A multilevel Bayesian approach for modeling the time-to-serve in professional tennis

Stephanie A. Kovalchik
  • Corresponding author
  • Tennis Australia, Melbourne Victoria, Australia
  • Victoria University, Institute of Sport, Exercise and Active Living, Victoria, Australia
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and Jim Albert
  • Bowling Green State University, Department of Mathematics and Statistics, Bowling Green, USA
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  • degruyter.comGoogle Scholar


Temporal characteristics have been a main area of focus in the study of pre-performance routines in elite sports. Ball and player tracking data is currently available that precisely measures service preparation times in professional tennis. However, this data has yet to be utilized for studying service pre-performance routines. In this paper, we present a Bayesian multilevel model of the time-to-serve in a professional tennis match, which includes heterogeneous means, variances and covariate effects. Applying the model to a sample of serves played at the 2016 Australian Open reveals that the typical time-to-serve was 19 s for male players and 20 s for female players. Point importance and the length of the previous rally account for approximately 15% of the within-match variance. However, even with this adjustment, within-match variation is notably larger than between-player variation, 60% greater for men and 30% greater for women. The proposed Bayesian modeling approach is demonstrated to be a useful tool for analyzing in-competition temporal data on preparation time for tennis and other sports.

    • Supplementary material
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JQAS, an official journal of the American Statistical Association, publishes research on the quantitative aspects of professional and collegiate sports. Articles deal with subjects as measurements of player performance, tournament structure, and the frequency and occurrence of records. Additionally, the journal serves as an outlet for professionals in the sports world to raise issues and ask questions that relate to quantitative sports analysis.