Racial Discrimination among NBA Referees · NBA misunderstood our analysis (Effect of player or ref race v. player*ref) 2. NBA mistreated their data 3. Even then, their results are

1 Joe Price & Justin Wolfers, Racial Discrimination Among NBA Referees

Racial Discrimination among NBA Referees

Joseph Price Brigham Young University

& NBER

Justin Wolfers Wharton – U.Penn

CEPR, IZA & NBER


Introduction Research question: Do NBA referees display own-race biases?

Motivation: Many settings involve individuals making subjective evaluations of the actions of

others: – Enforcer-offender (judges, officers, etc.) – Employer-employee – Customer-proprietor – Teacher-student

Is there an own-race bias in these evaluations? – Employer hiring: Stoll, Raphael, and Holzer (2004) – Police arrests: Donohue and Levitt (2001): – Police vehicle search: Antonovics and Knight (2005) – Judicial sentencing: Schanzenbach (2005)

Economics of discrimination: – Own-race bias cannot be statistical discrimination – In-group preference by majority Anti-minority bias


Why Examine NBA Referees? Analytic advantages

– (Essentially) random assignment of referee crews to games

– Small set of agents, repeated interaction An unlikely place to find discrimination

– High levels of transparency and monitoring – Incentives to make the right decision – NBA referees “are the most ranked, rated, reviewed,

statistically analyzed and mentored group of employees of any company in any place in the world.” (David Stern, NBA commissioner)

Intriguing context – Quick decisions – Subjective evaluation (interpretation of physical

contact)


ATLANTA (99)

ft rb

minutes m-a m-a o-t a fouls points S Jackson 43 7-18 0-0 0-5 3 4 16 S Abdur-Rahim 43 8-14 9-10 1-10 3 2 26

T Ratliff 38 3-4 0-0 1-9 4 5 6

J Terry 47 10-15 7-13 1-4 8 4 29

D Glover 38 5-16 3-4 1-4 2 2 14

Technical fouls: Indiana - 3 (COACH Carlisle,3:33 1st; A Harrington, 9:47 3rd; A Harrington, 10:06 4th). Atlanta - 2 (S Jackson, 2:23 3rd; J Terry (ejected), 0:21 5ot).

Flagrant fouls: None. A: 18,818. T: 2:45.

Officials: Bernie Fryer, David Jones, Gary Benson.

NBA Box Scores ATLANTA (99)

ft rb

minutes m-a m-a o-t a fouls points S Jackson 43 7-18 0-0 0-5 3 4 16

S Abdur-Rahim 43 8-14 9-10 1-10 3 2 26

T Ratliff 38 3-4 0-0 1-9 4 5 6

J Terry 47 10-15 7-13 1-4 8 4 29

D Glover 38 5-16 3-4 1-4 2 2 14

...

Technical fouls: Indiana - 3 (COACH Carlisle,3:33 1st; A Harrington, 9:47 3rd; A Harrington, 10:06 4th). Atlanta - 2 (S Jackson, 2:23 3rd; J Terry (ejected), 0:21 5ot).

Flagrant fouls: None. A: 18,818. T: 2:45.

Officials: Bernie Fryer, David Jones, Gary Benson.


Our Data

Full boxscore info – Regular season games – Omit referee strikes (Nov. 1995; Dec. 1998-Jan .1998) – 1991/92-2003/04 seasons (12,263 games; 266,984 player-games) – Recent update: 2004/05-2006/07 seasons

Race: Appears Black v. Non-black (“white”) – Players:

» Kahn and Shah (2005), Timmerman (2000) » Photos in NBA Register

– Referees » Visual inspection of press photos » Input from a former referee

– Coach » Photos in NBA register

Player characteristics (height, weight, position) – www.basketball-reference.com


Comparison of Foul Rates

n=266,984 player-game observations

Player-game observations weighted by minutes played ***, **, * denote statistically significant at 1%, 5% and 10% (Standard errors in parentheses)


Personal Fouls Analysis


Broader Impacts Outcome Mean

(Standard dev.) Estimate effect (Standard error)

Placebo: No Effects

Free Throw % 74.6% (23.3)

+0.4% (0.8)

Other Margins: Consistent patterns Points per 48 min 19.54

(10.1) -0.430* (0.221)

Player aggression: No visible increase Steals per 48 min 1.63

(1.89) -0.053 (0.046)

Blocks per 48 min 1.02 (1.81)

-0.022 (0.038)

Estimated coefficient on %White referee * Black player from most complete regression equation: – including referee effects, player*year, team*year, and team*game fixed effects.


Impacts on Winning Margins


Probability of Winning

Notes: Sample = 12,263 home game observations (IV regressions: n=12,247) Each column in each panel represents a separate regression. (Standard errors in parens) Coefficient on %White refs * (%Blackhome-%Blackaway) measures own-race bias. %Black measured as share of minutes played by black players. Observable controls include home-away differences in: out-of-contention, home*attend and black coach. IV: Instrumenting for %Blackhome-%Blackaway and its interaction with %white referees, using the average %Black for the home team over the preceding ten games less the average %Black for the away team over the preceding ten games, interacted with %white referees.


Interpreting the Magnitudes

Average racial difference between teams: – One team gives 15% more playing time to blacks – That team wins 48.6% of all games

Implications: Consider an “average” game (x% black v. x-15%) Two extreme cases:

– If all white referees: The “black” team would win 47.6% of all games – If all black referees: The “black” team would win 51.0% of all games – Implies: Outcomes of 3.4% of games could change if the racial composition

of the refereeing crew changed Alternative policy: If referee pool matches player pool (83% black)

– The “black” team would win 50.5% of the time – Implies: Race-norming would have changed outcomes in 1.8% of all games


Referee-Level Analysis


Additional Evidence from Betting Markets

NBA betting markets should incorporate all of the available information about who wins the game.

Can you use information about the racial mix of the two teams and the referee crew to systematically beat the spread?


Simple betting rules don’t make money.

Win % Rate of return All teams 50% -4.55%

Home 49.43% -5.63%

Away 50.57% -3.47%

Favorites 50.01% -4.52%

Underdogs 49.99% -4.57%

Home favorites 49.62% -5.28%

Home underdogs 48.99% -6.47%

Away favorites 51.01% -2.62%

Away underdogs 50.38% -3.81%


Betting based on race made money |%Blackhome-%Blackaway|

Rate of Return

>0.1 -1.06% (1.88)

>0.2 +3.74% (2.70)

>0.3 +7.48%** (4.21)

>0.4 +18.13%*** (7.35)


Supportive Evidence from Baseball

– Pitchers get more strikes, give up fewer hits, more strike outs, and more wins when umpire is the same race.

– This effect goes away in stadium’s with Questec monitoring system (35% of ballparks).

Parsons, Sulaeman, Yates, and Hamermesh (2011)


Some criticisms of our study

Lebron James: "It's stupid." P.J. Brown: "Somebody's got too much time on

their hands." Phil Jackson: "If you have a conclusive evidence

you want to come out with, you can almost make statistics prove what you want to prove.

Charles Barkley: “This is the stupidest stupid stupid study I’ve ever seen.”… “The thing that bothered me most is these guys didn't even go to the game. They looked at box scores.”… “Of course, black players get more fouls, 80% of the players are black.”


NBA’s Criticism of Our Study

"My major concern about it is that it's wrong.“ “They dealt from the box-score, which doesn’t identify which

referee made the call.” “We ran the data and came up with

something that said quite starkly that there is no bias amongst NBA officials.”


The NBA Study

Analyze 2½ seasons of data: Nov. ’04 – Jan. ’07 Analyze #Fouls earned by a player in a game

– Despite claims that they are analyzing fouls per player*referee per game

Break data into four separate sub-samples: Four key points:

1. NBA misunderstood our analysis (Effect of player or ref race v. player*ref)

2. NBA mistreated their data 3. Even then, their results are supportive of our results 4. Treating the NBA data appropriately yields estimates

consistent with ours


Problems with NBA Dataset We can recover summary statistics from NBA analysis NBA Analysis of average #fouls per game, by race

Price-Wolfers boxscores:

Which is more plausible? – Number of fouls per game – Sample size (148,205 v. 69,047 from 3,482 games)

=>

#Fouls per player-game = a + b*Player_Black Usual playing time

0-10 mins

10-20 mins

20-30 mins

≥30 mins

White players 2.728 3.044 3.483 3.486 Black players 2.562 3.091 3.361 3.456 N (Total=148,205) 6,235 35,266 51,440 55,264

Usual playing time 0-10 mins

10-20 mins

20-30 mins

≥30 mins



NBA Dataset: What is Going On? We can re-create the NBA Data by:

1. Drop all observations with zero fouls 2. Weight observations by #fouls

– If a player earns 4 fouls: Record 4 observations, each with 4 fouls

NBA Data 0-10 mins

10-20 mins

20-30 mins

≥30 mins


Price-Wolfers Replication of NBA Data 0-10 mins

10-20 mins

20-30 mins

≥30 mins



NBA Analysis Driven by Mis-specification

Independent variable is an interaction: Player*referee race – But NBA do not control for direct terms

» Player race » Referee race

– We can sign the bias: » White players commit more fouls » White players are more likely to have own-race

referees » Thus failing to control for white-player effect biases

own-race coefficient Makes it too positive (we expect it to be

negative)


Understanding the NBA Analysis

The NBA analysis (model 9) compares: – The weighted average of the own-race cells

=(28%*2.656+39%*2.582)/(28%+39%) = 2.613 – The weighted average of the opposite-race cells

=(29%*2.533+4%*3.187)/(29%+4%) = 2.612 This is why the NBA find no effect But because white players are much more likely to face own-race referees (see above) ,

this confounds two facts: – White players earn fewer fouls under own-race referees

» Which should lead to a negative “own-race” effect – White players earn more fouls than black players

» And because they are likely to have own-race referees, this leads to an offsetting positive bias to the “own-race” effect

Our difference-in-difference analysis takes account of underlying differences between black and white players.

An example using players who typically play 0-10 minutes


(Partly) Rehabilitating the NBA Estimates

0-10 minute players 10-20 minutes players Black

Players White

Players Difference:

Black – White Foul Rate

Black Players White Players Difference: Black – White

Foul Rate

White referee 2.533 2.656 -0.123 3.089 2.994 0.095 Black referee 2.582 3.187 -0.605 3.094 3.081 0.013 Difference: White ref- Black ref

-0.050 -0.532 Diff-in-diff +0.482 -0.005 -0.087

Diff-in-diff +0.083

20-30 minute players 30+ minute players White referee 3.353 3.479 -0.126 3.433 3.479 -0.046 Black referee 3.372 3.488 -0.116 3.466 3.499 -0.033 Difference: White ref- Black ref

-0.019 -0.009 Diff-in-diff -0.010 -0.033 -0.021

Diff-in-diff -0.012

Note: The means in this table were recovered by algebraic manipulation of the NBA’s reported results. Unfortunately we could not recover standard errors.

Fouls per player per game (Using NBA data and NBA weighting system)


Conclusion

Evidence of own race bias on the part of referees Large enough to affect the outcome of the game Evidence in betting markets as well NBA’s analysis also supports it. Surprising, since we were looking in very unlikely place

for racial discrimination to occur. – everyone watching, lots of supervision – large incentives to make the right call

Implications for other settings?

Documents

Racial Discrimination among NBA Referees · NBA misunderstood our analysis (Effect of player or ref race v. player*ref) 2. NBA mistreated their data 3. Even then, their results are