Email this article A new markovian model for tennis matches
Abstract
In this paper we present a generalisation of previously considered Markovian models for Tennis that overcome the assumption that the points played are i.i.d. Indeed, we postulate that in any game there are two different situations: the first 6 points and the, possible, additional points after the first deuce, with different winning probabilities. We are able to compute the winning probabilities and the expected number of points played to complete a game and a set in this more general setting. We apply our results considering scores of matches between Novak Djokovic, Roger Federer and Rafael Nadal.
References
Barnett, T., Brown, A., and Pollard, G. (2006). Reducing the likelihood of long tennis matches. Journal of Sports Science and Medicine, 5(4):567–574.
Carter Jr, W. H. and Crews, S. L. (1974). An analysis of the game of tennis. The American Statistician, 28(4):130–134.
Ferrante, M. and Fonseca, G. (2014). On the winning probabilities and mean durations of volleyball. Journal of Quantitative Analysis in Sports, 10(2):91–98.
Kemeny, J. G. and Snell, J. L. (1976). Finite markov chains, undergraduate texts in mathematics.
Klaassen, F. and Magnus, J. R. (2014). Analyzing Wimbledon: The power of statistics. Oxford University Press, USA.
Klaassen, F. J. and Magnus, J. R. (2001). Are points in tennis independent and identically distributed? evidence from a dynamic binary panel data model. Journal of the American Statistical Association, 96(454):500–509.
Newton, P. K. and Keller, J. B. (2005). Probability of winning at tennis i. theory and data. Studies in applied Mathematics, 114(3):241–269.
Norris, J. R. (1998). Markov chains. Number 2. Cambridge university press.
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