of a team’s scoring. To understand this point, we need to consider the impact of shooting efficiency on wins. Berri (2008) details how the statistics tracked for NBA players’ impact on team wins. This work reveals the following marginal impact for the statistics tracked specifically for scoring: a point scored = 0.033 wins; a field goal attempt = −0.034 wins; and a free throw attempt = −0.015 wins. Given these marginal impacts, a player must achieve the following shooting efficiency marks to break-even: for two-point field goal attempts, 51.5%; for three-point field goal attempts, 34.4%; and for free throw attempts, 46.5%. During the 2009–2010 NBA season, players posted the following averages with respect to shooting efficiency from each place on the floor: two-point field goal attempts, 49.2%; three-point field goal attempts, 35.5%; and free throw attempts, 75.9%. These results indicate that players can generate significant returns at the free throw line in terms of points and ultimately wins. So, players who commit fouls impede their team’s ability to produce wins, and correspondingly, the ability to draw fouls and connect at the free throw line is quite valuable in producing wins.
The Case of Shaquille O’Neal
Shaquille O’Neal (“Shaq”) was selected by the Orlando Magic with the first pick in the 1992 NBA draft. Standing 7′1² and weighing 325 pounds, Shaq is an imposing physical presence. Not only is he big, Shaq is athletically gifted and a player whom less-agile big men clearly had trouble guarding. NBA coaches and players, though, learned there was one aspect of the game where Shaq came up short. Shaq was not very good at hitting free throws. In his first season, he only converted 59.4% of these shots. And rather than improving, Shaq actually became less efficient in each of his first five seasons. In 1996–1997, Shaq only hit on 48.4% of his free throws. Shaq’s inability to hit free throws led opponents to adopt a strategy that became known as “Hack-a-Shaq,” the use of continued intentional fouling of the player in order to minimize his ability to score. Over his career, Shaq hit 58.2% of his shots from two-point range and only 52.7% of his free throws. Given these percentages, it made sense to force Shaq to score from the charity stripe. And that meant that teams frequently intentionally fouled Shaq.
A sample of the most productive players in NBA history
Career free throw percentage (%)
Two views of Shaquille O’Neal
Career free throw percentage (%)
O’Neal (actual FT%)
O’Neal (average FT%)
As a player vulnerable to the Hack-a-Shaq strategy, O’Neal offered a career WP48 mark that is not quite as good as the marks offered by our sample of all-time greats. The same story is told for Shaq’s career-best mark. However, if we imagine Shaq as an average free throw shooter, his career marks are only surpassed by Magic Johnson. Across Shaq’s entire career, he produced 251.1 wins. But had he hit his free throws at an average rate (74.9%), he would have produced 331.3 wins or 80.3 additional victories. If Shaq had converted free throws at the average rate, one would suspect that his ability to draw fouls would decline. Therefore, the estimate of wins offered is likely too high, but it does give an indication of the losses incurred by his below-average free throwing. Although Shaq was clearly a very productive player, his inability to hit free throws consistently was costly to his team in terms of wins.
Value of Shaquille O’Neal hitting free throws at an average rate
Value of wins
Change in wins
Impact of wins
Why Do Celebrities Misbehave and How Should Coaches Respond?
Shaquille O’Neal’s inability to shoot free throws prevented him from producing as many wins for his team as other star players, such as Michael Jordan and Magic Johnson. But, he was still an incredibly productive player, especially in his prime. In fact, from 1992–1993 to 2005–2006, Shaq’s teams won 754 regular season games. Of these wins, 234.3 could be traced to the statistical production of Shaq. In other words, Shaq produced 31.1% of his team’s regular season wins during his most productive years.
The dominance of Shaq is not entirely unusual in the NBA. As noted in Berri and Schmidt (2010), most wins in the NBA are produced by a minority of players. In fact, the Pareto Principle – initially observed by Vilfredo Pareto in a discussion of wealth in Italy – appears to apply to the NBA. Pareto argued that 80% of observed outcomes come from 20% of the people involved. Although it is not clear that the Pareto Principle has many applications [see Fox (2009) for details], Berri and Schmidt (2010) report that from 1977–1978 to 2007–2008, 80% of all wins were produced from 22.6% of player season observations. An average NBA team employs about 16 players, so for an average NBA team, about 80% of wins are produced by the team’s three most productive players.
The relative scarcity of productive players creates a problem for NBA coaches. Imagine if one of these players does not follow the rules? Can an NBA team afford to discipline these players? Kendall (2008) investigated this issue and found that, after controlling for a variety of factors, the highest paid player on a team was charged with a technical foul about 7% more often than the second highest paid player. Kendall considered a variety of explanations for this increase in misbehavior but ultimately argued that the evidence “suggests a significant role for the lack of substitutability in the production process” (p. 245). Essentially, highly paid players know teams cannot easily replace their talents. Consequently, misbehavior is harder to punish.
Although teams cannot easily punish a player who engages in behavior that earns technical fouls, teams do routinely sit players who get in foul trouble. And this is even true for “star” players. Does this practice make sense? To answer this question, Maymin et al. (2011) utilize play-by-play data from four NBA seasons (2006–2007 to 2009–2010). Via a model designed to explain the probability that a team will win a given game, the authors looked at the impact of removing a player in foul trouble from the game. The results indicate that unless a player is substantially better than his replacement, it makes sense for a coach to remove a player in foul trouble. As the authors argue, foul trouble may lead a player to play tentatively. Consequently, although a player might normally be quite productive, foul trouble reduces his effectiveness.
The study of crime and punishment in the NBA encompasses a variety of issues. As we note, crime and punishment in the NBA mirrors that in other sports (Bard and Kurlantzick 2002) and society in general. Greenberg et al. (1985), citing Brickman (1977), concluded that penalties in sports have the aim of restoring equity or serving as a deterrent. Referee bias, even that of the nonvolitional variety, has the potential to disrupt equitable rule enforcement. More so, as Anderson and Pierce (2009) make clear, such uneven rule enforcement may incentivize aggressiveness, causing increased physicality. Similarly, given the NBA’s move to proactively reign in excessive violence and aggression on the court, our findings regarding the efficacy of fouling on team wins and the impact of aggressive play on revenue tell a similar story of how the teams’ objective of winning games may sometimes be at odds with the league’s policy and public relation goals.
When we move from league issues to the level of a team, we see that personal fouls do have a negative impact on player salaries. Similarly, the failure to hit free throws can have a substantial negative impact on team success. Nevertheless, because star players are difficult to replace, disciplining players in the NBA is difficult.
- Abbott H (2008) Justin Wolfers and the Quality of an NBA Denial. ESPN.com, posted June 12. Accessed online: http://www.espn.go.com.
- Abbott H (2010) Study on Referees and Race Still Dogs NBA. ESPN.com, posted December 8. Accessed online: http://www.espn.go.com.
- Adande JA (2008) In Official Conduct, Personal Bias Still the Great Unanswered Question. ESPN.com, posted October 3. Accessed online: http://www.espn.go.com.
- Aldridge D (2007) NBA Referee Bias Story Has Many Gray Areas. Pantagraph.com, posted May 5. Accessed online: http://www.pantagraph.com/sports.
- Aldridge D (2009) The State of Officiating: What’s Wrong and How to Fix It. NBA.com, posted June 16. Accessed online: http://www.nba.com.
- Associated Press (AP) (2007a) Stern Criticizes Study on Refs, Rips New York Times. ESPN.com, posted May 4. Accessed online: http://www.espn.go.com.
- Associated Press (AP) (2007b) Players, NBA Dismiss Racial Bias in Officiating. ESPN.com, posted May 4. Accessed online: http://www.espn.go.com.
- Bachman R (2009) Researchers’ NBA Officiating Study Detects Biases, but Not Necessarily the Ones Fans Suspect. The Oregonian, posted June 3. Accessed online: http://www.people.oregonstate.edu/~stonedan/oregonian.htm.
- Bard RL, Kurlantzick L (2002) Knicks-Heat and the Appropriateness of Sanctions in Sport. Cardozo Arts and Entertainment Law Journal 20:507–524.Google Scholar
- Berri DJ (2006) Economics and the National Basketball Association: Surveying the Literature at the Tip-off. In Handbook of Sports Economic Research, ed. Fizel J, pp. 21–48. ME Sharpe: Armonk, NY.Google Scholar
- Berri DJ (2008) A Simple Measure of Worker Productivity in the National Basketball Association. In The Business of Sport, eds. Humphreys B, Howard D, pp. 1–40. Praeger: Westport, CT.Google Scholar
- Berri DJ, Schmidt MB (2010) Stumbling on Wins: Two Economists Explore the Pitfalls on the Road to Victory in Professional Sports. Financial Times Press: Princeton, NJ.Google Scholar
- Berri DJ, Brook SL, Schmidt MB (2007) Does One Simply Need to Score to Score? International Journal of Sport Finance 2(4):190–205.Google Scholar
- Bialik C (2007a) Parsing the NBA’s Study on Refs and Race. Wall Street Journal, posted May 14. Accessed online: http://www.blogs.wsj.com.
- Bialik, C (2007b). Follow-up on NBA’s Study of Race and Refs. Wall Street Journal, posted May 22. Accessed online: http://www.blogs.wsj.com.
- Brimberg J, Hurley WJ (2009) Are National Hockey League Referees Markov? Operations Research Insight 22(4):234–243.Google Scholar
- Donaghy T (2009) Personal Foul. Four Daughters LLC: Sarasota, FL.Google Scholar
- Feigen D (2007) Study Detailing Refs’ Racial Bias Goes Way Off Course. Houston Chronicle, posted May 5. Accessed online: http://www.chron.com.
- Fluhr H (2007) Superior Data, Analysis Shows No Race Bias among NBA Referees. Sports Business Journal, July 23, p. 44.Google Scholar
- Fox J (2009) The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street. Harper Collins: New York, NY.Google Scholar
- Greenberg J, Mark MM, Lehman DR (1985) Justice in Sports and Games. Journal of Sport Behavior 8(1):18–33.Google Scholar
- Griffin SP (2011) Gaming the Game. Barricade Books: Fort Lee, NJ.Google Scholar
- Hassett KA (2008) NBA Home Bias Suggests Referees Committing Fouls. American Enterprise Institute, posted June 23. Accessed online: http://www.aei.org.
- Hollinger J (2007) Closer Look at Ref Study. ESPN.com, posted May 9. Accessed online: http://www.espn.go.com.
- Kim JY, Parlow MJ (2009) Off-Court Misbehavior: Sports Leagues and Private Punishment. Journal of Criminal Law and Criminology 99(3):573–597.Google Scholar
- Larson T, Price J, Wolfers J (2008). Racial Bias in the NBA: Implications in Betting Markets. Journal of Quantitative Analysis in Sports 4(2):Article 7.Google Scholar
- Lehman DR, Reifman A (1987) Spectator Influence on Basketball Officiating. Journal of Social Psychology 127:673–675.Google Scholar
- Maymin A, Maymin P, Shen E (2011) How Much Trouble is Early Foul Trouble? Strategically Idling Resources in the NBA. Unpublished manuscript.Google Scholar
- McCann MA (2006) The Reckless Pursuit of Dominion: A Situational Analysis of the NBA and Diminishing Player Autonomy. Pennsylvania Journal of Labor and Employment Law 8(4):819–860.Google Scholar
- Morgan H, Rotthoff K (2010) Bias in Sequential Order Judging: Primacy, Recency, Sequential bias, and Difficulty bias. Unpublished manuscript.Google Scholar
- Moskowitz T, Wertheim LJ (2011) Scorecasting. Crown Books: New York, NY.Google Scholar
- Munson L (2007) Even NBA Study Might Confirm Racial Bias in Officiating. ESPN.com, posted May 15. Accessed online: http://www.espn.go.com.
- Page L, Page K (2010) Evidence of Referees’ National Favoritism in Rugby. Unpublished manuscript.Google Scholar
- Parsons CA, Sulaeman J, Yates MC, Hamermesh DC (2011) Strike Three: Umpires’ Demand for Discrimination. American Economic Review, forthcoming.Google Scholar
- Pedowitz LB (2008) Report to the Board of Governors of the National Basketball Association. NBA, posted October 1. Accessed online: http://www.nba.com.
- Price J, Remer M, Stone DF (2011) Sub-Perfect Game: Profitable Biases of NBA Referees. Journal of Economics and Management Strategy, forthcoming.Google Scholar
- Price J, Wolfers J (2011) Biased Referees? Reconciling Results with the NBA’s Analysis. Contemporary Economic Policy, forthcoming.Google Scholar
- Rodenberg RM (2011). Perception ≠ Reality: Analyzing Specific Allegations of NBA Referee Bias. Journal of Quantitative Analysis of Sports, forthcoming.Google Scholar
- Ryan B (2007) Position on Foul Calls is Offline. Boston Globe, posted May 3. Accessed online: http://www.boston.com.
- Sheridan C (2007) NBA: Claims of Racial Officiating Bias ‘Flat-Out Wrong.’ ESPN.com, posted May 4. Accessed online: http://www.espn.go.com.
- Schwarz A (2007) Study of NBA Sees Racial Bias in Calling Fouls. New York Times, posted May 2. Accessed online: http://www.nytimes.com.
- Schwirtz M (2010) Hoping to Stir a Revival of Basketball in Russia. New York Times, posted October 10. Accessed online: http://www.nytimes.com.
- Shmanske S (2008) Point Spreads and Referee Bias in the NBA. In Threats to Sports and Sports Participation, ed. Rodriguez P, Kesenne S, Garcia J, pp. 115–136. Ediciones de la Universidad de Oviedo: Oviedo, Spain.Google Scholar
- Standen J (2009) The Manly Sports: The Problematic Use of Criminal Law to Regulate Sports Violence. Journal of Criminal Law and Criminology 99(3): 619–642.Google Scholar
- Stein M (2008) Heft Alone Unlikely to Change Perceptions of Officiating. ESPN.com, posted October 5. Accessed online: http://www.espen.go.com.
- Showalter BD (2007) Technical Foul: David Stern’s Excessive Use of Rule-Making Authority. Marquette Sports Law Review 18(1):205–223.Google Scholar
- Thu KM, Hattman K, Hutchinson V, Lueken S, Davis N, Linboom E (2002) Keeping the Game Close: ‘Fair Play’ among Men’s College Basketball Referees. Human Organization 61(1):1–8.Google Scholar
- Winston WL (2009) Mathletics. Princeton University Press: Princeton, NJ.Google Scholar
- Zillgitt J (2010) ‘Respect for the Game’: NBA Wants Players on Best Behavior. USA Today, posted September 24. Accessed online: http://www.usatoday.com.
- Zimbalist A (2007) Study’s Credibility Suffers in Race to Report NBA Referees’ Race Bias. Sports Business Journal, May 21, p. 37.Google Scholar
- Zimmer T, Kuethe TH (2009) Testing for Bias and Manipulation in the NBA Playoffs. Journal of Quantitative Analysis of Sports 5(3):Article 4.Google Scholar