Identifying key factors in momentum in basketball games

Abstract

Momentum as elaborated under a recent novel definition has been shown quantitatively to have a significant impact on basketball game outcomes. This paper makes two contributions to the analytical literature on sports momentum: (1) two aspects of the new definition are operationalized so that its practicality becomes evident; and (2) through a dimension-reduction technique (elastic net), key factors associated with momentum are identified. Both technical variables such as field goals, assists, rebounds, etc. and environmental variables such as the spectator attendance rate and player salary dispersion are considered, and the potential for useful real-time analyzes is illustrated.

Keywords:

• Basketball
• momentum
• elastic net
• attendance rate
• Gini coefficient

2010 Mathematics Subject Classifications:

• 62-07
• 62P99

Acknowledgments

The authors are grateful to the anonymous referees and Jie Chen (the Editor-in-Chief) for helpful comments, and would like to thank S. Fu, P. Oyer, S. Rigdon and participants in 2018 CAAS conference on high dimensional statistics, 2017 WISE econometrics/statistics group brown bag seminars, etc., for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 According to the play-by-play data, each team averages approximately 100 possessions per game, that is, 15 seconds per possession.

2 For the $k^{th}$ game, $k=1,\dots ,K$ with K being the total number of games ${\mathrm{Gini}}_k^{\mathbb{I}}=\frac{\sum _{i=1}^{k(\mathbb{I})}\sum _{j=1}^{k(\mathbb{I})}|{\mathrm{inc}}_i-{\mathrm{inc}}_j|}{2k(\mathbb{I})\sum _{i=1}^{k(\mathbb{I})}{\mathrm{inc}}_i},$ where ${\mathrm{inc}}_i$ is the salary of player i, $\mathbb{I}=1$ or 0 denotes the home or visiting team, respectively, and $k(\mathbb{I})$ means the number of players, including those on the bench.

3 The results in this section are run on a 2.60 GHz dual core CPU and R Software Version 3.6.2. The total run-time is approximately 1.20 minutes.

4 The responsibility of the general manager often includes player transactions, contract negotiations, and hiring and firing of the coaching staff. Some GMs also take responsibility for team operations, including the promotion of games (attracting more fans).

5 This strategy is famously used by some coaches such as Phil Jackson, who was one of the best basketball coaches in the NBA. The coaching strategy has received much criticism and drawn controversy in some games, but that is not the focus here.

Additional information

Funding

Fan's research, in part, was supported by the National Natural Science Foundation of China Grants 71671149, 71801183 and 71631004 (Key Project) and the Science Foundation of the Ministry of Education of China (18YJC790073).