CONSTRUCTION OF AN EFFICIENT

EVALUATION MODEL FOR ATHLETIC

ATHLETES' COMPETITIVE ABILITY BASED

ON DEEP NEURAL NETWORK ALGORITHM

Yuhan Niu*

School of Human Settlements and Civil Engineering, Xi’an Jiaotong University,

Xi'an, Shaanxi, 710000, China - Xi'an Jiaotong University City College, Xi'an, Shaanxi,

710000, China

18602977530@163.com

Reception: 05/11/2022 Acceptance: 01/01/2023 Publication: 01/02/2023

Suggested citation:

N., Yuhan (2023). Construction of an efﬁcient evaluation model for athletic

athletes' competitive ability based on deep neural network algorithm. 3C

Empresa. Investigación y pensamiento crítico, 12(1), 111-131. https://doi.org/

10.17993/3cemp.2023.120151.111-131

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ABSTRACT

This paper analyzes the data of this year's athletes' physical fitness test scores and

manages the classification of different physical qualities of the farmer. In order to

reduce the manual calculation and increase the prediction efficiency, as well as to

unify the scoring criteria of previous years, this paper proposes a comprehensive

performance prediction model based on deep neural network algorithm. First, principal

component analysis is used to transform multiple attributes with strong correlation into

independent attributes that are not related to each other, and to reduce the time and

space for model training by eliminating redundancy. Second, a back propagation (BP)

neural network algorithm is used to build a physical fitness test prediction model, and

the model is applied to the test dataset for model performance evaluation. Finally, the

physical fitness test model was applied to other years for comprehensive performance

prediction, and the differences between the model prediction results and the actual

teachers' manual calculation results were observed. The results showed very good

prediction results for 2021, in which 92.95% of the data had an absolute value of error

less than 2 and only 0.06% had an absolute value of error greater than 4, which

indicated that the prediction performance of the model was extremely significant. At

the same time, a new athletic athletic scoring standard was also developed based on

the neural network BP model to provide a more scientific theoretical basis and

guidance for the evaluation of athletic ability of athletes.

KEYWORDS

BP neural network; athletic ability; track and field; prediction; evaluation

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PAPER INDEX

ABSTRACT

KEYWORDS

1. INTRODUCTION

2. RESEARCH METHODS AND MODELS

2.1. Key data processing theory

2.1.1. Data standardization

2.1.2. Data correlation analysis

2.1.3. Principal component analysis algorithm

2.2. BP neural network model optimization

2.2.1. Forward propagation of data

2.2.2. Error back propagation

3. RESULTS AND DISCUSSION

3.1. Validation of the physical test score prediction model

3.2. Application of physical test performance prediction model

3.3. Analysis of track and field scoring correction scheme

3.3.1. Scoring reasonableness analysis

3.3.2. Selection of scoring incremental functions

3.4. Neural network development of the allometric rating scale

4. CONCLUSION

REFERENCES

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1. INTRODUCTION

Athletics is a sport with a long history, with the largest number of gold medals in the

Olympic Games and the most widely practiced sport in the world [1, 2]. Therefore,

track and field is known as the mother of sports, and it plays a pivotal role in the

development of each sport. Track and field is the cornerstone of the Olympic

movement and best embodies the Olympic concept of "faster, higher, stronger". In the

2008 Beijing Olympic Games, China's athletes fought hard and achieved very

impressive results, ranking first in the world with 51 gold medals, 21 silver medals and

28 bronze medals, achieving a historic breakthrough and reflecting the strong strength

of a major sports nation. But at the same time, we should also clearly see that China's

track and field projects, such as men's 110m hurdles, women's middle and long

distance running, women's chain ball, etc. have been declared defeated in this

Olympic Games, which is a big regret for Chinese sports in this Olympic Games.

Athletics is an important constraint to the progress of Chinese sports from a large

sports country to a strong sports country [3]. For this reason, an ambitious goal of

Chinese sports in the post-Olympic era is to accelerate the pace of revitalizing

Chinese athletics and promoting the perfection of Chinese sports [4]. Athletics can be

studied from several perspectives, such as the study of competition performance.

Athletic performance is the result of athletes' participation in the competition, which is

the substantial reflection of athletes' comprehensive ability, especially the reflection of

athletic ability, and also the direct reflection of training results. The intuitive nature of

athletic performance fully demonstrates the results of coaches in the whole sports

training and competition activities, which is an objective criterion for scientific

diagnosis of training and competition results, as well as a basis for the implementation

of scientific training methods [4]. Therefore, the analysis of track and field results can

provide coaches with an objective basis for training control, which is of great

significance for the development of indoor track and field in China [5]. zheng et al.

used gray theory and methods to analyze the results of Chinese and foreign

outstanding decathletes by multi-level correlations, revealing the correlations between

total performance and speed, jumping, throwing, and endurance categories, between

each classification, and between total performance and each constituent item. Yu [6]

et al. compared and analyzed the factor loading matrices of the top 150 athletes in the

world in 2006, and concluded that the intrinsic factors limiting the development of the

athletes' performance were the relatively weak basic quality of the athletes, especially

the significant differences in the strength factor, and the overall low level. Chen [7]

established a multiple regression prediction model for decathlon based on the data of

the decathlon competition in track and field championships. The predicted values

extrapolated from the dynamic trends of athletes' performance in each individual sport

were highly correlated with the actual values with high accuracy and no variability.

Artificial neural networks, also known as neural networks, have their origin in

neurobiology [8, 9]. Neural networks, which are composed of a large number of nerve

cells, are a simplification, abstraction and simulation of the human brain [10].

Researchers have built artificial neural models by simulating the response processes

of nerve cells [11]. A neural network is a parallel interconnected network composed of

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simple units that can simulate the interactive responses of the biological nervous

system to the real world [12]. In recent years several studies have tried to apply neural

networks to sports and athletic ability analysis, i.e., to improve the original algorithm

combined with BP neural networks for modeling and combining it with practical

applications, mainly for prediction or evaluation of some indicators [13]. As yan et al.

provided a basis for the use of neural network modeling in biomechanics, opening a

wide prospect of research in this area. They explored the problem of generalized

inverse transformations of information in sports biomechanics by using neural network

techniques to model the transformation of the characteristic quantities and the original

information, taking shot put sports as an example.

The purpose of this paper is to trace the characteristics of various nonlinear

functions by analyzing each physical test ability of track and field athletes and the all-

around analysis standard published by IAAF, and then select the appropriate function

for progressive scoring, so that the progressive method is not constrained by the

average performance of athletes, i.e., it is universal. Based on the decathlon scoring

scale developed by the progressive scoring method, the scoring criteria were revised

based on the neural network method, and its good nonlinear mapping ability was used

to try to make the scoring of each item more scientific and reasonable. Based on the

successful establishment of the evaluation model of athletic ability of track and field

athletes, it provides help for athletes to develop targeted training plans.

2. RESEARCH METHODS AND MODELS

2.1. KEY DATA PROCESSING THEORY

2.1.1. DATA STANDARDIZATION

Along with the progress of human society, the fields of study that humans are

involved in have become more and more complex. In fact it has become very difficult

to describe things in detail using individual attributes, and it is necessary to consider

the problem from a holistic point of view, thus giving birth to the method of multi-

indicator evaluation. In the system of multi-indicator evaluation, there are different

units of attributes, and there are significant differences in magnitude and order of

magnitude between them. Therefore, it is necessary to standardize each attribute of

the original data, thus ensuring the reliability of the analysis results.

Currently, there are various methods of data standardization [14, 15], among which

the most typical method is data normalization, which is to map the data to the [0, 1]

interval uniformly. In this paper, the z-score standardization method is used to

standardize the athlete physical measurement data to eliminate unit restrictions and

dimensional relationships between variables and also to reduce the prediction time

and increase the prediction accuracy [15, 16]. z-score standardization is based on the

mean and standard deviation of the original data to standardize the data (Equation 1).

This standardization method mainly converts the original data into standard normally

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distributed data with mean 0 and variance 1, and is suitable for scenarios with large

data volumes.

where i is the original data, E() is the mean of the data, and 

is the standard

deviation of the data. The conversion of raw data into dimensionless evaluation index

values by standardization makes the values of each index at the same level and

facilitates the ability to sum weight attributes of different units or magnitudes.

2.1.2. DATA CORRELATION ANALYSIS

In today's era of big data, data correlation analysis can quickly and efficiently

discover the intrinsic connections that exist between different things [17, 18].

Correlation, which refers to the pattern that exists between two or more variables in

some sense, aims to explore the intrinsic information hidden in the data set. The

correlation coefficient can be used to describe the relationship between variables,

where the sign of the correlation coefficient indicates whether the direction of the

relationship is positive or negative, and the magnitude of its value represents the

strength of the relationship between the two variables, where the correlation

coefficient is 0 when there is no correlation at all and 1 when there is a perfect

correlation. There are various methods for calculating correlation coefficients in

correlation analysis, including Pearson correlation coefficient [19], Spearman

correlation coefficient [20], partial correlation coefficient [21], Kendall correlation

coefficient [22], and so on. In this paper, the Pearson correlation coefficient is used to

calculate the magnitude of correlation between the attributes. Standardization of the

original data does not change the correlation between the attributes of the original

data. Therefore, the standardized data can be used to directly calculate the correlation

between the attributes. The correlation coefficient is calculated as shown in Equation

where i and  are the data of the two attributes involved in the calculation, and 

and  are the mean values of the corresponding attributes.

2.1.3. PRINCIPAL COMPONENT ANALYSIS ALGORITHM

Principal component analysis is a commonly used technique for reducing the

dimensionality of a data set, allowing exploration and simplification of certain complex

(1)

E( )

x x

−

(2)

( )( )

( ) ( )

2 2

i i

x x y y

− −

∑

∑ ∑

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relationships between variables. It can transform several original variables with strong

correlation characteristics into several uncorrelated variables through coordinate

transformation, and the uncorrelated ones calculated as principal components. The

principal component is a linear combination of the original variables, and its model is

shown in Figure 1.

Figure 1 Principal component analysis (PCA) model

The principal components reflect most of the characteristics of the primitive

variables and can remove strong correlations between the primitive variables. The

principal components are linear combinations of the original variables. The first

principal component explains the most variance of the primitive variables, while the

second principal component explains the second variance of the original variables and

is orthogonal to the first principal component, which means it is completely

uncorrelated. By analogy, the remaining principal components are all orthogonal to

each other. Suppose, there exist  variables in the original data, namely 1, 2

,…,,

which are linearly combined to form a new 

mutually independent principal

component variable p

, whose mathematical model expression is shown in Equation

(3).

The model is changed into matrix form as shown in Equation (4):

PCA1

PCA2

(3)

1 11 1 12 2 1 1

2 21 1 22 2 2 2

1 1 2 2

i i p p

i i i ii i ip p

p p p pi i pp p

y x x x x

µ µ µ µ

= + + + + +

⎧

⎪= + + + + +

⎪

⎨= + + + + +

⎪

⎪= + + + + +

⎪

⎩

 



 



 

(4)

11 12 1 1

21 22 2 2

1 2

p p pp p

y Ux

µ µ µ

⎡ ⎤ ⎡ ⎤

⎢ ⎥ ⎢ ⎥

= =

⎢ ⎥ ⎢ ⎥

⎣ ⎦ ⎣ ⎦







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where the sum of squares of the principal component coefficients

 is 1, as

shown in Equation (5):

Next, to obtain the principal component values p

, the principal component

coefficients  are to be calculated, and first the covariance matrix is calculated from

the original data as shown in Equation (6):

Since the data have been standardized, then the variance 2 of the original data is 1

see equation (7), the

Changing equation (7) to equation (8), the

At this point, we can obtain equation (9)

From Equation (9), the correlation coefficient matrix of the original data is actually

equivalent to the covariance matrix. The eigenvalue i

of the covariance matrix

represents the variance of the principal components, while the eigenvalue of the

covariance matrix with the principal component coefficients p

is calculated from the

correlation coefficient matrix and the eigenvalue  is calculated by the formula  = .

Theoretically, a smaller number of principal components is selected to replace the

original full data based on the contribution of principal components, and the number of

principal components with a contribution of 90% is generally selected, but in this

paper, the same number of principal components as the number of original variables

will be selected, which does not throw away the information of the original data and

removes the influence of strong correlation between the original variables on the

model training. Next, the neural network model is built using eight new variables that

are not correlated with each other, which increases the persuasiveness of the model

accuracy and excludes the influence of the data itself factors on the model building

and parameter optimization.

2.2. BP NEURAL NETWORK MODEL OPTIMIZATION

(5)

2 2 2

1 2

i i ip

µ µ µ+ + + =

(6)

( )( )

cov

i i

x x y y

=− −

∑

(7)

( )

s x x

=−=

∑

(8)

( )

x x ns n

=−= =

∑

(9)

( )( )

( ) ( )

( )( )

1 1

2 2

1 1

cov

n n

i i i i

i i

n n

i i

x x y y x x y y

rn n

x x y y

= =

− − − −

= = =

− −

∑ ∑

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BP neural network as a part of neural network is a supervised learning algorithm

[23]. It is a multilayer nonlinear feedforward network trained by an error back

propagation learning algorithm. The network consists of an input layer, an implicit

layer and an output layer. The BP learning algorithm consists of two processes, a

forward propagation of the data and a backward propagation of the error signal.

2.2.1. FORWARD PROPAGATION OF DATA

The interconnection pattern between neural networks is formed by interconnecting

neurons, and the initial weights between each connection are randomly assigned by

the computer. The forward propagation phase of the data signal is the process of the

original data signal from the input layer through the implicit layer to the output layer,

i.e., the output of the upper layer nodes is used as the input of the lower layer nodes.

The basic structure of the forward propagation of the BP neural network is shown in

Figure 2.

Figure 2 Basic structure of forward propagation stage BP neural network

Figure 2 shows that each neuron cell i

has a corresponding computational weight

. The output value of the input layer in the hidden layer 1

is obtained by

summing and weighting the input values, connection weights and threshold k,

calculated as Equation (10) shows:

In the process of prediction, better prediction accuracy can be obtained by applying

activation function processing. There are many kinds of activation functions, such as

step function, Sigmoid function, tanh function, and ReLU function. In this project, the

Sigmoid function is used to activate the output information. The output value of the

input layer is activated by the activation function as (1k), then the implicit layer k is

obtained by Equation (11).

( )

(10)

1 1 2 2

k ik i k k k nk n k

net w y b w y w y w y b

= + = + + +

∑

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Next, the implicit layer data is passed to the output layer as an input layer. The

output value 2j is obtained from the weighted sum of the implied layer value and

the connection weight k between the implied layer and the output layer, plus the

threshold  as shown in Equation (12):

Equation (13) activates the output values to obtain the data of the final output layer.

2.2.2. ERROR BACK PROPAGATION

The error function is used to detect whether the training process of the neural

network is finished when the signal is passed to the output layer. The condition for the

neural network to stop is that the error function limit is satisfied or a set maximum

number of iterations is reached. When the output error function is less than the

predefined value, the training will stop. If the condition is not satisfied, the error will be

back-propagated. The error function (E) is used to measure the magnitude of the error

between the actual output j and the desired output , which is calculated as shown

in Equation (14).

The error signal obtained at each layer is used to adjust the weights of the

connections between neurons. Equation (3.15) simulates the process of error back

propagation.

The error is reduced along the gradient direction by continuously adjusting the

connection weights and thresholds. After calculating the change value ∆j of the

weight connection value between the implicit layer and the output layer, each

connection weight is updated as shown in Equation (16) and Equation (17).

(11)

( ) ( )

11 exp 1

k k

z f net net

= = +−

(12)

1 1 2 2

j kj k j j j nj n j

net v z b v z v z v y b

= + = + + +

∑

(13)

( ) ( )

net 2 1 exp 2

j j

o f net

= = +−

(14)

( )2

1 1

E ( )

2 2

j j

d o d o

=−=−

∑

(15)

( )2

1 1

E ( )

2 2

j j

d o d o

=−=−

∑

(16)

2 2

kj k

kj j kj j

net

E E E

v z

v net v net

η η η

∂

∂ ∂ ∂

Δ=−=−=−

∂ ∂ ∂ ∂

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Further extending the error to the input layer as in equation (18)

The connection weights between the input layer and the implied layer are updated

as shown in Eqs. (19) and (20).

After all the weights are readjusted, signal forward propagation will continue to be

executed. When the model reaches the convergence criterion, the training is stopped,

the model is built, and the model parameters are adjusted to optimize the model. The

established model is used to predict the physical fitness test data, and the error

magnitude between the predicted and actual values is calculated to verify the

feasibility of the model, and then the model is applied.

3. RESULTS AND DISCUSSION

3.1. VALIDATION OF THE PHYSICAL TEST SCORE

PREDICTION MODEL

The physical fitness test data were preprocessed and standardized, and principal

component analysis was used to eliminate strong correlations between the data. The

model was built using BP neural network after transforming the original data using

principal component analysis method. In this project, the physical fitness test data of a

provincial track and field team in 2019 were selected to build the model, in which 80%

of the athlete samples were used as the training set and the remaining 20% were

used as the test set to evaluate the model. The scoring criteria and methods for male

and female distance athletes are different, so the male and female distance athletes

test data were separated and separate models were built for prediction. The model

was continuously adjusted and optimized using 80% of the training set, and the final

model parameters are shown in Table 1.

(17)

kj kj kj

v v v= + Δ

(18)

( )

()( )

()

( )

1 1 1 1 1

1 1

2 2

n n n n n

j kj k j kj ik i

j k j k i

d f v z d f v f w y

= = = = =

=−=−

∑ ∑ ∑ ∑ ∑

(19)

(20)

1 1

ik i

ik k ik k

net

E E E

w y

w net w net

η η η

∂

∂ ∂ ∂

Δ=−=−=−

∂ ∂ ∂ ∂

ik ik ik

w w w= + Δ

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Table 1 The parameters of model

As shown in Table 1, the threshold value is used as a conditional value for training

stop, which specifies the predetermined value in the error function. The maximum

number of iterations forces the training to stop when the predetermined value is not

always reached and the iteration cannot be stopped. The algorithm used for training,

"rprop+", is the error back propagation algorithm with weights, also known as BP

neural network algorithm [24]. The error function "sse" is used to calculate the

magnitude of the error at the end of the forward propagation. The activation function

uses the parameter "logistic" for the Sigmoid activation function. Where the number of

neurons in the hidden layer is determined by the mean square error (MSE) with

equation (21).

Where  in equation (21) is the number of input neurons, 

is the number of output

neurons, and  is a constant in the range 1 to 10, so the number of hidden layers ℎ

takes values in the range 4 to 13.

In order to increase the accuracy of the model, prediction models for male and

female students were built separately, and the accuracy of the model was evaluated

using the data from the test set. The test set data that were not involved in the model

training process were brought into the model for prediction separately, and the

prediction results for both boys and girls were finally combined to observe the overall

model prediction performance. A sample of 40 athletes was randomly selected from

the test set of 2019 data, and the difference between the actual values of these 40

athlete samples and the predicted values of the model was compared as shown in

Figure 3. The line graph shown in Figure 3 shows the comparison between the

predicted and actual values of the randomly selected sample of 40 athletes in the test

set. The solid line is the actual value and the dashed line is the predicted value. It is

obvious that the two lines have a high overlap rate and only a few samples can be

Parameter Name Parameter Value

Number of neurons in the input layer 8

Number of neurons in the output layer 1

Number of neurons in the hidden layer 11

Threshold 0.005

Learning rate 0.1

Maximum number of iterations 1.0e10

Training algorithm rprop+

Error function sse

Activation function logistic

(21)

h m n α= + +

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viewed with significant errors. The results show that the prediction model established

in this project is very accurate and has good performance, and the value of mean

square error MSE of the model is 1.361713.

Figure 3 Comparison of predict data with actual data samples

3.2. APPLICATION OF PHYSICAL TEST PERFORMANCE

PREDICTION MODEL

After the performance evaluation of the model, the next step is to observe the

practical application of the model. In this paper, we chose to apply the model

developed from the 2019 athletes to the 2021 athletes to predict the overall

performance of the 2019 students, to better observe the changes in the overall

performance of the 2019 athletes under a uniform grading scale, and to observe the

actual application of the 2019 model in another year. The 2021 athletes' test scores

were pre-processed and standardized, and the strong correlation was reduced using

principal component analysis. The data of male and female students were separated

and brought into the model of male and female students built from the 2019 data

separately to obtain the model prediction results. The absolute values of the absolute

errors between the 20% test set of 2019 and the predicted results of 2021 data were

boxed into six intervals, [0,1), [1,2), [2,3), [3,4), [4,5), [5,∞

), and their distributions are

shown in Table 2.

0 5 10 15 20 25 30 35 40

Synthesis scores

Sample number

Actual data

Predict data

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Table 2 Percentage of absolute error distribution predicted by the model

established 2019 data

As shown in Table 2, the prediction results for 2021 are very good, in which 92.95%

of the data have an absolute error value less than 2, and only 0.06% have an absolute

error value greater than 4. This indicates that the prediction performance of the model

is very high. When the model built from the 2021 scoring criteria is applied to 2021,

the accuracy of the model prediction decreases, and the percentage of absolute error

distribution in the range of 0 to 1 decreases by 23.54%, but the overall prediction

result is still considerable. If the scoring criteria of previous years are strictly adhered

to, the model criteria of 2019 must be fully applicable to 2021, and the accuracy of the

model prediction will be very close to the prediction results of the 2019 test set, while

the significant decrease in prediction results indicates that there is a difference

between the scoring criteria of 2019 and 2021 due to human calculation.

This model was built based on data from 2019, and the weights between models

used the 2019 scoring criteria. When the 2019 scoring scale was used to predict the

2021 composite score, the results showed differences in the scoring scale. Apparently,

the scoring criteria for the composite scores of the physical fitness tests were not

uniform due to the manual involvement of the coaches in the calculations. The

different scoring standards in previous years resulted in the composite score of the

physical fitness test not accurately reflecting the changes in the basic physical fitness

of the farrier, and it was difficult to infer whether the physical fitness of the farrier had

improved or decreased over time, which obviously did not maximize the value of the

physical fitness test data from previous years. Using the model to predict the

composite score, the constant relationship between the measured item data and the

composite score is explored through the learning ability of the model, which can well

avoid the whole complicated process of traditional physical fitness test calculation

while saving the time of composite score calculation. It is necessary to use the model

for predicting the physical fitness test scores because it is possible to see the changes

in the physical fitness of the farriers more clearly by classifying them according to the

composite score levels after the uniform scoring criteria and combining the radar chart

visualization data information.

3.3. ANALYSIS OF TRACK AND FIELD SCORING CORRECTION

SCHEME

This section first analyzes the problems of the current decathlon scoring scale

published by the IAAF, then proposes our basic correction scheme and develops a

new scoring scale using the progressive scoring method and the neural network

model. Finally, the existing scoring scale, the scoring scale developed by the

[0,1) [1,2) [2,3) [3,4) [4,5) [5,∞)

2016 63.38 27.57 5.27 1.7 0.04 0.02

2019 39.84 28.16 15.71 8.06 4.06 4.17

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progressive scoring method, and the scoring scale developed based on the neural

network model are compared and analyzed, and finally a more scientific and

reasonable set of scoring scale is screened and determined.

3.3.1. SCORING REASONABLENESS ANALYSIS

As the level of all-around sports continues to improve, the more difficult it is to

improve, the more time and energy athletes pay, in order to motivate athletes and

promote the development of all-around sports performance to a higher level, so it

should be reflected and rewarded through the incremental value. That is, the all-

around performance of each single item from low to high points of the corresponding

coordinate points of the line, should be a positive parabolic type with the sports

performance and the score increases rapidly. At present, some of the projects with the

improvement of the level of sports, but the value of the corresponding linear growth

relationship, and even some of the project sports performance incremental rate is

gradually reduced.

Scoring from a low score loses its meaning in all-around sports competitions.

Because its score is too low and rarely used, then the score of that part of the

performance becomes unused and makes the score sheet too large. For example,

men's decathlon such as 100m starting point is 17.83s, shot put 1.53m, high jump

0.77m, pole vault 1.03m. Such results can be achieved for children and teenagers

with a little training, not to mention for adult professional athletes. If the scoring table is

also applicable to children and teenagers, but the IAAF decathlon is quite difficult, and

most of its individual events are beyond the physical ability of children and teenagers

due to competition conditions and equipment specifications, so a separate scoring

table should be developed to meet the needs of children and teenagers. Thus, it

seems that the IAAF scale has no meaningful use for children and teenagers.

Secondly, the scoring table has certain restrictions, and with the improvement of the

level of all-around sports, the scoring table must be constantly widened, but the wide

application of the object extends the minimum score of the scoring table, the result is

that the original scoring table is too wide to become even wider, making the scoring

table more massive, bringing difficulties to the reasonable preparation of the scoring

table, bringing trouble to the evaluation of the scoring table.

Some of the projects due to technical innovation, improvement of equipment, the

use of more scientific training methods and means, so that the level of sports to

improve quickly, while some of the projects training science and technology and

means development is slow, so that the difficulty of the individual scoring is not

balanced. In the decathlon, a more reasonable score should be equal or approximate

scores for different items of equal difficulty, so as to avoid some athletes to get good

results, too biased towards an easy to score items, thus not really promote the

development of the decathlon in the direction of the whole. For example, some

subjects can be achieved with a little training in a certain scoring section, while some

items require some effort.

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3.3.2. SELECTION OF SCORING INCREMENTAL FUNCTIONS

According to the progressive idea, with the improvement of sports performance, the

corresponding score should be increased sharply to encourage the improvement of

the sports level of excellent members. That is, sports performance at low levels and

high levels to improve the same interval, the increase in score should not be the

same, high levels because of the difficulty, the score increased more, the score should

be progressive trend with the improvement of performance. Next, we try to describe

this phenomenon by using mathematical functions to find out the correspondence

between grades and scores. In higher mathematics, monotonicity is actually the

portrayal of some functions when the self-varying process is the change of the

dependent variable from small to large changes in a given range when the change in

the dependent variable presents a special law. There are generally the following four

cases: ① from small to large ② from large to small ③ suddenly large and small ④

unchanged. Which has ①, ②

these two special laws of the function is an important

type of function - monotonic function. Therefore, the monotonicity of a function is a

concept used to describe the tendency of a function to change in a certain range. By

studying the monotonicity of the function can be reduced to the study of complex

functions to some of the more typical, simple types of functions. This phenomenon

can be described as monotonically increasing. A monotonically increasing

mathematical function can be used to implement the process of increasing.

Definition of increasing monotonicity: Let there be a function y=f(x), x is called the

independent variable and y is the dependent variable. If for any x1, x2 ∈

[a, b]

contained in M, if when x1 < x2, there is y1 < y2, that is, f(x1) < f(x2), y increases as x

increases, the image of the function rises from left to right, then f(x) is said to be

increasing on [a, b], said y is the increasing function on the interval, [ab] is called the

monotonic increasing interval of y = f(x). In the interval greater than 0, incremental

functions in the primary functions are power functions (such as y = xn), exponential

functions (such as y = ex), logarithmic functions (such as y = lnx), tangent functions

(such as y = tanx). The four types of functions are shown in Figure 4. From the figure,

we can see that as x increases, except for the tangent function, which increases

periodically, the y values of the other three types of functions increase to varying

degrees, with the exponential function growing the fastest, followed by the power

function, and the slowest being the logarithmic function. From Figure 4, we can see

that the tangent function periodically increasing, and even appear to calculate the y-

value appears negative, so it is not suitable for the development of the score table.

We chose the power function, exponential function, and logarithmic function to

participate in the initial fitting of the scoring table.

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Figure 4 Incremental function diagram

3.4. NEURAL NETWORK DEVELOPMENT OF THE ALLOMETRIC

RATING SCALE

Artificial neuronal network is a theorized mathematical model of the neural network

of the human brain, an information processing system based on imitating the structure

and function of the neural network of the brain [25, 26]. It is an artificially constructed

neural network capable of achieving certain functions based on the existing human

understanding of the neural network of the brain, which absorbs many advantages of

biological neural networks and thus has its special characteristics: (1) highly parallel

computing and distributed storage functions: artificial neural networks are composed

of many identical basic processing units grouped in parallel, and although the function

of each unit is simple, both each Although the function of each unit is simple, both the

small unit and the whole neural network have the dual capability of processing and

storing information, and these two functions are naturally integrated in the same

network, which makes its processing capability and effect on information amazing [27,

28]. (2) Highly nonlinear global action: An artificial neural network is a large-scale

nonlinear dynamical system in which each neuron can receive inputs from a large

number of other neurons and produce outputs that affect other neurons through

parallel networks. It has a strong nonlinear processing capability. Globally, the overall

performance of the network is not a simple superposition of local performance, but

some kind of collective behavior that exhibits the characteristics of complex nonlinear

dynamical systems in general [29]. (3) Good fault tolerance and associative memory

function: Artificial neural networks can store information in the weights between

1.0 1.5 2.0 2.5 3.0

-40

-30

-20

-10

y=e

y=lnx

y=x

y=tanx

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neurons, and through their own network structure can achieve memory of information.

This storage is distributed and the extraction of information is collaborative as a

whole, each information processing unit contains both a contribution to the collective

and cannot determine the overall state of the network, so a failure of the local network

does not affect the correctness of the overall network output, which makes the

network fault-tolerant [30].

From Figure 4, we can see that the exponential function and the power function are

more in line with our design purpose. Therefore, We take the starting and ending

points of the new scale initially formulated in the section, remove the ultra-low

achievement segments below the starting point, and remove the ultra-high score

segments above the stopping point, and use the exponential function and power

function to fit the simplified scale in origin9.0, and take the best fitting effect among the

many fitting results [31-32]. Then use the function with the best fit, still using the

interval of each score segment in the original score table, and bring the scores of the

original score table into the fitting function to find the corresponding score, which is

the result we get in this section using the progressive idea. The results of the optimal

exponential and power function fitting for each item are shown in Tables 3 and 4.

Table 3 Best-fit exponential function

Project Best-fit function

100m y=1+27583.7556*e(-0.3196*x)

Long Jump y=1+71.8068*e(0.3345*x)

Shot Put y=1+149.3857*e(0.1071*x)

High Jump y=1+43.2982*e(1.2941*x)

400 m y=1+17297*e(-0.0637*x)

110m hurdles y=1+10352.2147*e(-0.1258*x)

Discus y=175+27.1458*e(-0.0566*x)

Pole vault y=1+68.0512*e(0.4288*x)

Javelin y=135+38.4222*e(0.0528*x)

1500m y=1+13345.0214*e(-0.0208*x)

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Table 4 Best-fit power functions

4. CONCLUSION

In this paper, we propose a model for predicting the overall performance of physical

fitness test, and successfully apply the machine learning algorithms such as BP

neural network and principal component analysis to predict the overall performance of

physical fitness test. The following conclusions were obtained:

(1) The use of the prediction model for predicting the composite scores reduces the

calculation time of the scores and solves the problem of inconsistent scoring

standards due to manual calculation in previous years. The results show that the

prediction results for 2021 are very good, with 92.95% of the data having an absolute

value of error less than 2 and only 0.06% having an absolute value of error greater

than 4, which indicates that the prediction performance of the model is very high.

(2) In addition, this paper also explores the rationality of the athletics scoring

method, and by training the existing samples and building a BP neural network model

to obtain the expected output, the nonlinear relationship between the score and the

athletic performance is better resolved.

(3) By comparing the IAAF scoring scale, the exponential fitting scoring scale, and

the scoring scale based on the neural network model, it is shown that the neural

network scoring method is better than the former two in terms of scoring progressivity

and item balance.

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