Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports

Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. These results are based on the transition matrices of the Markov chain, associated with the adjacency matrices of a network with n nodes and allowing for a more robust analysis of the variability of interactions in team sports. The proposed models refer to individual and collective rates and indexes of total variability between players and teams as well as the overall passing capacity of a network, all of which are demonstrated in the UEFA 2020/2021 Champions League Final.

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Node and Network Entropy—A Novel Mathematical Model for Pattern Analysis of Team Sports Behavior

Mathematics ◽

10.3390/math8091543 ◽

2020 ◽

Vol 8 (9) ◽

pp. 1543

Author(s):

Fernando Martins ◽

Ricardo Gomes ◽

Vasco Lopes ◽

Frutuoso Silva ◽

Rui Mendes

Keyword(s):

Mathematical Models ◽

Pattern Analysis ◽

Team Sports ◽

Sports Performance ◽

Winning Team ◽

Relative Transition ◽

Network Transition ◽

Network Entropy ◽

Transition Entropy

Pattern analysis is a well-established topic in team sports performance analysis, and is usually centered on the analysis of passing sequences. Taking a Bayesian approach to the study of these interactions, this work presents novel entropy mathematical models for Markov chain-based pattern analysis in team sports networks, with Relative Transition Entropy and Network Transition Entropy applied to both passing and reception patterns. To demonstrate their applicability, these mathematical models were used in a case study in football—the 2016/2017 Champions League Final, where both teams were analyzed. The results show that the winning team, Real Madrid, presented greater values for both individual and team transition entropies, which indicate that greater levels of unpredictability may bring teams closer to victory. In conclusion, these metrics may provide information to game analysts, allowing them to provide coaches with accurate and timely information about the key players of the game.

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Eco-Dynamics Approach to the study of Team Sports Performance~!2009-07-05~!2009-11-01~!2010-04-29~!

The Open Sports Sciences Journal ◽

10.2174/1875399x01003010056 ◽

2010 ◽

Vol 3 (1) ◽

pp. 56-57 ◽

Cited By ~ 14

Author(s):

B. Travassos ◽

D. Araujo ◽

V. Correia ◽

P. Esteves

Keyword(s):

Team Sports ◽

Sports Performance

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Do We Share the Same View? Validating the Shared Mental Models in Team Sports Questionnaire

Perceptual and Motor Skills ◽

10.1177/0031512521990335 ◽

2021 ◽

Vol 128 (2) ◽

pp. 831-850

Author(s):

Charlotte Raue ◽

Dennis Dreiskaemper ◽

Bernd Strauss

Keyword(s):

Mental Models ◽

Team Sports ◽

Positive Influence ◽

Shared Mental Models ◽

Model Fit ◽

Sports Performance ◽

Measurement Instruments ◽

Team Members ◽

Confirmatory Factor ◽

Good Internal Consistency

Shared mental models (SMMs) can exert a positive influence on team sports performance because team members with SMMs share similar tasks and team-related knowledge. There is currently insufficient sports research on SMMs because the underlying theory has not been adapted adequately to the sports context, and different SMMs measurement instruments have been used in past studies. In the present study we aimed to externally validate and determine the construct validity of the “Shared Mental Models in Team Sports Questionnaire” (SMMTSQ). Moreover, we critically examined the theoretical foundation for this instrument. Participants were 476 active team athletes from various sports. While confirmatory factor analysis did not support the SMMTSQ’s hierarchical model, its 13 subfactors showed a good model fit in an explorative correlative approach, and the model showed good internal consistency and item–total correlations. Thus, the instrument’s subfactors can be applied individually, even while there are remaining questions as to whether other questionnaires of this kind are an appropriate means of measuring SMMs in sport.

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Accuracy, inter-unit reliability and comparison between GPS and UWB-based tracking systems for measuring centripetal force during curvilinear locomotion

Proceedings of the Institution of Mechanical Engineers Part P Journal of Sports Engineering and Technology ◽

10.1177/1754337120961601 ◽

2020 ◽

pp. 175433712096160

Author(s):

Paulino Granero-Gil ◽

Alejandro Bastida-Castillo ◽

Daniel Rojas-Valverde ◽

Carlos D Gómez-Carmona ◽

Ernesto de la Cruz Sánchez ◽

...

Keyword(s):

Team Sports ◽

Ultra Wideband ◽

Centripetal Force ◽

Sports Performance ◽

Tracking Systems ◽

Force Measurements ◽

Global Positioning ◽

Ethical Approval ◽

Elite Level ◽

Centripetal Forces

Curvilinear locomotion is important for team sports performance and requires data collection and monitoring of centripetal forces. Currently, the centripetal force can be measured by different sensors that compose inertial devices, but its accuracy needs to be assessed. Therefore, this research aimed to analyze the accuracy and inter-unit reliability of both global positioning (GPS)-based and ultra-wideband (UWB)-based systems for practical application in the field. Following institutional ethical approval and familiarization, 10 elite-level male soccer players performed six circuits on four tracks (6-m radius circle, 9.15-m radius circle, 12-m radius circle, and combined track locomotion) in both directions (three counter-clockwise and three clockwise) and were monitored by two tracking systems (GPS and UWB). The direct measurement was compared with the theoretical centripetal force calculated by photocells and spatial references. The UWB technology showed better accuracy (clockwise, bias =−1.34 N; counter-clockwise, bias = 1.09 N) than the GPS (clockwise, bias = −2.19 N; counter-clockwise, bias = 1.75 N) in centripetal force measurements. However, both tracking technologies obtained very large to nearly perfect reliability results (GPS: ICC = 0.76-0.96; UWB: ICC = 0.76–0.98). In conclusion, even though both technologies proved to be reliable and data could be compared between units, the UWB-based system demonstrated better accuracy than the GPS-based system to detect centripetal force during curvilinear locomotion.

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The Role of Hypernetworks as a Multilevel Methodology for Modelling and Understanding Dynamics of Team Sports Performance

Sports Medicine ◽

10.1007/s40279-019-01104-x ◽

2019 ◽

Vol 49 (9) ◽

pp. 1337-1344 ◽

Cited By ~ 10

Author(s):

João Ribeiro ◽

Keith Davids ◽

Duarte Araújo ◽

Pedro Silva ◽

João Ramos ◽

...

Keyword(s):

Team Sports ◽

Sports Performance

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Importance of the Mental Preparation for Competition Among Young Athletes

STADIUM - Hungarian Journal of Sport Sciences ◽

10.36439/shjs/2018/1/8 ◽

2021 ◽

Vol 1 (1) ◽

Author(s):

Orsolya Borók ◽

Éva Bácsné Bába

Keyword(s):

College Graduates ◽

Negative Impact ◽

Team Sports ◽

Talent Management ◽

Sports Performance ◽

Young Athletes ◽

Online Questionnaire ◽

Urban Background ◽

Mental Preparation ◽

Sports Organizations

The mental preparation of athletes for competition has become more appreciated. In this paper, we asked young athletes in Hungarian team sports about their experiences and expectations in mental preparation. In the research, we used an online questionnaire where 165 valuable responses were received. Most of the respondents were women, between 15-24 years of age, high school and college graduates, with urban background. Almost 90% of respondents have been confronted an obstacle with a negative impact on performance in sports before. Most athletes know well the activities of sports psychologists, however, only 10% of them have been mentally trained so far, while 70% of them would need it. Those sports associations achieve more successful results in the talent management, where sports psychologist was involved in the assessment of young children. Based on these, sports organizations should use a sports psychologist, because it could help achieve better sports performance for players and teams.

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Mathematics and Fiction: Thomas Pynchon, Gravity’S Rainbow

Modernism, Fiction and Mathematics ◽

10.3366/edinburgh/9781474416238.003.0005 ◽

2018 ◽

pp. 126-156

Author(s):

Nina Engelhardt

Keyword(s):

Probability Theory ◽

Thomas Pynchon ◽

Decisive Factor ◽

Mathematical Concepts ◽

Gravity’S Rainbow ◽

Gravity's Rainbow ◽

New Perspective ◽

Ontological Uncertainty

Chapter 4 sets the engagement with modernist mathematics into broader context when examining the rise, fall and transformation of Enlightenment thinking and science in Pynchon’s Gravity’s Rainbow. This chapter also zeroes in on a topic that runs through all chapters: the interrelations of mathematics and fiction. The analysis focuses on illustrations of fictionality regarding the mathematical concepts of infinitesimals, the calculus, and probability theory and their philosophical and ethical consequences. The examination of interdependent ‘real’ and ‘fictional’ elements in mathematics provides a new perspective on Brian McHale’s identification of ontological uncertainty as the novel’s definitive postmodernist trait: the chapter shows that the novel’s renegotiation of mathematics is a decisive factor in its introduction of postmodernist features. As the title ‘Gravity’s Rainbow’ with its combination of a scientific and a poetical image implies, Pynchon’s novel suggests that the shared use of fictional concepts both in mathematics and in literature connects the seemingly opposed realms.

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