CC BY
3Influence of the viewers on the performance
results of sports teams
UDC 796.015.865.22
PhD, Associate Professor V.N. Yushkin1 1Volgograd State Agricultural University, Volgograd
Corresponding author: aup-volgau@yandex.ru
Abstract
Objective of the study was a theoretical substantiation and description of the calculation of the rating using numerical methods in team sports.
Methods and structure of the study. The formation of rating classifications in team sports was carried out using mathematical modeling using high-level programming languages and numerical calculation methods. The requirements that must be met by the general targets, guidelines that form the rating of teams are determined: taking into account the results of previous performances, the factor of influence of one's field, the number of spectators at the stadium, the potential of teams. The mathematical model was evaluated by the indicator of the convergence of the current rating of the teams participating in the match with the actual result of the game. The analysis of the results of the performance of teams in the matches of the championships of Russia in 1992-2022 was carried out.
Results and conclusions. Three variants of calculation were performed: 1) calculation of a unified system of equations, taking into account the factor of influence of one's own field; 2) calculation with the calculation of the index of the coefficient of influence of spectators on the results of games; 3) calculation of the coefficients of influence of the home field factor and spectators on the results of the games. The system of linear equations has a unique solution if the results of the teams' performance do not have zero uncertainty during the entire period of the competition. The developed rating system is aimed at numerical confirmation of the level of readiness and potential of teams, the accuracy of predicting the performance of teams in the short and long term in all team sports.
Keywords: rating, system, viewers, classification, modeling, numerical method.
Introduction. The relevance of the research topic is that the athletes' performance is never been realized without the attention of the audience, who directly affect the results of the teams' performance by their behavior and reaction. The spectators are the ones who create a positive or negative mood for the athletes, stimulate, activate and motivate their efforts to achieve results in the competition. Consequently, competition conditions, the internal and the external environmental factors have a direct impact on team's success.
A.A. Polozov together with other Russian scientists S.V. Mikhryakov, E.S. Naboychenko, E.M. Bozhko, E.A. Suvorova, A.V. Melnikova and A.V. Korelin have devoted research works to the improvement of the rat-
ing calculation methods in sports [1]. Foreign authors are also engaged in improving the methods of the rating evaluation [7].
The impact of fans' benevolent or negative mood on the success and results of a sports team has not been well studied. The practical examples of the spectators' influence on the results of teams' performances are considered. The introduction of the rating is essential for further development, an analysis and prediction of the performance results in team sports.
Objective of the study was а theoretical foundation and description of the rating calculation with the use of numerical methods in team sports. For the first time the notion of mathematical model correspondence to real results, tending to the maximum, is in-
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troduced, as well as the calculation of impact factor indices: one's own field and spectators on the result of the game. The following parameter is suggested as an indicator of the degree of compliance for the mathematical model: the percentage of matches with the converged result based on the results of the rating evaluation for two teams with the actually obtained result of match to a total number of matches with the identified winner.
Methods and structure of the study. The methodology for determining the teams' rating, based on the factor of own field, which was used in the first variant of calculation, is presented in the works [3, 4].
In the second calculation variant, let us determine the teams' ratings only including the factor of the spectators' impact on the result of the game.
The value of the spectators' factor influence index is calculated by the following formula
k=1+v ■ S, 1
s s '
where S - is a number of matches with the home field advantage of one of the teams; vs - is a value of one spectator's impact on the result of the game.
In the third variant of calculation, we will determine the teams' ratings, including the impact of the factor: own stadium and spectators on the result of game. The necessity of the calculation for given variant is obvious - the result of match is affected not only by a number of spectators, but also by the psychological factor of being at own stadium during the game.
Considering the spectators factor (1), a total number of goals scored and conceded will be:
/ (</ ■ Vv) • 4K] . 4-=Ê
j=1 ' M
2
where i - is a number of teams, calculated in the system; F , A:- is a total given number of goals scored
and conceded by i-th team, correspondingly; Gf, Ga - is a number of goals scored and conceded by i - th team in j - th game, correspondingly; R - is the opposing team rating in j-th game; kv - is an index of the impact factor of the game on home field.
Results of the study and their discussion. For the analysis, we choose the results of 7492 matches, played by the teams in the championships of Russia 1992-2022, with the period from April 29, 1992 to April 3, 2022.
After calculating a system of the equations for the first variant, we summarize the obtained results in Table 1, using the following notations: PM - is a number of the outcomes, which matched the result of the opponents' rating assessment, RM - is a number of matches with the identified winner.
The sixth line shows the results of calculating for one's own field factor, obtained using the formula described in [5]. All other results were obtained using the assigned own field factor, which were changed in the increments of 0.1.
The results show that the maximum convergence of the model was 70.414%, when calculating the factor of own field according to the proposed formula.
After calculating a system of the equations for the second variant, using the spectators' impact index on the game results, we obtain the following results (Table 2).
The results show that with the value = 0.370 per 10000 spectators the degree of model consistency was a maximum and it is equal to 70.725. The factor of the spectators impact on the results of matches is ks = 1.37 per 10,000 spectators. So, if we ignore a fact of the impact of the stadium on the result of the game and we assume that only a number of spectators affects, it turns out that if the team gathers on home field
Table 1. The degree of model consistency with different values of the indicators for own field factor
níii \ PM RM
K v i=1 X(g2! -Vrjr ) i=\ consistency, %
1,000 3615 5479 65,979
1,100 3733 5479 68,133
1,200 3809 5479 69,520
1,300 3844 5479 70,159
1,400 3854 5479 70,341
1,430 10533,59 7366,49 3858 5479 70,414
1,500 3860 5479 70,451
1,600 3854 5479 70,341
1,700 3824 5479 69,794
1,800 3794 5479 69,246
1,900 3767 5479 68,753
2,000 3738 5479 68,224
Table 2. The degree of model consistency with different indicators of the value for spectators' impact on the result of the game
VS for 10,000 spectators PM RM Degree of model consistency, %
0,100 3732 5479 68,115
0,200 3803 5479 69,410
0,300 3866 5479 70,560
0,350 3867 5479 70,579
0,365 3872 5479 70,670
0,370 3875 5479 70,725
0,375 3870 5479 70,633
0,385 3868 5479 70,597
0,400 3867 5479 70,579
0,450 3858 5479 70,414
0,500 3850 5479 70,268
0,600 3826 5479 69,830
0,700 3815 5479 69,629
0,800 3804 5479 69,429
0,900 3781 5479 69,009
1,000 3752 5479 68,480
1,500 3684 5479 67,239
2,000 3635 5479 66,344
Table 3. The degree of model consistency with the indicators of home field factor and the value of the spectators' impact on the result of the game
VS for 10,000 spectators K v ¿ [gj^rj r2 ) i—1 ¿ (g2i -VRjR2 ) i=\ PM RМ Degree of model consistency, %
0,100 1,290 10002,98 7754,90 3869 5479 70,615
0,200 1,179 9568,27 8116,24 3879 5479 70,798
0,210 1,169 9528,78 8151,13 3882 5479 70,852
0,2125 1,167 9519,01 8159,83 3883 5479 70,871
0,220 1,159 9489,92 8185,82 3879 5479 70,798
0,250 1,131 9376,92 8288,71 3874 5479 70,706
0,300 1,088 9199,51 8456,44 3863 5479 70,506
0,400 1,011 8879,47 8779,36 3867 5479 70,579
0,500 0,946 8597,11 9087,71 3851 5479 70,287
0,600 0,889 8344,84 9383,53 3838 5479 70,049
0,700 0,840 8117,18 9668,39 3838 5479 70,049
0,800 0,795 7910,02 9943,52 3826 5479 69,830
0,900 0,756 7720,23 10209,95 3820 5479 69,721
1,000 0,721 7545,31 10468,52 3825 5479 69,812
of 10000 spectators, the chances of winning increases by 1.37 times.
In the third variant of the calculation, we obtained the results of the application for the factor impact coefficients: own field and spectators (tab. 3).
As we can see from the obtained, results with the value vs = 0, 2125 per 10000 spectators and kv = 1.167, as the degree of model consistency was the maximum and it is equal to 70.871. The factor of the spectators
impact on the results of the matches is ks = 1.2125 per 10000 spectators. It means that together with the factor of the stadium's impact on the result of the game, that increases the chance of winning in 1.167 times, the impact of a number of spectators increases the chance of winning in 1.2125 times, if the team gathers on home field 10000 spectators.
Conclusion. The obtained data indicate the compliance of the proposed mathematical model and a
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possibility of the rating application for the evaluation of team performance and chances for success in the future tournaments in team sports.
A conclusion can be made that the influence of spectators on the results of teams' performance, as well as the choice of the venue of sports competitions are highly significant. Both factors have a direct impact on the motivation for the athletes, their level of the energy and activity, as well as psychological disposition for winning the competition, success and leadership. We believe that it is required to provide an integrated approach to the problem's solution for the psychological and pedagogical preparation of the athletes, both on the part of specialists-psychologists and on the part of coaches.
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