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Ekstrøm CT, Jensen AK. Having a ball: evaluating scoring streaks and game excitement using in-match trend estimation. ADVANCES IN STATISTICAL ANALYSIS : ASTA : A JOURNAL OF THE GERMAN STATISTICAL SOCIETY 2023; 107:295-311. [PMID: 35730005 PMCID: PMC9205152 DOI: 10.1007/s10182-022-00452-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2020] [Accepted: 04/26/2022] [Indexed: 11/30/2022]
Abstract
Many popular sports involve matches between two teams or players where each team have the possibility of scoring points throughout the match. While the overall match winner and result is interesting, it conveys little information about the underlying scoring trends throughout the match. Modeling approaches that accommodate a finer granularity of the score difference throughout the match is needed to evaluate in-game strategies, discuss scoring streaks, teams strengths, and other aspects of the game. We propose a latent Gaussian process to model the score difference between two teams and introduce the Trend Direction Index as an easily interpretable probabilistic measure of the current trend in the match as well as a measure of post-game trend evaluation. In addition we propose the Excitement Trend Index-the expected number of monotonicity changes in the running score difference-as a measure of overall game excitement. Our proposed methodology is applied to all 1143 matches from the 2019-2020 National Basketball Association season. We show how the trends can be interpreted in individual games and how the excitement score can be used to cluster teams according to how exciting they are to watch. Supplementary Information The online version contains supplementary material available at 10.1007/s10182-022-00452-w.
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Affiliation(s)
- Claus Thorn Ekstrøm
- Biostatistics, Department of Public Health, University of Copenhagen, Øster Farimagsgade 5, 1353 Copenhagen K, Denmark
| | - Andreas Kryger Jensen
- Biostatistics, Department of Public Health, University of Copenhagen, Øster Farimagsgade 5, 1353 Copenhagen K, Denmark
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Francesca F, Naccarato A, Terzi S. Evaluating countries’ performances by means of rank trajectories: functional measures of magnitude and evolution. Comput Stat 2022. [DOI: 10.1007/s00180-022-01278-5] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
AbstractCountries’ performance can be compared by means of indicators, which in turn give rise to rankings at a given time. However, the ranking does not show whether a country is improving, worsening or is stable in its performance. Meanwhile, the evolutionary behaviour of a country’s performance is of fundamental importance to assess the effect of the adopted policies in both absolute and comparative terms. Nevertheless, establishing a general ranking among countries over time is an open problem in the literature. Consequently, this paper aims to analyze ranks’ dynamic by means of the functional data analysis approach. Specifically, countries’ performances are evaluated by taking into account both their ranking position and their evolutionary behaviour, and by considering two functional measures: the modified hypograph index and the weighted integrated first derivative. The latter are scalar measures that are able to reflect trajectories behaviours over time. Furthermore, a novel visualisation technique based on the suggested measures is proposed to identify groups of countries according to their performance. The effectiveness of the proposed method is shown through a simulation study. The procedure is also applied on a real dataset that is drawn from the Government Effectiveness index of 27 European countries.
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Carroll C, Bhattacharjee S, Chen Y, Dubey P, Fan J, Gajardo Á, Zhou X, Müller HG, Wang JL. Time dynamics of COVID-19. Sci Rep 2020; 10:21040. [PMID: 33273598 PMCID: PMC7712909 DOI: 10.1038/s41598-020-77709-4] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Accepted: 11/12/2020] [Indexed: 01/09/2023] Open
Abstract
We apply tools from functional data analysis to model cumulative trajectories of COVID-19 cases across countries, establishing a framework for quantifying and comparing cases and deaths across countries longitudinally. It emerges that a country's trajectory during an initial first month "priming period" largely determines how the situation unfolds subsequently. We also propose a method for forecasting case counts, which takes advantage of the common, latent information in the entire sample of curves, instead of just the history of a single country. Our framework facilitates to quantify the effects of demographic covariates and social mobility on doubling rates and case fatality rates through a time-varying regression model. Decreased workplace mobility is associated with lower doubling rates with a roughly 2 week delay, and case fatality rates exhibit a positive feedback pattern.
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Affiliation(s)
- Cody Carroll
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA
| | | | - Yaqing Chen
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA
| | - Paromita Dubey
- Department of Statistics, Stanford University, Stanford, CA, 94305, USA
| | - Jianing Fan
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA
| | - Álvaro Gajardo
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA
| | - Xiner Zhou
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA
| | - Hans-Georg Müller
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA.
| | - Jane-Ling Wang
- Department of Statistics, University of California, Davis, Davis, CA, 95616, USA
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