Some statistical solutions and methods in evaluation of efficiency in sport and effectiveness in the phenomenon of sportsmen' training.

Author:Savoiu, Gheorghe


The analysis of the efficiency is not a recent and exclusive concern of the economists, but even of the coaches in sports, of all managers, in general. The efficiency measurement emerges naturally from the distance between a real effect or observation and the empirical estimate of the theoretical effect. Between 1933 and 1951, economics and econometrics had revealed and quantified the economic concept of efficiency and F.H. Knight G. Debreu and T. C. Koopmans are the pioneers of scientific presentation of the results of their studies regarding the calculation of the efficiency. Kamatchi et al. (2009); Muralidhar et al. (2009); Ulrichs et al. (2009); Carifio and Perla (2010); Elforgani and Rahmat (2010); Eldos and Almazyad (2010); Ismail et al. (2010); Cage and Kluck (2010); Iskandarani (2010) and Sarabian and Lee (2010) and others have brought important contributions through their recently published materials in the study of efficiency in sports and different domains, using both parametric and nonparametric methods. There have been made numerous applications of the stochastic frontier method, using diverse specifications of the production function, stochastic or determinist ones, parametric or non-parametric ones, based on cross-section or panel data. The authors of this study try to underline the applied efficiency in sport using new solutions and methods from statistics, mathematics, physics and genetic algorithms.


There is neither communication between coach and sportsman without knowledge or sportive training and nor efficient results without communication and also there is no knowledge and no training without communication in sportive activity. The simplest model of representational communication is that of Karl Buhler synthesized by the first variant of the sender-message-receiver type in the next Fig. 1.


In Roman Jakobson's intermediary variant there appear three other elements, code, channel and context (referent), offering the possibility of outlining, through pluralism, a potential model with six components: Sender-code-message-channel-context-receiver, as in the next Fig. 2.


In the cybernetic model of communication of Claude Shannon and Warren Weaver the contextual component is missing, the model avoids the semantic information, in favour of the selective one and it additionally contains three new components, the transmitter, the receiver and the noise and in order to constitute itself statistically and mathematically, that is to submit its object to measurement one resorts to a special characteristic of information, the fact that it benefits from an invariance all along a series of reversible operations and for this reason it quantizes in bits (which thus became units of measurement).Warren Weaver, through a relevant question, regarding the exactness with which the symbols of communication can be transmitted, generated the next Fig. 3 of the complex/classical system of communication.


The fundamental theorem of the statistical-mathematical theory of communication, considered valid for a channel without noise and for discreet signals, refers to the channel of communication having the capacity of C bits per second, receiving symbols from a source with the entropy of H bits per second (the information communicated) and it states that, thanks to the procedures of coding adequate to the sender it is possible to transmit symbols through the channel with an average debit considered close to the maximum value C/H. This fact, based on the background of the similarity with economy (production-exchange-consumption) reduce sports communication to an exchange of messages, just as economy is an exchange of merchandise, which also allows to attach to the process of communication in sports activities one of the five methods of multidisciplinary analysis, considered as possible solutions of the method of the four "E", regarded as a chain of logical approach of the type efficaciousness-degree of economy-efficiency-effectiveness:

* Efficaciousness in the model of communication message and noise

* Degree of economy in the model of communication: the C/H relation or the limit of the resource of h type

* Efficiency in the model of communication maximization of the C/H relation for a given level of H

* Effectiveness in the model of communication monitoring/controlling the communication channel

* Statistical evaluation of indexes of procedural transformation through the law of equivalence and the dynamics of the factorial asymmetries (the index-numbers method)

* A delimitation of the informational transformation thresholds, of the maximum and minimum type, with the help of the law of the minimum and the law of the maximum (the method of the smallest squares through the use of the partial derivatives)

* A mathematical and physical interpretation of the economic relations centred upon the principle of losses, successive inequalities and of the inclinations of the slopes of effect and cause or of the angular coefficients of the m =([Y.sub.1]-[Y.sub.2])/([X.sub.1]-[X.sub.2])type

* A determination of the informational energy (S =sigma[p.sub.i.sup.2])

* A modern sports efficiency vision with the help the general methodology support from genetic algorithms

* This study underlines the...

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