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  • 1
    Digitale Medien
    Digitale Medien
    The Effects of Home-Away Sequencing on the Length of Best-of-Seven Game Playoff Series (2006)
    Berkeley, Calif. : Berkeley Electronic Press (now: De Gruyter)
    Journal of quantitative analysis in sports 2 (2006), S. 5 
    Details
    ISSN: 1559-0410
    Quelle: Berkeley Electronic Press Academic Journals
    Thema: Sportwissenschaft
    Notizen: We analyze the number of games played in a seven-game playoff series under various home-away sequences. In doing so, we employ a simple Bernoulli model of home-field advantage in which the outcome of each game in the series depends only on whether it is played at home or away with respect to a designated home team. Considering all such sequences that begin and end at home, we show that, in terms of the number of games played, there are four classes of stochastically different formats, including the popular 2-3 and 2-2 formats both currently used in National Basketball Association (NBA) playoffs. Characterizing the regions in parametric space that give rise to distinct stochastic and expected value orderings of series length among these four format classes, we then investigate where in this parametric space that teams actually play. An extensive analysis of historical 7-game playoff series data from the NBA reveals that this home-away model is preferable to the simpler, well-studied but ill-fitting binomial model that ignores home-field advantage. The model suggests that switching from the 2-2 series format used for most of the playoffs to the 2-3 format that has been used in the NBA Finals since a switch in 1985 would stochastically lengthen these playoff series, creating an expectation of approximately one extra game per playoff season. Such evidence should encourage television sponsors to lobby for a change of playoff format in order to garner additional television advertising revenues while reducing team and media travel costs.
    Materialart: Digitale Medien
    URL: http://www.bepress.com/jqas/vol2/iss1/5
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  • 2
    Digitale Medien
    Digitale Medien
    Data Clustering for Fitting Parameters of a Markov Chain Model of Multi-Game Playoff Series (2008)
    Berkeley, Calif. : Berkeley Electronic Press (now: De Gruyter)
    Journal of quantitative analysis in sports 4 (2008), S. 2 
    Details
    ISSN: 1559-0410
    Quelle: Berkeley Electronic Press Academic Journals
    Thema: Sportwissenschaft
    Notizen: We propose a Markov chain model of a best-of-7 game playoff series that involves game-to-game dependence on the current status of the series. To create a relatively parsimonious model, we seek to group transition probabilities of the Markov chain into clusters of similar game-winning frequency. To do so, we formulate a binary optimization problem to minimize several measures of cluster dissimilarity. We apply these techniques on Major League Baseball (MLB) data and test the goodness of fit to historical playoff outcomes. These state-dependent Markov models improve significantly on probability models based solely on home-away game dependence. It turns out that a better two-parameter model ignores where the games are played and instead focuses simply on, for each possible series status, whether or not the team with home-field advantage in the series has been the historical favorite - the more likely winner - in the next game of the series.
    Materialart: Digitale Medien
    URL: http://www.bepress.com/jqas/vol4/iss1/2
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  • 3
    Digitale Medien
    Digitale Medien
    Relaxed asynchronous flow-control algorithms for multiclass service networks (2000)
    Springer
    IIE transactions 32 (2000), S. 873-880 
    Details
    ISSN: 1573-9724
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau
    Notizen: Abstract This paper addresses resource sharing in a multiclass service center. The flow of service requests from each class of customers are regulated by a class manager who attempts to maximize the class net benefit (throughput reward less delay cost). Relaxed asynchronous algorithms are proposed for obtaining a Nash equilibrium among these competing classes in which each manager iteratively updates his throughput strategy in response to local (and possibly delayed) information on the strategies of the others. The novelty of these flow-control algorithms are in the relaxation, whereby each manager employs a strategy update that is a convex combination of his previous strategy and his best-reply strategy to current information. Alternatively, this relaxation can be viewed as an exponential smoothing of all previous best-reply strategies. For a particular number of classes with specified cost/reward parameters, relaxation conditions for asymptotic convergence to the unique interior Nash equilibrium are presented. For more than two classes, it is shown that relaxation not only accelerates convergence (at least in a special case), but also is a necessary condition for convergence. Due to an equivalent functional form, these results can be directly translated to a network of users employing a power criterion, a common objective in the communications literature.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1007651430168
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