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On an Entropy-based Performance Analysis in Sports
* 1, 2 , 3, 4 , 3, 4 , 3 , 3, 5 , 3
1  Institute of Systems and Robotics, University of Coimbra, Pinhal de Marrocos, Polo II, 3030-290, Coimbra, Portugal
2  Ingeniarius, Lda., Rua da Vacariça, n.37, 3050-381, Mealhada, Portugal
3  Polytechnic Institute of Coimbra, ESEC, RoboCorp, ASSERT, Rua Dom João III Solum, 3030-329 Coimbra, Portugal
4  Faculty of Sport Sciences and Physical Education, University of Coimbra, Estádio Universitário de Coimbra, Pavilhão 3, 3040-156 Coimbra, Portugal
5  Instituto de Telecomunicações, Delegação da Covilhã, Convento Santo António, 6201-001 Covilhã, Portugal

Abstract: This paper discusses the major assumptions of influential ecological approaches on the human movement variability in sports and how it can be analyzed by benefiting from well-known measures of entropy. These measures are exploited so as to further understand the performance of athletes from a dynamical and chaotic perspective. Based on the presented evidences, entropy-based techniques will be considered to measure, analyze and evaluate the human performance variability under three different case studies: i) golf; ii) tennis; and iii) soccer. At a first stage, the athletes' performance will be analyzed at the individual level by considering the golf putting (pendulum movement) and the tennis serve (ballistic movement). Under these gestures, the approximate entropy is considered to extract the variability inherent to the process variables. Afterwards, the athletes' performance will be analyzed at the collective level by considering the soccer case (team sport). To that end, both approximate entropy and Shannon's entropy are mutually considered to assess the variability of football players' trajectory. To outline the applicability of entropy-based measures to analyze sports, this article ends with an overall reflection about the potential of such measures towards an increased understanding on the overall human performance. This methodology proves to be useful to provide decisive information and feedback for coaches, sports analysts and even for the athletes.
Keywords: Sport sciences; chaos and nonlinear dynamics; entropy; performance analysis
Comments on this paper
Joao Valente-Dos-Santos
Comment on 'On an Entropy-based Performance Analysis in Sports'
I read with interest the recent article written by Couceiro, Clemente, Dias, Mendes, Martins & Mendes: ‘On an Entropy-based Performance Analysis in Sports’. In summary, the authors reported that nonlinear techniques are extremely useful to analyze the human movement within sports context. Consequently, the authors discussed that entropy-based measures can be considered as one of the main methods to study the human variability, thus making up for the limitations inherent to linear techniques typically used to quantify the motor performance. In light of their findings and discussion, it is of my opinion  that the current approach (i.e., nonlinear methods) may represent an alternative that may deepen our understanding around the human movement science. Overall, this is a very interesting and well-written paper that is an important contribution to the literature. I expect that it will become highly cited in the field.

Joao Valente-dos-Santos
Micael Couceiro
Dear João,

Thank you for your feedback!

We've been working in the topic of performance analysis in sports for quite a while now and this paper tries to grab all the important pieces related with the nonlinear perspective, namely the use of entropy-based measures to further understand such performance.

The main problem we always face while using these (nonlinear) measures is how the outcome may be understood from a research/coach/athlete perspective. As you say, these techniques may represent an alternative that may deepen our understanding around the human movement science. Yet, there isn't still a consensus about the meaning of human variability depicted during the execution of a given gesture - while some authors state that variability may be seen as something negative, wherein athletes are unable to reproduce a given result, some other authors argue that human variability is a representation of how the athlete can adapt and adjust his/her process variables to some given constraints. Additionally to all that, typical mathematical measures of variability, such as the approximate entropy, are really just that: mathematical tools. As such, they do not really consider the whole intel about a given sports gesture/modality.

In other words, even though one can compute the variability of a given gesture (e.g., golf putting), we still have to consider which time-series inherent to such gesture may be more or less relevant to classify it. For instance, in this paper, one of the examples we consider to classify the variability of a given golfer is the horizontal trajectory of the golf club. Although it was previously considered to be rather relevant time-series in a previous setup using a front camera to acquire the process variables, new experiments using a recently created engineered putter ( told us, through an evolutionary computational process, that there are other variables we should look at, namely the duration of each phase of the movement, the backswing and downswing amplitudes, or even the speed and acceleration during impact.

This may suggest that one may need to produce a single time-series that may adequately represent a given gesture out of all these important variables. This is the next step we are aiming at and we've been already acquiring data from novice and expert athletes for that purpose (

Once again, thank you for your feedback João! Always a pleasure to discuss with colleagues :)

Garrison Livingston
Sit ducimus deleniti
Perspective of the performance on the dancing and the teams after to the matches which have been played on the morning were decisive. That conference was only electronic conference on website direct entropy has been analyzed.