Gray correlation analysis of physical training and competitive performance in tennis sports

As a beautiful and competitive sport, the unique charm of tennis has been widely sought after all over the world, and has been crowned as noble, elegant and civilized sports. As a sport that combines speed, strength, endurance, skill and strategy, tennis has high physical requirements for athletes [1-2]. As a key link to improve the athletes’ competitive level, the science and effectiveness of physical training directly affect the athletes’ performance [3]. In tennis, athletes need to have excellent cardiorespiratory endurance, strong strength and explosive force, agile speed and reaction, as well as good balance and stability, therefore, physical training occupies a pivotal position in tennis [4-6].

Tennis physical training focuses on simulating the actions and scenarios in actual matches, and emphasizes the coordinated work of all parts of the athlete’s body in order to enhance his or her core strength, balance, agility, and endurance, so as to make him or her more competitive in matches [7-10]. Through systematic strength training, tennis players can enhance their leg strength so that they can exert faster movement speed and higher jumping ability to better cope with various emergencies on the court [11-13]. Coordination and flexibility training helps athletes to better control their technical movements during matches, which in turn improves the stability and accuracy of their techniques [14-16]. In addition, endurance is a key factor for tennis players to maintain stable performance during the match [17]. Aerobic endurance training mainly improves the cardiorespiratory function and oxidative metabolism of athletes through prolonged moderate-intensity exercise, so that they can maintain a high level of exercise for a long period of time during the game [18-20]. Analyzing the correlation between physical training and competitive performance in tennis sports and adjusting the training program in time is particularly important for improving athletes’ competitive performance.

Tennis sport is a physical dominant endurance program, and the level of physical fitness is crucial to the competitive performance of tennis athletes. In this paper, we firstly choose the gray correlation analysis method, for the defects of the gray correlation analysis method in the global measure, combine it with the TOPSIS method which can choose the best global solution, and construct the TOPSIS-gray correlation analysis model. Subsequently, the model was used to correlate and analyze the test results of 170 athletes in the general and excellent tennis groups in a provincial training camp on the indicators of body form, function and quality, and thus analyzed the nine indicators of physical fitness that have a greater impact on the performance of various specialties. Based on the nine indicators, a set of physical training and competitive performance analysis model was established for the general and excellent tennis players. Combined with the analytical model, this paper develops the physical fitness structure model scoring table for tennis athletes.

2

Gray correlation analysis model construction based on TOPSIS method

Gray correlation analysis is a method of decision-making by determining the degree of correlation between the alternative and the ideal program, it is based on the relevant factors between the two programs over time or the object of constant change, by examining the alternative and the preferred program of the time series curve changes to determine the degree of correlation between the two. This analysis has certain application limitations, it can only measure the correlation between the same factors of each program, and cannot be comprehensively measured. On the other hand, the TOPSIS method is able to rank the alternatives by comparing them with the ideal and negative ideal alternatives to select the best alternative. In this paper, we try to combine the TOPSIS method and gray correlation analysis to construct an improved gray ideal value approximation model.

2.1

Deficiencies and Improvements in Gray Correlation Analysis Methods

Gray system theory provides an index quantitative metric for project preference decision-making, and the numerical relationship of the same factors between the options is derived by performing gray correlation analysis.

2.1.1

Gray correlation analysis methods

In this paper, the tennis player physical fitness index weights are established by applying to the method of gray correlation analysis, and the model is as follows:

1)

Establish the index matrix. $A = {[x_{i j}]}_{m \times n}$ , m is the number of preferred items, n is the number of indicators, and the weight of each indicator is W = (w₁, w₂, w₃,………w_n).

2)

Assigning weights on the basis of indicator matrix A and constructing weight matrix B : B = AN.

3)

According to the weight index matrix can be obtained positive and negative ideal program a⁺ and a⁻.

4)

The formula for calculating the correlation between each program and the positive and negative programs is shown in equation (1): (1) $L_{i j} = \frac{\min_{i} \min_{j} | a_{0 j} - a_{i j} | + θ \max_{i} \max_{j} | a_{0 j} - a_{i j} |}{| a_{0 j} - a_{i j} | + θ \max \max_{j} | a_{0 j} - a_{i j} |}$

L_ij is the correlation coefficient of a_i for a₀ at point j. The correlation coefficient takes the value of [0,1], which indicates the similarity of the two factors being compared at a certain point in time. In the formula θ for the resolution coefficient, said to weaken the maximum absolute difference value is too large caused by the distortion, θ of the range of [0,1], according to empirical values, θ generally take the value of 0.5, i = 1,2,⋯, m ; j = 1,2,⋯, n. The overall correlation of the program is the average value of the correlation coefficient of each type of

The average value of the correlation coefficient is: $R_{i} = \frac{1}{n} \sum_{j = 1}^{n} L_{i j}$

5)

The formula for the relative closeness of each scheme to the ideal party is given in equation (2): (2) $r_{i} = \frac{R_{i}^{+}}{R_{i}^{+} + R_{i}^{-}}$

6)

The option with the largest relative closeness is the optimal option, and the alternatives can be ranked according to the size of the closeness.

2.1.2

TOPSIS method

This year, gray correlation analysis has been developing in the fields of social sciences, economic management and natural sciences, and has been combined with other related principles and methods in system science to make it widely used. It is used as a technical analysis tool to quantify, visualize and serialize the unclear grey relations in the operation mechanism and physical prototype by establishing a grey correlation analysis model. However, gray correlation analysis also has certain application limitations, it can only measure the correlation between the same factors of each scheme, and compare the correlation degree of each scheme to the same reference sequence according to the closeness of the factors. Therefore, relying solely on gray correlation analysis to make decisions on project selection is not comprehensive, and another method needs to be applied to improve its shortcomings, and the method used in this paper is the TOPSIS method based on gray correlation analysis.

TOPSIS (superiority and inferiority distance method) is a multi-attribute, multi-objective decision-making evaluation method, which derives its core viewpoint from the research on discrimination in the theory of multivariate statistical analysis, and is a method of optimization that approaches the ideal point. By ranking the advantages and disadvantages of the evaluation object by the proximity of the evaluation object to the ideal goal, the first step determines the positive ideal program and negative ideal program of the evaluated object, and uses this as a criterion for the comparison of other programs. The second step will be evaluated by the program or object one by one in order to compare with the positive and negative ideal program, if an evaluation object or program is closer to the positive ideal program and farther away from the negative ideal program, it can be judged that the evaluation program is the optimal program, and so on according to the degree of proximity to the program sorting. The specific calculation steps are as follows: 1)

Assuming that there is n evaluated program, each of which has m evaluation indicators, X_ij represents the original value (i = 1,2,…, m; j = 1,2, …, n) corresponding to the i th evaluation indicator of the j th evaluation program, and the original matrix is established as shown in equation (3). (3) $X = [\begin{matrix} x_{11} & \dots & x_{i j} & \dots & x_{1 n} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ x_{i 1} & \dots & x_{i j} & \dots & x_{i n} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ x_{m 1} & \dots & x_{m j} & \dots & x_{m n} \end{matrix}] = {(x_{i j})}_{m \times n}$

2)

Normalize the raw indicator values to obtain the processed matrix as equation (4) (4) $Z = [\begin{matrix} Z_{11} & \dots & Z_{1 j} & \dots & Z_{1 n} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ Z_{i n} & \dots & Z_{i j} & \dots & Z_{i n} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ Z_{m 1} & \dots & Z_{m j} & \dots & Z_{m n} \end{matrix}] = {(Z_{i j})}_{m \times n}$

3)

Determine the positive and negative ideal scenarios for the evaluation program as equations (5) and (6) (5) $Z^{+} = {Z_{j}^{+} | Z_{j}^{+} = \max_{1 \leq 1 \leq m} Z_{i j}, j = 1, 2, \dots, n}$ (6) $Z^{-} = {Z_{j}^{-} | Z_{j}^{-} = \min_{1 \leq 1 \leq m} Z_{i j}, j = 1, 2, \dots, n}$

4)

Calculate the distance from each evaluation program to the positive and negative ideal programs $D_{i}^{+}$ , $D_{i}^{-}$ for equations (7), (8) (7) $D_{i}^{+} \sqrt{\sum_{j = 1}^{n} {(Z_{i j} - Z_{j}^{+})}^{2}} (i = 1, 2, \dots, m; j = 1, 2, \dots, n)$ (8) $D_{i}^{-} \sqrt{\sum_{j = 1}^{n} {(Z_{l j} - Z_{j}^{1})}^{2}} (i = 1, 2, \dots, m; j = 1, 2, \dots, n)$

5)

Calculate the degree of resolution of each evaluation program with the ideal program, i.e., the closeness C_i as equation (9) (9) $C_{i} = \frac{D_{i}^{-}}{D_{i}^{+} + D_{i}^{-}}$

The closer the final result C_i value is to 1, the closer the evaluated scheme is to the optimal scheme Euclidean clustering, and the better the comprehensive evaluation results are, from which the priority ranking of each evaluation scheme can be obtained.

2.2

Constructing the TOPSIS-gray correlation analysis model

1)

Construct a weighted standardized decision matrix as in equation (10): (10) $t_{i j} = y_{i j} w_{i} (i = 1, 2, \dots, m; j = 1, 2, \dots, n)$

Obtain the weighted normalized matrix T = (t_ij)m×n

2)

Determine the positive and negative ideal solutions of the weighted normalization matrix T = (t_ij)m×n. The positive ideal solution T⁺ is equation (11): (11) $T^{+} = (t_{1}^{+}, t_{2}^{+}, \dots, t_{j}^{+}) = {maxt}_{j}$ where $t_{j}^{+}$ - takes the maximum value in t_j, i.e. maxt_j.

The negative ideal solution T is Eq. (12): (12) $T^{-} = (t_{1}^{-}, t_{2}^{-}, \dots, t_{j}^{-}) = 0$ Where $t_{j}^{-}$ equation - take the t_j smallest value, i.e. 0.

3)

Calculation of Euclidean distance

The Euclidean distance $d_{i}^{+}$ of each scheme to the positive ideal solution T⁺ is equation (13): (13) $d_{i}^{+} = \sqrt{\sum_{j = 1}^{n} {(t_{i j} - t_{j}^{+})}^{2}}$

The Euclidean distance $d_{i}^{-}$ from each scheme to the negative ideal solution T is equation (14): (14) $d_{i}^{-} = \sqrt{\sum_{j = 1}^{n} {(t_{i j} - t_{j}^{-})}^{2}}$

4)

Calculate the gray correlation coefficient matrix between each scheme and the positive and negative ideal solutions.

The gray correlation coefficient matrix between each scheme and the positive ideal solution $R^{+} = {(r_{i j}^{+})}_{m \times n}$ is equation (15): (15) $r_{i j}^{+} = \frac{\min_{i} \min_{j} | t_{j}^{+} - t_{i j} | + λ \max_{i} \max_{j} | t_{j}^{+} - t_{i j} |}{| t_{j}^{+} - t_{i j} | + λ \max_{i} \max_{j} | t_{j}^{+} - t_{i j} |}$ Where λ - the discrimination coefficient, λ ∈ (0,1), is taken as λ = 0.5.

The matrix of gray correlation coefficients between the schemes and the negative ideal solution $R^{-} = {(r_{i}^{-})}_{m \times n}$ is Eq. (16): (16) $r_{i j}^{-} = \frac{\min_{i} \min_{j} | t_{j}^{-} - t_{i j} | + λ \max_{i} \max_{j} | t_{j}^{-} - t_{i j} |}{| t_{j}^{-} - t_{i j} | + λ \max_{i} \max_{j} | t_{j}^{-} - t_{i j} |}$ Where λ - discrimination coefficient, λ ∈ (0,1), take λ = 0.5.

5)

Calculate the gray correlation coefficients between different sports quality indicators and positive and negative ideal solutions.

The gray correlation coefficient $r_{i}^{+}$ of different sports quality indicators is equation (17): (17) $r_{i}^{+} = \frac{1}{n} \sum_{j = 1}^{n} r_{i j}^{+}$

The gray correlation coefficients $r_{i}^{-}$ of different sport quality indicators with negative ideal solutions are equation (18): (18) $r_{i}^{-} = \frac{1}{n} \sum_{j = 1}^{n} r_{i j}^{-}$

6)

The Euclidean distances $d_{i}^{+}$ and $d_{i}^{-}$ are dimensionless as in Eqs. (19), (20): (19) $D_{i}^{+} = \frac{d_{i}^{+}}{\max d_{i}^{+}}$ (20) $D_{i}^{-} = \frac{d_{i}^{-}}{\max d_{i}^{-}}$ Where $D_{i}^{+}$ - The larger the value the further away from the positive ideal solution;

$D_{i}^{-}$ - the larger the value the closer to the positive ideal solution.

7)

Gray correlation coefficients $r_{i}^{+}$ and $r_{i}^{-}$ are dimensionless, as shown in equations (21) and (22). (21) $R_{i}^{+} = \frac{r_{i}^{+}}{\max r_{i}^{+}}$ (22) $R_{i}^{-} = \frac{r_{i}^{-}}{\max r_{i}^{-}}$

Where $R_{i}^{+}$ - The larger the value the closer it is to the positive ideal solution;

$R_{i}^{-}$ - the larger the value the further away from the positive ideal solution.

8)

Seek a synthesis reflecting the closeness of the solution to the positive and negative ideal values $S_{i}^{+}$ and $S_{i}^{-}$ .

Degree of closeness to the ideal solution $S_{i}^{+}$ as equation (23): (23) $S_{i}^{+} = α D_{i}^{-} + β R_{i}^{+}$

The degree of deviation $S_{i}^{-}$ from the ideal program is equation (24): (24) $S_{i}^{-} = α D_{i}^{+} + β R_{i}^{-}$ Where α - indicates the degree of preference of the decision maker for location;

β - represents the degree of preference of the decision maker for shape.

The above parameters α, β have the following characteristics, α + β = 1, and α, β ∈ (0,1). The values of α and β are all taken as 0.5 according to experience in general.

9)

Calculate the relative closeness of physical evaluation as $Q_{i}^{+}$ , as in equation (25): (25) $Q_{i}^{+} = \frac{S_{i}^{+}}{S_{i}^{+} + S_{i}^{-}}$

The larger the corresponding composite closeness $Q_{i}^{+}$ of the program is, the better the program is; the smaller the corresponding composite closeness $Q_{i}^{+}$ is, the worse the program is.

In summary, this paper constructs an improved gray correlation analysis model based on the TOPSIS method: the TOPSIS-gray correlation analysis model, which is then used to analyze the gray correlation between physical training and competitive performance of tennis athletes in a certain province.

3

Analysis of the association between physical training and competitive performance in tennis players

The 170 male tennis players aged 12 to 17 years old who participated in the 2017 National Tennis Sports Talent Base Training Camp were used as test subjects. The principle and basis of grouping are: the grouping of tennis competitive performance scores, the excellent group for athletes whose tennis competitive performance scores are at the national level of Grade 2 and above, and the ordinary group for athletes whose tennis competitive performance scores are below the national level of Grade 2 and above the national level of Grade 3. As shown in Table 1, it is the specific situation of the grouping of athletes in this test. There were 51 athletes in the excellent group, with the height range of 178.04 ± 5.92cm, weight range of 66.18 ± 5.45kg, and the score range of tennis performance at 93.13 ± 2.62. There were 119 athletes in the general group, with the height range of 172.25 ± 7.96cm, weight range of 58.29 ± 8.69kg, and the score range of tennis performance at 89.13 ± 2.62. Athletic performance score interval was at 89.93 ± 3.32.

Table 1.

Young men’s tennis players performance group

Index	Outstanding group	General group	t	P
Height (cm)	178.04 ± 5.92	172.25 ± 7.96	2.067	0.045
Weight (kg)	66.18 ± 5.45	58.29 ± 8.69	4.870	0.000
Tennis competitive performance	93.13 ±2 .62	89.93 ± 3.32	-9.209	0.000
Number of people (N)	51	119

In 2017 (August 2-August 28) in a province, 170 young male tennis sportsmen who participated in the National Tennis Sports Talent Base Training Camp were tested for body morphology, function, and quality indicators.

1)

Physical morphology test: the height, weight, lower limbs A and B, calf length A, Achilles tendon length, shoulder width, iliac width, thigh circumference, and ankle circumference indexes were tested on the subjects using a height and weight meter, Martin’s ruler, and standard tape measure.

2)

Physiological function test: using electronic spirometer (FCS-10000 type), EP105 type metronome, POLAR FT4 meter, stopwatch, blood collection consumables (blood collection needle, vacuum blood collection tube) for the subjects to test lung capacity, cardiac function index and blood biochemical indexes collection.

3)

Physical fitness test: using stopwatch, 2 kg solid ball, steel ruler, tape measure, 5 M long rope ladder (ten frames), seated forward bending tester, Kistler three-dimensional dynamometer table (Type:9281EA, No:4432230), and 40 cm jumping box, subjects were tested for 30 M running, 60 M running, 100 M running, 150 M running, backward throwing solid ball, standing long jump, Vertical triple jump, CMJ:squat jump without swinging arm, 40 cm DJ:40 cm deep jump high jump, seated forward bending, running rope ladder 1 (1 step, 1 frame), running rope ladder 2 (2 steps, 1 frame).

3.1

Gray correlation analysis between physical fitness index and special performance

Exploring the relationship between the main indicators reflecting the physical fitness level of tennis athletes in a certain province and the special performance, in order to distinguish the size of the contribution of each indicator in the special performance, can be reflected by the weight of the indicators. The establishment of weight coefficients can deepen the understanding of the relationship between indicators and sports performance, correctly recognize the contribution of each factor of athletes’ physical fitness to the size of the special performance, and help to make a comprehensive evaluation of athletes’ physical fitness characteristics, so as to provide scientific theoretical basis for sports training and scientific selection of athletes.

Table 2 shows the gray correlation results of nine physical fitness indicators of tennis players in a province. As shown in Table 2, the gray correlation between each index and special performance is ranked: X9>X5>X2>X1>X7>X6>X8>X3>X4. The 150m run, 60m standing start, 30m marching run, standing triple jump, and standing 10th long jump are ranked first, second, fifth, sixth, and seventh in the 10th long jump, and their correlation with the special results is: 0.9875, 0.9809, 0.9328, 0.9154, 0.9127, and the arm length, weight/height reflecting the body form are ranked third and fourth, and their correlation with the special results is: 0.9608, 0.9385. Blood testosterone and serum creatine kinase, which reflect physiological functions, were ranked: eighth and ninth, and their correlation with specialized performance was: 0.8678 and 0.8084.

Table 2.

The processing results of gray correlation degree of nine indexes

Serial number	Index	Grey correlation degree	Associated sequence number	Weight
1	Weight/height	0.9395	4	0.1135
2	Arm length	0.9658	3	0.1152
3	Serum testosterone	0.8675	8	0.1040
4	serum creatine kinase	0.8075	9	0.0968
5	60m standing start	0.9885	2	0.1176
6	Standing triple jump	0.9150	6	0.1097
7	30m run in between	0.9325	5	0.1198
8	Set the level 10 long jump	0.9125	7	0.1095
9	150m run	0.9870	1	0.1189

Through the weight analysis of each factor, among the categorical indicators, the sports quality contributes the most to the special performance, which complements the characteristics of the tennis sports program. Among the five quality indicators, 150m running and 60m standing start ranked first and second among the nine physical fitness indicators. The high front ranking of these two indicators shows that male tennis athletes in a certain province must have good speed endurance quality and absolute speed quality in order to achieve excellent results. Morphological indicators arm length and weight/height ranked third and fourth before the functional indicators, indicating that tennis nowadays requires athletes to have a high degree of morphological specialization. The inclusion of arm length suggests that we should try to select athletes with longer arms and innate advantages. The length of the arm is favorable to the swing of the racket of the athlete. The inclusion of the weight/height indicator also suggests that relative weight is quite important for tennis sports players. The two function indicators, blood testosterone and serum creatine kinase, ranked eighth and ninth, respectively, and the selection of blood testosterone also indicates the importance of explosive power in tennis, and serum creatine kinase is one of the key enzymes in the functional metabolism of the ATP ~ CP system, suggesting that we should pay special attention to strengthening the training of the metabolic level of the muscle anaerobic capacity of the athletes.

The weight of the physical fitness classification index of men’s tennis players in a province is very small, and the athletic quality (R=0.5695)> physical form (R=0.2287) > physiological function (R=0.2018), reflecting that the physical fitness level of men’s tennis players in the province is based on sports quality as the core, physical form and physiological function, and the function and form of athletes must be effectively transformed into quality in order to effectively achieve the purpose of physical training.

3.2

Characterization and hierarchical modeling of physical fitness structure

In this paper, by analyzing and screening the input values of the indicators in the physical fitness test in the TOPSIS-gray correlation analysis model, nine indicators that effectively reflect the physical fitness level of men’s tennis athletes in a certain province are structurally determined. These indicators reflect the basic requirements of the program for the physical fitness of male tennis athletes in a province, which are mainly reflected in the three aspects of body shape, physiological function and sports quality. The establishment of the physical fitness structure model characteristics of male tennis players is a prerequisite for the realization of scientific selection and training of athletes’ physical fitness, which has important theoretical and practical value for the scientific selection and training of male tennis athletes in a certain province. As shown in Table 3, the nine indicators and their weight coefficients of physical fitness level of male tennis athletes in a province are shown. As can be seen from the table, the top three selection standards for male tennis athletes in this province are: 150-meter run at 16.39 ± 0.17 seconds, 60-meter standing at 6.82 ± 0.61 seconds, and arm length at 77.62 ± 1.94 centimeters.

Table 3.

Structural characteristics and hierarchical model of excellent group

Physical structure	Index	Eigenvalue (X±S)	Weight coefficient	Sort
Sport quality	150m run	16.39 ± 0.17	0.1185	1
	60m standing start	6.82 ± 0.61	0.1176	2
	30m run in between	2.79 ± 0.27	0.1128	5
	Standing triple jump	9.39 ± 2.68	0.1097	6
	Set the level 10 long jump	32.09 ± 0.42	0.1095	7
Body shape	Arm length	77.62±1.94	0.1152	3
Body shape	Weight/height	0.48 ± 0.11	0.1125	4
Physiological function	Serum testosterone	564.11 ± 107.25	0.1040	8
Physiological function	Serum creatine kinase	192.15 ± 111.4	0.973	9

3.3

Structural Model of Physical Fitness Rating Scale

In order to diagnose the individual fitness level of male tennis athletes, we need to develop a unified standard to evaluate them based on the performance of different groups in the test, in order to reflect the fitness level more objectively and quantitatively. In this study, the percentile method was used to develop the scoring standard for individual indexes. The steps are as follows: ① Use the software SPSS17.0 to find out the 4 percentile points of each index of the special performance and physical fitness structure model: P10, P25, P75, P90; ② Different score intervals based on four different percentile points (below P10, P10 to P25, P25 to P75, P75 to P90, and above P90); ③ Based on the above five different intervals, the following five grades were determined: inferior, lower middle, medium, upper middle and superior; ④ The scores for each indicator level follow the principle of “lower: lower middle: middle: upper middle: upper = 20:40:60:80:100”; ⑤ Combine the weighting coefficients of each indicator and calculate their scores at different levels; ⑥ Based on the above steps, develop individual scoring scales for the physical fitness structure model for the excellent and average groups of male tennis sports players, respectively. Individual score of each index = grade score × weighting coefficient. The criteria for the individual scores of the fitness structure model of tennis sports players in the excellent and ordinary groups are shown in Tables 4 and 5.

Table 4.

Individual rating table for outstanding group athletes

	Inferior Less than 10%	Lower middle 10%~25%	Medium 25%~75%	Better than average 75%~90%	First-class More than 90%
150m run(s)	16.39	16.22~16.39	16.00~16.22	15.78~16.00	15.78
Score	1.72	3.33	4.82	6.63	7.98
60m standing start(s)	7.43	6.82~7.43	6.21~6.82	5.60~6.21	5.60
Score	1.62	3.12	4.78	6.39	7.49
30m run in between	3.06	2.80~3.06	2.54~2.80	2.28~2.54	2.28
Score	1.78	2.31	3.21	3.56	4.85
Standing triple jump(m)	9.39	9.39~12.07	12.07~14.75	14.75~17.43	17.43
Score	1.58	2.97	4.73	5.94	7.66
Set the level 10 long jump(m)	32.09	32.09~32.51	32.51~32.93	32.93~33.35	33.35
Score	1.52	3.02	4.25	5.87	7.63
Arm length	77.62	77.62~79.56	79.56~81.5	81.5~83.44	83.44
Score	1.62	3.33	4.54	6.25	7.98
Weight/height	0.48	0.48~0.59	0.59~0.70	0.59~0.70	0.70
Score	1.54	2.96	4.54	5.77	7.42
Serum testosterone(ng/dl)	456.92	456.92~564.17	564.17~671.36	671.36~778.61	778.61
Score	1.74	3.38	4.86	6.47	8.31
Serum creatine kinase(U/L)	192.17	192.17	192.17~304.1	304.1	304.1
Score	1.56	3.24	4.85	6.25	7.76

Table 5.

Individual rating table for general group athletes

	Inferior Less than 10%	Lower middle 10%~25%	Medium 25%~75%	Better than average 75%~90%	First-class More than 90%
150m run(s)	16.73	16.39~16.56	16.22~16.39	16.00~16.22	16.00
Score	1.62	3.25	4.78	6.52	7.89
60m standing start(s)	8.65	7.43~8.04	6.82~7.43	6.21~6.82	6.21
Score	1.58	3.04	4.75	6.33	7.45
30m run in between	3.32	3.06~3.32	2.80~3.06	2.54~2.80	2.54
Score	1.56	1.98	2.41	3.03	3.76
Standing triple jump(m)	6.71	6.71~9.39	9.39~12.07	12.07~14.75	14.75
Score	1.51	2.97	4.68	5.83	7.36
Set the level 10 long jump(m)	31.67	31.67~32.09	32.09~32.51	32.51~32.93	32.93
Score	1.38	2.98	4.37	5.69	7.52
Arm length	75.68	75.68~77.62	77.62~79.56	79.56~81.5	81.5
Score	1.52	3.13	4.68	6.38	7.95
Weight/height	0.37	0.37~0.48	0.37~0.48	0.48~0.59	0.59
Score	1.45	2.94	4.56	5.78	7.43
Serum testosterone(ng/dl)	456.92	456.92~564.17	564.17~671.36	671.36~778.61	778.61
Score	1.74	3.38	4.86	6.47	8.31
Serum creatine kinase(U/L)	192.17	192.17	192.17~304.1	304.1	304.1
Score	1.56	3.24	4.85	6.25	7.76

Table 6 shows the superiority and inferiority values of the specific subordinate indicators of each system level, from which it is possible to judge and analyze the posture of the three system levels and the specific indicators of the composition of athletes’ physical fitness in different groups. In this study, the score advantage value = mean + standard deviation and score disadvantage value = mean - standard deviation were used in the posture analysis. As shown in the table, in the excellent group, the best performance was 15.78 seconds for 150 meter run, 5.60 seconds for 60 meter standing style run and 83.44 cm for arm length. In the average group, the worst performance in the 150-meter run was 16.73 seconds, the worst performance in the 60-meter standing run was 8.65 seconds, and the worst performance in arm length was 75.68 centimeters. Combining the different performances of the three indexes of 150-meter run, 60-meter standing run and arm length in the excellent group and the ordinary group, a preliminary judgment can be made on the athletes’ competitive performance.

Table 6.

The advantages and disadvantages of individual indicators of physical fitness

	Outstanding Group			General group
	Dominance value	Disadvantageous value		Dominance value	Disadvantageous value
150m run	15.78	16.39	150m run	16.00	16.73
60m standing start	5.60	7.43	60m standing start	6.21	8.65
30m run in between	2.28	3.06	30m run in between	2.54	3.32
Standing triple jump	17.43	9.39	Standing triple jump	14.75	6.71
Set the level 10 long jump	33.35	32.09	Set the level 10 long jump	32.93	31.67
Arm length	83.44	77.62	Arm length	81.5	75.68
Weight/height	0.48	0.70	Weight/height	0.37	0.59
Serum testosterone	778.61	456.92	Serum testosterone	778.61	456.92
Serum creatine kinase	304.1	192.17	Serum creatine kinase	304.1	192.17

4

Conclusion

By using the TOPSIS-grey correlation analysis model constructed by combining the grey correlation analysis method and the TOPSIS method, the physical fitness test results of athletes in the excellent group and the ordinary group of tennis sports training camp in a certain province were analyzed, and it was found that the nine physical fitness test indicators affecting the competitive performance of tennis athletes from high to low were: 150m run, 60m standing start, arm length weight/height, 30m running between marches, standing triple jump, standing 10 long jump, blood testosterone, and serum creatine kinase. Five of the nine indicators belong to the specialization of sports quality, and the 150m run and 60m standing start are the top two indicators in this specialization. That is to say, in the physical training for improving the athletic performance of tennis players, sports quality training should be the core.

The nine physical fitness indicators established in this paper are used to construct a set of physical fitness structure characteristics and hierarchical model of tennis players, and based on the performance of different groups in the test to develop the model scoring table, scoring standards, the advantages and disadvantages of the indicators of different groups, which is expected to be able to provide reference for the scientific selection of tennis athletes and effective training in the future.

Langue:: Anglais

Périodicité:: 1 fois par an
Sujets de la revue:: Sciences de la vie, Sciences de la vie, autres, Mathématiques, Mathématiques appliquées, Mathématiques générales, Physique, Physique, autres

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Gray correlation analysis of physical training and competitive performance in tennis sports

Jieqiong Chen

Publié en ligne: 19 mars 2025

Reçu: 23 oct. 2024

Accepté: 13 févr. 2025

DOI: https://doi.org/10.2478/amns-2025-0534

Mots clésTennis sports, Gray correlation analysis: TOPSIS method, Physical fitness structure

© 2025 Jieqiong Chen, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Tennis sports, Gray correlation analysis: TOPSIS method, Physical fitness structure