Bradley-Terry model; maximum likelihood estimation; round-robin tournament; sport performance analysis; strength model; Competitive Behavior; Humans; Likelihood Functions; Models, Statistical; Monte Carlo Method; Athletic Performance; Probability; Tennis; Orthopedics and Sports Medicine; Physical Therapy, Sports Therapy and Rehabilitation
Abstract :
[en] We propose a new performance measure for table tennis players: the mutual point-winning probabilities (MPW) as server and receiver. The MPWs quantify a player's chances to win a point against a given opponent, and hence nicely complement the classical match statistics history between two players. These new quantities are based on a Bradley-Terry-type statistical model taking into account the importance of individual points, since a rally at 8-2 in the first set is less crucial than a rally at the score of 9-9 in the final set. The MPWs hence reveal a player's strength on his/her service against a given opponent as well as his/her capacity of scoring crucial points. We estimate the MPWs by means of maximum likelihood estimation and show via a Monte Carlo simulation study that our estimation procedure works well. In order to illustrate the MPWs' versatile use, we have organized two round-robin tournaments of ten respectively eleven table tennis players from the Belgian table tennis federation. We compare the classical final ranking to the ranking based on MPWs, and we highlight how the MPWs shed new light on strengths and weaknesses of the players.
Disciplines :
Mathematics Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others Orthopedics, rehabilitation & sports medicine
Author, co-author :
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) ; a Department of Applied Mathematics, Computer Science and Statistics , Ghent University , Ghent , Belgium
Dominicy, Yves; b Université libre de Bruxelles, SBSEM, ECARES , Brussels , Belgium
Bruneel, Wim; c Ghent University , Ghent , Belgium
External co-authors :
yes
Language :
English
Title :
Mutual point-winning probabilities (MPW): a new performance measure for table tennis.
Fonds National de la Recherche Scientifique - FNRS
Funding text :
We thank two anonymous referees for insightful comments that helped us improve the presentation of the present paper. We would like to warmly thank the 21 table tennis players that took part in the two round-robin tournaments that we organised for the purpose of our research, as well as the 29 table tennis players that took the time to rank the intermediate scores appearing in Table 1. Yves Dominicy further acknowledges financial support via a Mandat de Chargé de Recherche FNRS.Yves Dominicy?s work was supported by the Fonds De La Recherche Scientifique - FNRS (BE). We thank two anonymous referees for insightful comments that helped us improve the presentation of the present paper. We would like to warmly thank the 21 table tennis players that took part in the two round-robin tournaments that we organised for the purpose of our research, as well as the 29 table tennis players that took the time to rank the intermediate scores appearing in Table 1. Yves Dominicy further acknowledges financial support via a Mandat de Charg? de Recherche FNRS.
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