Monte Carlo Tennis: A Stochastic Markov Chain Model
We develop a stochastic Markov chain model to obtain the probability density function (pdf) for a player to win a match in tennis. By analyzing both individual player and 'field' data (all players lumped together) obtained from the 2007 Men's Association of Tennis Professionals (ATP) circuit, we show that a player's probability of winning a point on serve and while receiving serve varies from match to match and can be modeled as Gaussian distributed random variables. Hence, our model uses four input parameters for each player. The first two are the sample means associated with each player's probability of winning a point on serve and while receiving serve. The third and fourth parameter for each player are the standard deviations around the mean, which measure a player's consistency from match to match and from one surface to another (e.g. grass, hard courts, clay). Based on these Gaussian distributed input variables, we use Monte Carlo simulations to determine the probability density functions for each of the players to win a match. By using input data for each of the players vs. the entire field, we describe the outcome of simulations based on head-to-head matches focusing on four top players currently on the men's ATP circuit. We also run full tournament simulations of the four Grand Slam events and gather statistics for each of these four player's frequency of winning each of the events and we describe how to use the results as the basis for ranking methods with natural probabilistic interpretations.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 5 (2009)
Issue (Month): 3 (July)
|Contact details of provider:|| Web page: http://www.degruyter.com|
|Order Information:||Web: http://www.degruyter.com/view/j/jqas|
When requesting a correction, please mention this item's handle: RePEc:bpj:jqsprt:v:5:y:2009:i:3:n:7. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.