Set-level strategic and psychological momentum in best-of-five matches in professional tennis

ABSTRACT

We provide a theoretical and empirical analysis of set-level strategic and psychological momentums in a sample of 8,193 ATP best-of-five-set tennis matches where players have asymmetric abilities. Theoretical predictions match observed Set 1 outcomes, the only set with no set-level psychological momentum, but do not match any other sets. We find evidence of psychological reversal: in every set following a non-tie net score, the winner of the previous set underperforms compared to theoretical predictions.

KEYWORDS:

• Tennis
• best-of-N tournaments
• contests

JEL CLASSIFICATION:

• L83
• C73
• Z20

Acknowledgments

Financial support from the Center of Distributive Justice at Institute of Economic Research (SNU) is gratefully acknowledged.

Disclosure statement

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

Notes

¹ Tullock contests (Malueg and Yates 2010), all-pay auctions (Gauriot and Page 2019) and minmax (Walker and Wooders 2001) have been used to model tennis matches. Game theory has also been used to model other sports such as football (Brocas and Carrillo 2004; Zülch, Palme, and Jost 2020), rugby (Delbianco, Fioravanti, and Tohmé 2021) and beach volleyball (Sonnabend 2020).

² It is plausible for psychological momentum to be carried between matches, say, if player did unexpectedly well in the previous match. However, as long as this information is public it is likely to be priced in the betting odds for the next match.

³ The Matlab code for this analysis is available upon request.

Additional information

Funding

This work was supported by the Center for Distributive Justice of Institute of Economic Research, Seoul National University.