To discriminate or not to discriminate – Is data aggregation the question?

Abstract

Previous professional sports discrimination studies rely heavily on aggregated data to the game level and therefore do not control for unobservable within game heterogeneity. This article uses an established testing methodology for assessing discrimination among professional sports adjudicators and compares inferences when data are and are not aggregated above an influential factor that affects within game foul/penalty rates. Substantial differences in conclusions are found suggesting that a number of inferences in the literature relating to discrimination in various contexts may be fragile. The issue and findings have potential relevance to a wide range of related studies.

Keywords:

• aggregation
• inferences
• discrimination
• hockey

JEL Classification:

• D7
• J7
• J44
• J71
• L83

Notes

1 In contrast, regarding baseball, and the analysis of PA, each umpire ball/strike decision is an observable record that can be used for analysis purposes.

2 By score margin we mean the difference in cumulative points or score of the two teams competing in a contest.

3 The individual player events are hits, take-aways, give-aways, shots, missed shots and blocked shots.

4 Note that we are using the abbreviated terms English and French to denote English Canadian and French Canadian ethnicities.

5 There were only a small number of games (7) that were officiated by one International referee in our sample, and these were excluded from the regression.

6 Hockey games consist of 60 minutes of regulation time. An observation on a player's penalty rate, the number of penalties per 60 minutes, refers to either the entire game for the AM or conditional on various within game score margins for the DM.

7 The event count is player specific. For example, only a count of the number of shots that player p took on his shift are included in the shot count, not the number of team shots that occurred during his shift.

8 See Mongeon and Longley (2013) for an example using basketball data.

9 See Mittelhammer (1996, pp. 186–7).

10 The cells in columns (4) and (5) for International player are left blank because there are no International referees’ in our sample to whom to compare the rates of International players.

11 PW made a substantial contribution by discerning that the assignment of refereeing crews to games does not literally need to be random to test for discrimination, only that the racial/ethnic mix of the refereeing crews is unrelated to the racial/ethnic characters of the teams that they officiate. We performed a test for independence similar to that of PW between the number of referees of a given ethnicity in a game and the number of same-ethnicity players in that game. In 32 of the 36 cases, the null hypothesis of independence was not rejected, providing a general assurance that referee assignments are unrelated to the ethnicity of players they officiate. These results are available from the authors upon request.