Dr.Biol., Professor A.P. Isaev
Ph.D., Associate Professor V.V. Ehrlich
Ph.D., Professor V.I. Zalyapin
 Research Center of Sports Science, South Ural State University, Chelyabinsk

Keywords: model, athletic workability, status indicators, principal components, variance analysis, predictors

Introduction

Physical workability modeling in its athletic applications with due consideration for the afferent systems is a subject of high interest in modern sport science. Experimental data characteristic of the athlete’s physical status may be subject to statistical analysis to rate the correlation reliability of one or another group of factors and indicators and make well-grounded qualitative and quantitative studies of the revealed regularities. Research objectives may be attained through an integrated approach using the most effective athletic training technologies based on sound theoretical grounds and taking into account many factors of importance for the success-focused training process. The resultant physical workability models will be considered an inalienable component of the best possible ways to attain this objective.

Materials and methods

Subject to experimental studies in this work were 33 functional- and metabolic-status indicators of 15 elite middle distance runners qualified Candidates for Master of Sport and Masters of Sport and defending the colors of the national team of the RF and the first teams of their RF provinces/ areas. We used the principal component analysis [1] to analyze the original (directly tested in the experiments) status indicators that helped us notably cut down the number of indicators subject to the study and gave us the means to design a few models to effectively forecast athletic workability and highlight the top-priority factors for the success-focused training systems.

Results and discussion

Elite athletes’ training systems applied in the endurance-intensive sport disciplines have always been given the top priority in view of their obvious theoretical and practical importance [5; 6; 7; 8; 12]. Much attention is being given by the modern sport science to the projects to develop athletic status modeling and forecasting tools to support the athletic training process [9; 10; 4; 11]. Some works of that kind address the matters of organ-specific modeling of cardiovascular hypoxia [2] and morphological/ functional individual “portrait” characteristics.

Table 1 hereunder gives the principal component data valuing distribution of the 33 functional- and metabolic-status indicators subject to the study. It may be seen from Table 1 that it is the first four components that accumulate above 90% of the input data on the athletes’ physical statuses as provided by the 33 measured indicators. It should be further noted that the first 12 components contain virtually all (99.9%) information available from the input data. The principal component analysis that we performed gave the means to find correlations of the athletes’ success rates in competitions with their physical status indicators, with the relevant linear regression model [3] being produced.

Table 1. Principal component data valuing analysis

800 m race: Multi-component model equation including the 12 principal components looks as follows: Т_800 = 160, - 0,0299хPCOMP_1 + 0,0191хPCOMP_2 - 0,0312хPCOMP_3 + 0,0544хPCOMP_4 - 0,0939хPCOMP_5 + 0,209хPCOMP_6 - 0,276хPCOMP_7 - 0,0363хPCOMP_8 - 0,461хPCOMP_9 + 0,684хPCOMP_10 - 0,412хPCOMP_11 - 0,64хPCOMP_12.

Furthermore, statistical characteristics [3] of the model are the following:  = 99.9%,  (adjusted) = 99.2%, with the standard estimation error of 0.188 and the mean absolute error of 0.0592.

Table 2 hereunder gives the variance analysis of the model. The Fisher criterion [1] is indicative of the model being meaningful and adequate.

Table 2. Dispersion analysis of the 800 m race data

Since the significance, as provided by the above variance analysis, is under 0.05, it means that the subject indicators are in good correlation, with the reliability index of 95%. The adjusted model shows the following characteristics (Table 3 hereunder):

Table 3. Dispersion analysis of the 800 m race data, adjusted model

Table 4 hereunder gives the Full Model (based on 12 predictors) versus the Adjusted Model (excluding PCOMP 8 predictor) comparative statistics.

Table 4. Full Model versus Adjusted Model: comparative statistics

Model equation for the 11 predictors will be the following:

Т_800 = 162, - 0,0299хPCOMP_1 + 0,0191хPCOMP_2 - 0,0312хPCOMP_3 + 0,0544хPCOMP_4 - 0,0939хPCOMP_5 + 0,209хPCOMP_6 - 0,276хPCOMP_7 - 0,461хPCOMP_9 + 0,684хPCOMP_10 - 0,412хPCOMP_11 - 0,64хPCOMP_12

Given hereunder are the results of the similar regression analysis of the principal components in application to the 1500 m hurdles.

1500 m hurdles: Independent predictors include the principle components PCOMP_1 – PCOMP_12, with exclusion of PCOMP_5 and PCOMP_7. The latter predictors were excluded as insignificant. Modeled variable Т_1500 means the time of the athlete, with the number of measurements of 15.    

Model equation for the 10 predictors will be the following:

 Т_1500 = 319, - 0,0721хPCOMP_1 - 0,0577хPCOMP_2 + 0,0301хPCOMP_3 + 0,185хPCOMP_4 - 0,124хPCOMP_6 + 0,251хPCOMP_8 - 0,272хPCOMP_9 - 0,394хPCOMP_10 - 0,42хPCOMP_11 + 0,588хPCOMP_12

Given hereunder is the model variance analysis (Table 5):

Table 5. Variance analysis of the 1500 m hurdles data

Statistical characteristics of the model are the following:  = 97.1%,   (adjusted) = 89.7%, the standard estimation error of 0.752, and the mean absolute error of 0.312.

Since the significance, as provided by the above dispersion analysis, is under 0.05, it means that the subject indicators are in good correlation, with the reliability index of 95%. statistics are indicative of the fact that the model accumulated 97.1% of the Т_1500 indicator variability (times of the athletes on this distance). Adjusted  index equals 89.7 %. The standard estimation error of 0.752 may be used to generate forecast limits using the same model based on a new set of input data.

Conclusion

The principal component regression models (operating with the aggregate indicators) give the means to conclude that the runners’ integrative body activity indicators dominant for the success are the following: blood circulation indicators; energy supply indicators; lead links of lymphocyte corpuscles activity indicators; stomach/ pancreatic gland/ salivary gland functionality indicators etc.

References

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Corresponding author: tmfcs@mail.ru