CC BY
4Integral assessment of the level of preparedness of kissboxers based on the harrington-mencher function
UDC 796.012
Dr. Hab., Professor M.G. Kolyada1 Dr. Hab., Professor S.I. Belykh1 PhD, Associate Professor T.I. Bugaeva1 Postgraduate student O.S. Oleinik1 ''Donetsk National University, Donetsk, Ukraine
Corresponding author: kolyada_mihail@mail.ru
Abstract
Objective of the study was to reveal the mechanism for identifying a generalized assessment of the level of preparedness of kickboxers.
Methods and structure of the study. The application of the Harrington-Mencher desirability function to determine the level of preparedness of kickboxers is presented. The work of the desirability function is that it converts dimensional indicators into dimensionless ones, in fact, generalizes diverse indicators, bringing them to a single complex indicator.
Results and conclusions. The technique of an integral assessment of the level of preparedness of a kickboxer using the Harrington-Mencher function is given. A specific example shows the mechanism for converting actual indicators into a 10-point scale, and then into desirability coefficients. Thanks to a special system for translating desirability indicators into the usual rating scale, it is possible to obtain a complex indicator at the output that objectively evaluates their total set. Weight indicators of the significance of the preparedness of kickboxers were determined on the basis of expert assessments, which included reputable kickboxing coaches and referees.
Keywords: Harrington-Mencher desirability function, integrative indicator, kickboxer's level of preparedness, defining indicators of preparedness.
Introduction. As you know, the level of sports readiness is an indicator of sports and technical skills of an athlete. It is by comparing the values of the indicators of the properties of the athlete being evaluated with his previous indicators or with analogue samples that it is possible to determine whether there is an improvement in the training dynamics, or, accordingly, whether this athlete can be included in the team for competitions or high-level tournaments. Indicators of sports readiness related to the totality of its properties, according to which a coaching decision is made, are called defining indicators. But a set of less significant indicators sometimes makes such a significant contribution to the overall picture of the preparedness assessment that one has to resort to the definition of a complex (integrated) indicator.
There are many classifications of sports fitness, among which the main ones are those groupings
of properties and operating factors that show the functional (physiological - medical, anthropometric, biomechanical, etc.) capabilities of an athlete. But sometimes, having their high level, the athlete does not achieve the desired results, so it is necessary to take into account reliability indicators, as well as psychological, pedagogical and even social indicators. But these and many other indicators, as a rule, are expressed in different measuring scales, have a different order of numerical expression and different units of measurement. Therefore, decision makers have a problem with the generalization of indicators and the objective finding of an integrative overall indicator.
Objective of the study was to reveal the mechanism for identifying a generalized assessment of the level of preparedness of kickboxers.
Methods and structure of the study. There are many mathematical methods for integrating numer-
32
Theory and Practice of Physical Culture I teoriya.ru I June I № 6 2022
ous factors and causes that can generalize various indicators and, in this way, all of them can be reduced to a single integrative expression [9, 10].
American scientist E.S. Harrington [7, p. 37-41; 8] managed to translate the parameters, different in their essence and dimension, into a single di-mensionless evaluation scale. For this, a separate evaluation indicator d (from the French desirable -"desirable", "preferred") is translated into a dimen-sionless scale from 0 to 1, moreover, the value di=0 corresponds to an absolutely unacceptable level of this property of the indicator, and the value di=1 - to the most the best value of this property, where i = 1, 2, 3, 4, 5, ..., n; where n is the number of such indicators.
The desirability evaluation indicator is considered as a specific reliability or unreliability of the i-th indicator (that is, its best or worst value in this scale).
The desirability function corresponding to the acceptable/unacceptable level for a one-sided restriction is described by the formula:
Mencher [4, p. 7-12], who proposed to correct the formula of E.S. Harrington, taking into account the indicated shortcoming. To do this, he introduced an indicator of weight. This desirability function began to be called by a double name: the Harrington-Mencher formula [1,6]:
(4)
where di are dimensionless desirability parameters; Vi is their weight (significance); n is their number; i - 1, 2, 3, ..., n.
When determining the value of the weight (Vi), the most important indicator is assigned a value of 1, a little less important - 0.9, and so on in descending order, with a gradation step no more than 0.1, that is, in descending order: 1.0; 0.9; 0.8; 0.7; 0.6; 0.5; 0.4; 0.3; 0.2; 0.1.
To determine the final integral (generalized) indicator of desirability, a recalculation table is used, usually it looks like this (for five gradations) (Table 1).
d ~ e
-e*
(1)
d = e
(2)
Table 1. Table for converting desirability indicators into the usual rating scale
for a two-sided restriction - by another formula [5, pp. 24-30]:
where x* - the encoded value of a specific parameter x, that is, its value in the conditional scale (scale) of the measurement.
When all specific parameters (x) are listed in "their desirability" (d), a generalized assessment parameter is calculated, which E.S. Harrington called the generalized desirability function D. It is determined through the geometric mean of specific desirability, that is, according to the formula [8]:
(3)
In our case, the function D acts as an integral indicator, that is, it takes into account all internal parameters and, therefore, generalizes them as a complex value.
But for the practical use of this formula as a single generalized indicator, this function had a drawback, which is that all internal indicators used in it are considered only equilibrium, and in real life, experimenters often have to deal with parameters that have different weights (significance).
A way out of this situation was found by E.M.
Result Value D
Fine 1,00 - 0,80
Good 0,80 - 0,63
Satisfactorily 0,63 - 0,37
Badly 0,37 - 0,20
Very bad 0,20 - 0,00
Results of the study and their discussion. As
indicators of the sports readiness of kickboxers, the defining indicators for different classification categories were selected.
From the section of functional fitness, from its subgroup of physical fitness, the following indicators were selected: speed, strength qualities, as well as the level of development of flexibility, endurance, coordination of complex movements, mobility in the joints, flexibility of the kickboxer. From the subgroup of technical readiness: an indicator of the versatility of motor actions, an indicator of implementation efficiency, an indicator of noise immunity. From the subgroup of psychometric preparedness: threshold of sensitivity in various modalities, features of perception of spatial relationships, the pace of mental processes under the influence of interference, features of attention in combat with a forced pace and with a lack of time. From the section of sports reliability, the following were selected: the effective-
Table 2. Table of conversion of actual indicators to a 10-point scale, and then to desirability coefficients
Designation, Vi The name of the indicator, unit Quantitative expression of the indicator The value of the assessment by i-indi-cator, in a 10-point scale, ц Desirability ratio, d{
Vi Motor coordination, number / s 7,8/(0,31) 9,34 0,9274
V2 Muscular endurance, right/(left hand) kg 52,5/(48,6) 7,08 0,6788
V3 Simple visual-motor reaction (SVMR), ms 263,4 8,34 0,8174
V4 Choice reaction (CR), ms 363,6 9,20 0,912
V5 Concentration of attention, c. unit 1,04 8,17 0,7987
V6 Switching attention, points 31,5 6,56 0,6216
V7 Side impacts with the left and right foot for 30 s, quantity 78,5 8,95 0,8845
VS Frontal kicks with the left and right foot in 30 s, quantity 59,3 7,85 0,7635
V9 Punches(P) 47,1 8,98 0,8878
V10 Kicks (K) 18,2 6,24 0,5864
V11 Number of attacking strikes 25,0 7,10 0,681
V12 Number of retaliatory strikes 21,2 6,91 0,6601
Table 3. Values of expert weights of indicators of the level of athletic fitness of a kickboxer
Vi V2 V3 i V4 V5 V6 V, 1 V. 1 V9 V10 V11 V12
V 0,7 0,5 0,6 0,4 0,4 0,8 0,7 1,0 1,0 0,9 0,8
ness of the athlete's actions, the stability of preparedness in extreme conditions. From the section of psychophysiology and psychomotor: the degree of motivation, the will to win.
It should be noted that the selected indicators are not comprehensive, a large number of other indicators remain behind the scenes, but due to their cumbersomeness, we will leave only the 12 most significant indicators (Table 2).
The desirability functions described by Harrington have sigmoidal forms (see formulas 1 and 2). The mechanism for converting dimensional indicators into dimensionless ones, taking into account the linear dependence, is described in many works [2; 3, p. 128; 5]. As the simplest solution, we will take the formula for calculating the desirability coefficients: di = 0.11 *ui - 0.10, where 0.01<di<1. For substitution, values are taken from previously reduced values to a 10-point scale ui. For example, for the "Motor coordination" indicator, the value of the desirability coefficient is obtained: d1= 0.1*9.34 - 0.10 = 0.9274 (see Table 2, first line).
Weight indicators of the importance of indicators
of sports readiness of kickboxers were determined with the help of experts, which included authoritative coaches and referees in cocktail boxing (10 people). Together, they adopted the following values of weights for 12 indicators of the preparedness of athletes (Table 3).
According to formula (4), the generalized desirability function D was calculated:
f
,927*' ■ D.é79°s ■ 0.Я17°' - 0,912e-' - 0.7V)6■ 0,6ZZ^' ■ 0£3S°* ■ £>.7$4Л'Т ■ о.зяа1'3 ■ ij&si™ ■ 0,660°*
The value D = 0.760 is interpreted according to Table 1 as "good".
So, the integrative indicator of the kickboxer's sports readiness for our case is interpreted as "above average".
Conclusions. The application of the generalized Harrington-Mencher function as a complex indicator of the preparedness of a kickboxer according to diverse indicators is considered. The technique for identifying a generalized assessment of the level of preparedness of athletes makes it possible to evalu-
Theory and Practice of Physical Culture I teoriya.ru I June I № 6 2022
ate the internal consistency of the answers of experts, it makes it possible to verify the correctness of their conclusions by calculating the coefficient of concordance and the correspondence of the ranking to the natural laws of nature. If we add to the integrative indicator such indicators as the athlete's productivity, as well as the value of statistical sensitivity to the indicators used, it becomes clear that it can be used as a criterion for optimizing sports preparedness.
References
1. Dolgov Yu.A. Statisticheskoe modelirovanie [Statistical modeling]. Tiraspol: RIO PGU publ., 2002. 280 p.
2. Katernyuk A.V. Primenenie rejtingovyh oce-nok v reklamnoj otrasli [The use of ratings in the advertising industry]. Vestnik Tom-skogo gosudarstvennogo universiteta. Ekonomika. 2019. No. 45. p. 267-81. DOI: 10.17223/19988648/45/18.
3. Kuznetsov B.L. Modelirovanie sinergetich-eskih sistem v ekonomike [Modeling of synergistic systems in the economy]. Study guide. Naberezhnye Chelny: Kamskaya gos. inzhen-erno-ekonom. Akademiya publ., 2010. 142 p.
4. Mencher E.M., Zaslavskaya Yu.E., Minina N.P. Nekotorye metodicheskie voprosy prime-neniya obobshchennoj funkcii poleznosti pri izuchenii i optimizacii tekhnologicheskih pro-cessov [Some methodological issues of the application of the generalized utility function in the study and optimization of technological processes]. Proceedings of the VNII nerud. No. 39. Tolyatti, 1975. pp. 7-12.
5. Sosyukin A.E., Verveda A.B. Prakticheskie
aspekty ispolzovaniya funkcii zhelatelnosti pri provedenii psihofiziologicheskogo ob-sledovaniya personala avarijno-spasatelnyh formirovanij [Practical aspects of using the desirability function when conducting a psychophysiological examination of personnel of emergency rescue teams]. WWW.MEDLINE. RU. Vol. 16. Profilakticheskaya medicina, 2015. No. 429. pp. 872-884.
6. Fedorchenko S.G., Dolgov Yu.A., Kirsanova A.V. et al. Obobshchennaya funkciya poleznosti i ee prilozheniya [Generalized utility function and its applications]. Tiraspol: Pridnestrovskij universitet publ., 2011. 196 p.
7. Harrington E.C.Jr. The desirability Function. Industrial Quality Control, 1965. April. Vol. 21. No. 10. pp. 494-498.
8. Harrington E.S. Funkciya zhelatelnosti [Desirability function]. Promyshlennyj kontrol kachestva. 1965. No. 10. pp. 45-49.
9. Koliada M.G., Bugayova T.I., Kapranov G.A. Use of the Method of the Analysis of Hierarchies in Acceptance of Pedagogical Decisions. International Scientific Conference "Far East Con" (ISCFEC 2020), Advances in Economics, Business and Management Research. Vol. 128. pp. 1334-1345. https:// doi.org/10.2991/aebmr. k.200312.184 DOI: 10.2991/aebmr.k.200312.184.
10. Koliada M.G., Belykh S.I., Bugayova T.I., Oleinik O.S. Artificial intelligence method to detect psychological and pedagogical anomalies in physical education and sports activities. Teoriya i Praktika Fizicheskoy Kultury. 2021 (9). pp. 66-69.
