Game outcome uncertainty revisited – a clustering analysis of team-specific game attendance predictions

ABSTRACT

We provide evidence for heterogeneous game outcome uncertainty (GOU) effects across teams in Major League Baseball. Using attendance data from 2013 to 2019, we explore functional data clustering techniques and allow for nonlinear relationships to detect common patterns in predictive margins of team-specific winning probability. As a central result, we identify five groups of teams with similar GOU effects. However, only a few teams show GOU effects that resemble the typical hump shape that is postulated by the uncertainty of outcome hypothesis; the largest cluster is comprised of teams with fans whose attendance behaviour is relatively insensitive to differences in GOU.

KEYWORDS:

• Sport demand
• heterogeneous consumer behaviour
• uncertainty of outcome hypothesis
• clustering
• functional data analysis

JEL CLASSIFICATION:

• D12
• L15
• L2
• L83
• Z2

Acknowledgment

We thank seminar and conference participants at ESEA (online), Hamburg (University), and Kiel (University, IfW) and, in particular, Eren Aydin, Carsten Creutzburg, Georgios Nalbantis, Marius Ötting, Łukasz Skrok, and an anonymous referee, for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/00036846.2022.2115451

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Notes

¹ In general, the more teams are competing in a division, the harder it is to win the division, and vice versa. Between 1998 and 2012, both the National League (NL) and the American League (AL) comprised three divisions each, but the NL Central division consisted of six teams, whereas the AL West division comprised only four teams. After the 2012 season, the Houston Astros moved from NL Central to AL West, which has resulted in balanced Leagues with five teams per division from 2013 onward.

² A few games per season are typically not played at the corresponding home teams’ home stadiums because of bad weather conditions, international promotions, or other extreme events.

³ Unlike in sports such as European Football or cricket, in MLB, there is (practically) no possibility of a tie.

⁴ The funHDDC method is a model-based clustering approach that allows to cluster functional data in group-specific subspaces. The model parameters and group-specific functional subspaces are both determined via an estimation procedure that is based on the Expectation-Maximization (E-M) algorithm (Bouveyron and Jacques 2011) and we use k-means to initiate it. Moreover, concerning alternative functional data clustering methods, Bouveyron and Jacques (2011) show that funHDDC performs better than the fuzzy clustering method fclust proposed by James and Sugar (2003), and is suggested to be more stable than two-step clustering techniques, such as high-dimensional data clustering (HDDC) (Bouveyron, Girard, and Schmid (2007) and mixture of probabilistic principal component analysers (MixtPPCA) (Tipping and Bishop 1999). For further examples of applications of the funHDDC method, see, e.g. Bouveyron, Côme, and Jacques (2015), Leroy et al. (2018), Martínez-Álvarez et al. (2019), and Yao et al. (2022).

⁵ Regarding the big four US major leagues, NFL attendance has apparently recovered, whereas NBA, MLB, and NHL have not been able to draw as many fans to the stadium as in advance of the Covid-19 pandemic. For example, espn.com provides attendance numbers for various major leagues, see, e.g. http://www.espn.com/nba/attendance.