# Markov Model-Based Sports Training Risk Prediction Model Design and Its Training Control

Authors: Haibin Huang; Shaofei Wen
Journal: Journal of Sensors
 (2022)

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## Abstract

With the improvement of living standard, people gradually start to pay attention to physical health and figure maintenance, and sports training also gradually becomes a hot issue for people. Sports training can help people develop a healthy body and cultivate a persevering spirit, which can be of great help in all aspects of people’s development, but sports training also has a certain degree of risk, and only a reasonable response can make sports training give maximum value. In this paper, a Markov model is established, a probability transfer matrix is calculated, and this matrix is used to predict the risks arising from sports training since the statistical decade, and the risks of sports training in the next three years are predicted, and some suggestions are made for how to minimize and avoid the risks.


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## Body

## 1. Introduction

Physical training refers to a physical activity training that is aimed at physical and mental recreation, physical strengthening, health maintenance, and physical development by means of a variety of sports, combining health measures and natural forces such as air, water, and sunlight, and is a training that strengthens people’s bodies, develops their perseverance and character, and helps them learn skills, not only for military personnel but also for all kinds of people who want to strengthen their bodies and sharpen their will which has an important significance. With the improvement of living standards, people’s requirements for health are also getting higher and higher, and people begin to pursue a healthy body, a fit body; sports training activities also came into being; sports training can not only help people learn sports knowledge, exercise, and strengthen their bodies but also promote the metabolism of the cardiovascular system and respiratory system and other body functions and organs, more cultivate people’s willpower, and make people become happy, and it also promotes the development of mental health [1].The Markov model is a statistical model with a wide range of applications in the fields of speech and word recognition and identification, model prediction and analysis, and engineering design and manufacturing. The Markov model is a large concept; from the definition and nature of the model, stochastic processes or stochastic models with Markov properties and based on stochastic processes are collectively referred to as Markov models [2]. These include, for example, Markov chains, Markov decision processes, Hidden Markov Chains (HMM), and other stochastic processes or stochastic models. From the definition of Markov models, two main key words are important: stochastic process and Markovianity. The property that the conditional distribution of the state of a process or system at moment t0 is known, and the state of the process at moment t>t0 is independent of the state of the process before moment t0 and is Markovianity, also called posteriority-free. Simply put, a Markov process is a process in which the “future” state is independent of the “past” state. A stochastic process with Markovianity is called a Markov process, and a Markov process with discrete time and state is a Markov chain [3].As the quality of life has improved dramatically, the people’s attention to sports training has also increased dramatically, and people actively use a variety of sports training methods to strengthen their bodies and promote physical health. However, trainers are more or less likely to encounter sports injuries during sports training, causing a greater burden on the body and therefore need to promptly identify the main causes of sports injuries and implement targeted recovery strategies [4]. This requires the organizers of sports training to investigate and evaluate the possible risks of sports training in the process of organizing sports training, to build a decision model for the risks arising from sports training, to use the analytical method of building Markov models, to predict the possible risks arising from sports training, and to improve the ability to assess the risks of sports training and the ability to make decisions to avoid risks, therefore to build a model to predict the risks arising from sports training. Therefore, more and more attention has been paid to the development of models for predicting and evaluating the risks arising from sports training and proposing solutions. The use of Markov models for risk prediction in sports training is a very accurate research method [5].The risk management model in sports training consists of eight main aspects: firstly, internal environment and goal setting, secondly, risk identification and risk assessment, then risk countermeasures and control activities, and finally, information and communication and monitoring. These management models are for different management perspectives and are integrated in the whole management system of sports training [6]. The internal environment is the platform of the entire management system, and the internal environment is influenced by the “human” management philosophy and risk appetite, which determines the setting of risk management objectives; objective setting is the premise of risk identification, risk assessment, and risk countermeasures, and specific risk management strategies and processes must meet the requirements of risk management to achieve the risk management objectives. Risk identification, risk assessment, and risk countermeasures are the specific implementation processes of risk management, which are the refinement and execution of risk management objectives; in internal control, information and communication are the two elements that lubricate the unimpeded flow of all other elements; monitoring is the recontrol and reimprovement of the risk management system to maintain the systemic and up-to-date nature of the risk management system.This paper is mainly based on the Markov model, the investigation and analysis of common training methods of sports training, and the establishment of the Markov model for the risks encountered in sports training and research and prediction of these risks and put forward some opinions on the control and optimization of training methods for the risks, in order to reduce the adverse effects of sports injuries, improve the comprehensive level of sports training, make the sports training results more effective, and bring positive impact on people’s physical health, psychological health, and life goals to the maximum extent [7].


## 2. Literature Review

This paper focuses on the prediction of risks in sports training and the control of these risks through the development of Markov models, so we first introduce the current state of research on Markov models and some common research problems based on Markov models.In 1906, mathematician A.A. Markov proposed a class of stochastic processes in which the “future” of a system is only related to the “present” and does not depend on the “past.” The results obtained by such stochastic processes illustrate and generalize Huygens’ principle of no posteriority. In 1926, Bernstein named this class of stochastic processes with no posteriority after Markov chains, which was the first use of Markov chains, the mathematical model of Markov chains. Based on the basic Markov model, various improved Markovs were derived, and the most widely used one is the class of functions defined by Guo et al. [8] called hidden Markov models.Markov models have a good probabilistic underlying theory and an efficient and simple construction structure and are widely used in the fields of speech recognition, biological sequence analysis, image processing and computers, character recognition, financial data analysis, spatio-temporal data mining, and text information extraction. Given the current state, it consists of two aspects: firstly, for the observation model, the probability of issuing future information is independent of all previous states and issued information; on the other hand, for the state model, the probability of transferring the next step is independent of all previous states and issued information [9].The following is an example of an application of the Markov model.Markov models can evaluate the effectiveness of diabetes screening and prevention of cardiovascular disease in a population in a given region, with the process shown below: the highest quality of life without diabetes and cardiovascular disease is assumed, with a health utility value of 1, and the lowest quality of life corresponds to death, with a health utility value of 0. Quality-adjusted life years were calculated based on health utility values for each health state and state transition process accumulated over the course of disease progression [10]. Comparisons between groups were made using chi-square tests for categorical variables and t-tests for continuous variables, both using two-sided tests with significance level α taken as 0.05. Indicators for evaluating the effectiveness of screening strategies to prevent cardiovascular disease including the number of life years and QALYs available, the number of preventable cardiovascular disease episodes or all-cause deaths, and the corresponding number of people to be screened were calculated. Probabilistic sensitivity analysis was used to estimate the uncertainty in the incidence of diabetes, the sensitivity of the screening method, and the strength of the effect of the intensive intervention, with a random number set to 1. 10,000 simulations were performed, and 95% uncertainty intervals for the effect indicators were estimated from the distributions obtained from the probabilistic sensitivity analysis. This study suggests that systematic screening for diabetes in populations in developed regions of China can reduce cardiovascular morbidity and all-cause mortality according to the latest available guidelines, but the gain in cardiovascular disease prevention effect is not significant if the starting age of screening is lowered from 40 to 35 years, and the risk factors of overweight or obesity need to be taken into account if the starting age of screening is lowered to 35 years in order to improve screening efficiency and public health. In practice, screening strategies should be chosen appropriately according to the level of economic development and resource input [11].In addition, the Markov model can also be used to study and predict the fashionable color of textiles and to explore the change pattern of the fashionable color of daily textiles, so as to provide effective data support for guiding the R&D and design of daily textiles. As an important element in the process of home textile product design, color has its inherent characteristics, seasonality, and continuity. The color trend of home textile popular colors in recent years consists of 10 color components, which are green, blue, purple, red, yellow, blue-green, purple-blue, red-purple, yellow-red, and green-yellow [12]. Therefore, firstly, we analyzed the information of spring and summer colors released by the International Color Council between 2007 and 2013 and obtained the market share of each hue component in all colors over the years. Since the actual application of popular colors is subject to the interference of various factors, which may lead to noise in the obtained time-series data, it is difficult to ensure that the original 1D time-series data contains sufficient information for reconstructing the dynamical system, so here it is necessary to transform the 1D time-series data into multidimensional time-series data to generate training samples suitable for modeling. Then, suitable kernel functions and parameters are selected to train the SVR model, and finally, the obtained prediction model is used to predict the trend of textile fashion colors. It can be concluded that the coefficients of variation of purple-blue and blue-green are relatively small, indicating that their volatility is not very obvious. The coefficients of variation of other color shades are relatively large, showing that the changes of their corresponding colors have obvious volatility and present a highly nonlinear change relationship in the time series with a certain degree of randomness. The average relative error of the gray model for blue hue prediction is below 20%, and only the relative error of individual years is abnormal, and the overall prediction effect is good; after the correction of the Markov residual correction model, although the prediction error of 2011 is larger, the prediction accuracy of 2012 and 2013 is improved [13]. This also shows that the gray Markov prediction model has better trend extrapolation ability for trend prediction of home textile fashion colors than the single GM(1,1), which is more suitable for long-term prediction of home textile fashion colors [14].The Markov model can also predict the number of fatalities caused by accidents, and the process is shown as follows: based on the information of national coal mine accident statistics, the data of coal mine accident fatalities are obtained. The national coal mine accidents from 2008 to 2019 were used as the original data to predict the number of coal mine accident fatalities in 2020-2022, to compare and analyze the accuracy of the prediction results of three gray models and to optimize the Markov model for the results with better prediction accuracy. The three models are gray model, dimensional gray model, and unbiased gray model [15]. Both the dimensional gray model and the unbiased gray model are optimized gray models. The dimensional gray model uses the prediction results of the gray model to update the data, which adds and utilizes new information in a timely manner, improves the whiteness of the gray interval, and is mainly used for medium- and long-term forecasting. The unbiased gray model can eliminate the limitations of bias and weak anti-interference ability inherent in the traditional gray model itself. The C and P values of the three gray models satisfy the condition of “C<0.35, P=1,” which means that the accuracy level of the three gray models is “good” and the small error probability P value is 1. The average relative error ε value of the unbiased gray model is 0. 07186, which is the smallest among the three gray models. The unbiased gray model effectively eliminates the inherent bias of the data itself and effectively improves the accuracy of the prediction results [16]. The unbiased gray Markov model was used to predict the number of fatalities in coal mine accidents, and the predicted number of fatalities in coal mine accidents in 2021 was 170, which is very consistent with the overall development trend of stable improvement in China’s coal mine safety production situation, continuous decline in serious safety accidents, and continuous decline in the number of accidents and fatalities [17].In addition to the above model, the Markov model can also predict the time of road congestion. The Markov chain has powerful ability to predict the problem and choose the optimal route. The training set is used to obtain and analyze the real-time road congestion time to build the corresponding hidden Markov model, so as to predict the road congestion time in the next time period and analyze the optimal route. And the further improvement of Welch’s algorithm, adding the study of the previousn moments of data at a certain moment improves the algorithm, making the training set parameters closer to the actual, with higher prediction accuracy and more powerful applicability. Generally speaking, the main factors affecting road traffic congestion are temperature, visibility, peak driving hours, traffic accidents, etc. According to the data of the “Comprehensive Traffic and Travel Data Open Cloud Platform”, these factors are closely related to vehicle travel time. In this paper, the data is collected using a traffic microwave radar detector, RTMS, which is an online device used to observe real-time road conditions [18]. The RTMS detects objects in 2-meter levels in the direction of microwave beam emission, and with lateral mounting, the device is installed on roadside poles to keep the microwave projection perpendicular to the road, and the split-level beam can provide multiple detection areas for various road conditions. It measures the position of vehicles in the microwave projection area and enables the detection of traffic data such as traffic flow and vehicle travel time of multiple lanes by distance [19]. The prediction accuracies are 98.0%, 97.8%, 97.5%, 97.1%, and 96.3% during the experimental cycle, and the accuracies gradually level off.From the above development process and modeling examples, it can be seen that the Markov model has very wide application value in practice, which also provides solid theoretical support and credible experimental results for the research of this paper [20].


## 3. Establishment of the Markov Model and Prediction of Sports Training Risk

### 3.1. Establishment of the Markov Model

The Markov model is a stochastic time series analysis method, which predicts the future state of things by studying the initial probability of different states and the transfer probability between states. The most important feature of the Markov model is that it has no posteriority; that is, it is considered that the conditional distribution of the state of the process or system at the momentt>t0 is independent of the state of the process before the moment t0, if the state at the moment t0 is known. That is, the future state does not depend on the past but is only related to the current state. This property is very suitable for analyzing data with high volatility and no obvious time-varying characteristics.


#### 3.1.1. Markov Process

LetX=X1,X2,X3,⋯,Xt be a sequence of random variables, where each random variable takes values in a finite set S=s1,s2,s3,⋯,sn, called the state space. Markov is characterized by the following.
(1)
Finite history assumption(1)PXt+1=sk∣X1,⋯,Xt=PXt+1=skXt.(2)
Time invariance assumption(2)∀i∈1,2,3,⋯,T∀x,y∈S,PXi=y∣Xi−1=x=py∣x.IfX has these characteristics above, then this sequence of X is called a Markov process (chain).If this sequence is a Markov chain, it has then≫0 following i,j∈I, properties for all pijn integers and n-step transfer probabilities.
(3)pijn=∑kϵIpik1pkjn−1,PXn1=i1,Xn2=i2,⋯Xnm=im=∑ipi0pii1nipi1pi2n2−n1⋯pim−1pimnm−nm−1,Pn=Pn−1P.


#### 3.1.2. Markov Analysis Method

The basic model of Markov analysis is(4)XK+1=XK×P,where XK+1 denotes the state vector of the trend T=K analysis and prediction object at P the moment, denotes the one-step transfer probability XK+1 matrix, and denotes the state vector of the T=K+1 trend analysis and prediction object at the moment.Letpij=PXi=j∣X0=i,i,j∈I, and then pij be called transfer probability, which denotes the transfer probability from state i to state j. The transfer pij probability matrix thought of as an element is shown as follows.
(5)P=p11⋯p1m⋮⋱⋮pm1⋯pmm=pijm×n.If the Markov model is to be used to make a prediction about something, it is a very important prerequisite that such a thing must have Markovianity. Therefore, the thing needs to be tested first, and the test result is judged usingχ2. Assuming that the index series is divided into m states, the frequency of transformation of state i to state j is noted as fij, the transfer probability is pij, and the conditional probability of the state transfer frequency matrix is taken as the marginal probability. According fiji,j∈I to the calculation of each column of the matrix, calculate all the elements and, finally, the division operation. The calculation formula is as follows.
(6)Pj=∑i=1mfij∑j=1m∑i=1mfij,The formula for calculating theχ2 statistic is as follows.
(7)χ2=2∑j=1m∑i=1mfijlogpijPj.It should be noted here that the log in the equation is becauselnx is often written as logx in programming.The degrees of freedom are obtained by checking the table given the significantχα2m−12 level α. So χ2>χα2m−12, if then the test is passed.


#### 3.1.3. Constructing the Multistep Transfer Probability Matrix

The calculation of the multistep transfer probability matrix requires the use of the C-K equation (Chapman-Kolmogorov equation), which is calculated as follows.(8)Pu+v=PuPv.In the equation, if we makeu=1 and v=n−1, then we can get the following recurrence Pn=P1Pn−1=PPn−1=⋯=Pn relation, so for the chi-square Markov chain, the n-step transfer probability matrix is equal to the nth power of the one-step transfer probability.


#### 3.1.4. Calculating the Invariant Probability Measure

ForP, we can obtain a vector π such that ∑iπipij=πj not πj≥∀j all πj zero; then, π is called an invariant measure of P. And if ∑iπi=1, then it is called an invariant probability measure.It can be seen that the core problem of the Markov model is to determine the transfer probability matrixP. In this paper, we take unit year (one year) as the scale and investigate and count the different ways of sports training and the frequency of common risks occurring since the last decade, use it to construct the Markov model to predict the frequency of risks occurring in sports training in the next few years, and propose training improvement methods for each of these risks.


### 3.2. Analysis of Sports Training and Its Common Risks

#### 3.2.1. The Necessity of Sports Training

With the improvement of people’s living standard, people pay more attention to the health and shape of their bodies, and sports training has been paid more and more attention, and sports training becomes an indispensable basic sports ability for people after work and life. As shown in Figure1, the number of people who participated in sports training in the twenty-year period from 2002 to 2022 has been increasing year by year and more and more rapidly.Figure 1
Statistical chart of the change of the number of people participating in sports training in the past 20 years.First of all, the muscles in people’s body are responsible for some basic functions of the body, such as walking, jumping, and weight-bearing; people rely on muscles to send food into the digestive system, and the movement of muscles helps people digest, absorb, and excrete; muscles through the mouth breathe in fresh air into the body and expel carbon dioxide gas; muscles throughout the body move to send blood to the vascular system from the head to the feet and expand and contract according to the demand. It can be said that all the basic functions of the human body need to rely on muscles to complete; therefore, to keep yourself healthy, you should first make all of your own muscles energetic; otherwise, the body will not be able to afford the basic daily needs; people need cardiovascular endurance and muscular endurance to work for a long time; to move heavy objects or fight against resistance, muscle strength is needed; to do a large range of activities in order to perform movements with a large range of motion, it is necessary to have flexible joints and strong stretching of muscles and ligaments.Secondly, sports training helps people to master complex training movements, and the right sports training makes people get twice the result with half the effort. A very important feature of sports is that the sportsman needs to master the correct way of movement and skills, so that the results of sports can be shown on the human body. Different sports training programs have different degrees of requirements for trainers, and only when the trainer’s training ability is improved in sports can the effect of sports training be improved.Third, into the field for sports training which can improve the human body’s ability to withstand large loads of training and high-intensity sports, for athletes such as the high physical requirements of the population, it is necessary to constantly improve their sports, and only frequent sports training exists to ensure the human body’s ability to withstand the super-high requirements of training intensity; otherwise, the fatigue after training will be very serious, and the body’s soreness is also unbearable. The body may even cause serious damage to internal organs, joints, etc.Finally, sports training can help people maintain a stable and good mental state in daily training and competition. A large number of facts have shown that athletes with a stable and good mental quality in sports training competition is an important factor in achieving success and winning, because correct and safe sports training is a great way to form a stable and good mental state.In general, sports training has a very significant meaning and role in comprehensively improving the quality of the nation, improving the health and sports level of all people, and cultivating good spiritual qualities of the people, and with the development of the times, strengthening sports training for all people has become an urgent task.


#### 3.2.2. Analysis of the Common Ways of Sports Training and the Common Risks Caused

There are many types of sports training methods, which can be classified into the following categories from different exercise perspectives: endurance training programs, strength training programs, relaxation training programs, and corrective therapy programs.Among them, endurance training programs are good for improving immunity and increasing the body’s metabolism. This type of exercise includes medical walking, fitness running, bicycling, hiking, rope skipping, stair climbing, and other items that belong to the periodic, rhythmic repetitive exercise. Strength training program exercises are good for muscle building and fat loss, slimming, and shaping and can target different body parts for different muscle training. Relaxation program exercise is mainly to relax the body and to reduce the busy or irregular work and rest bringing harm to the body and mind; you can choose to walk and do tai chi, health exercises, qigong, and massage. Corrective treatment programs are mainly targeted treatment; the main audience is some patients with physical diseases or disabilities, such as medical gymnastics and massage, such as breathing gymnastics for the treatment of asthma and emphysema, gymnastics for the treatment of sagging internal organs to exercise the abdominal muscles, and spinal correction gymnastics for the correction of scoliosis.These different training methods also bring different risks, mainly divided into the following categories: training management risk, facility management risk, competition management risk, and trainer management risk.Training management risk is the existence of various types of accidental risks in sports training, such as physical function damage, dangerous hazards, fainting, and sudden death. Once these risks occur, they will produce both physical and psychological trauma to the trainer and will also affect the development and progress of the economy. Facility management risk, as the name implies, is the safety risks in the construction of hardware facilities used for sports training, such as the construction of sports venues not meeting national quality standards, unreasonable design of sports tracks, which can cause sports injuries to trainers, and sports equipment quality being not up to scratch, causing injury to trainers. Competition management risk is the existence of various types of risks in sports competition, such as the lack of sportsmanship in the competition, the lack of awareness of rules, the lack of means to win the game, malicious fouls against opponents, increasing the athletes’ sports injuries, and even intensifying the conflict between competitors. The risk of trainer management is that in sports management, trainers and coaches pay too much attention to the cultivation of ability and training results, ignoring the development of trainers’ psychological health; in addition, some competitive sports training management has “secret operation,” which is against fairness and causes athletes’ resistance and questioning to competition. This increases the risk of sports management.The probability of occurrence of the above-mentioned common sports training risks is shown in Figure2.Figure 2
Probability of occurrence of several common sports training risks.From Figure2, it can be seen that training management risk is the most probable risk in sports training, and this study will also focus on predicting and making recommendations for training management risk.The steps for prediction of training management risk in sports training using the Markov model are shown in Figure3. Firstly, the Markov transfer matrix needs to be established; secondly, the Markov transfer matrix is initially solved by using a statistical method, quadratic programming method, and other mathematical calculation methods; then, the results are normalized to obtain the transfer probability matrix, and finally, the probability matrix is analyzed and summarized.Figure 3
Steps to predict sports training risks using the Markov model.The most common training management risk is the sports injuries that may occur during sports training. According to Sports Weekly, the types of sports injuries due to improper sports training from 2012 to 2021 were investigated, and there are four main types: muscle and tendon strains, joint injuries, heart injuries, and fractures. The trend graph of the changes in the risk due to the above four types of sports injuries since the last decade is shown in Figure4.Figure 4
The trend of the change of risk caused by four kinds of sports injuries in the past ten years.In particular, it should be noted that since the total number of sports training people counted varies from year to year, the calculation of the impact caused by the risk of sports injuries is normalized.Based on the preliminary understanding and regular analysis of the changes in the above sports injuries, the following assumptions can be made about the Markov model for predicting the risk of sports training.(1)
The four injury states are set as 1, 2, 3, and 4, respectively, for modeling(2)
The four sports injury states are transferred to each other in order, where the time of transferring one state to the adjacent state is set as unit year (data are counted by years)(3)
The transfer order was transferred from state 1 to state 2, state 2 to state 3, state 3 to state 4, and state 4 to state 1, respectivelyFor the analysis of the statistical graph of the risk caused by sports injuries during the last ten years, the number of transfers of the four sports injuries can be calculated, and the transfer probability matrix can be calculated by the formula. Using this transfer matrix, the risk of sports training in the latter three years, especially the risk of sports injury in training management risk, can be predicted, and the results obtained are shown in Figures5–8, respectively.Figure 5
Prediction curve of the risk of muscle tendon strain in the next three years.Figure 6
Predicted risk curve for joint injuries over the next three years.Figure 7
Predicted risk of heart injury over the next three years.Figure 8
Fracture risk prediction curve for the next three years.


## 3.1. Establishment of the Markov Model

The Markov model is a stochastic time series analysis method, which predicts the future state of things by studying the initial probability of different states and the transfer probability between states. The most important feature of the Markov model is that it has no posteriority; that is, it is considered that the conditional distribution of the state of the process or system at the momentt>t0 is independent of the state of the process before the moment t0, if the state at the moment t0 is known. That is, the future state does not depend on the past but is only related to the current state. This property is very suitable for analyzing data with high volatility and no obvious time-varying characteristics.


### 3.1.1. Markov Process

LetX=X1,X2,X3,⋯,Xt be a sequence of random variables, where each random variable takes values in a finite set S=s1,s2,s3,⋯,sn, called the state space. Markov is characterized by the following.
(1)
Finite history assumption(1)PXt+1=sk∣X1,⋯,Xt=PXt+1=skXt.(2)
Time invariance assumption(2)∀i∈1,2,3,⋯,T∀x,y∈S,PXi=y∣Xi−1=x=py∣x.IfX has these characteristics above, then this sequence of X is called a Markov process (chain).If this sequence is a Markov chain, it has then≫0 following i,j∈I, properties for all pijn integers and n-step transfer probabilities.
(3)pijn=∑kϵIpik1pkjn−1,PXn1=i1,Xn2=i2,⋯Xnm=im=∑ipi0pii1nipi1pi2n2−n1⋯pim−1pimnm−nm−1,Pn=Pn−1P.


### 3.1.2. Markov Analysis Method

The basic model of Markov analysis is(4)XK+1=XK×P,where XK+1 denotes the state vector of the trend T=K analysis and prediction object at P the moment, denotes the one-step transfer probability XK+1 matrix, and denotes the state vector of the T=K+1 trend analysis and prediction object at the moment.Letpij=PXi=j∣X0=i,i,j∈I, and then pij be called transfer probability, which denotes the transfer probability from state i to state j. The transfer pij probability matrix thought of as an element is shown as follows.
(5)P=p11⋯p1m⋮⋱⋮pm1⋯pmm=pijm×n.If the Markov model is to be used to make a prediction about something, it is a very important prerequisite that such a thing must have Markovianity. Therefore, the thing needs to be tested first, and the test result is judged usingχ2. Assuming that the index series is divided into m states, the frequency of transformation of state i to state j is noted as fij, the transfer probability is pij, and the conditional probability of the state transfer frequency matrix is taken as the marginal probability. According fiji,j∈I to the calculation of each column of the matrix, calculate all the elements and, finally, the division operation. The calculation formula is as follows.
(6)Pj=∑i=1mfij∑j=1m∑i=1mfij,The formula for calculating theχ2 statistic is as follows.
(7)χ2=2∑j=1m∑i=1mfijlogpijPj.It should be noted here that the log in the equation is becauselnx is often written as logx in programming.The degrees of freedom are obtained by checking the table given the significantχα2m−12 level α. So χ2>χα2m−12, if then the test is passed.


### 3.1.3. Constructing the Multistep Transfer Probability Matrix

The calculation of the multistep transfer probability matrix requires the use of the C-K equation (Chapman-Kolmogorov equation), which is calculated as follows.(8)Pu+v=PuPv.In the equation, if we makeu=1 and v=n−1, then we can get the following recurrence Pn=P1Pn−1=PPn−1=⋯=Pn relation, so for the chi-square Markov chain, the n-step transfer probability matrix is equal to the nth power of the one-step transfer probability.


### 3.1.4. Calculating the Invariant Probability Measure

ForP, we can obtain a vector π such that ∑iπipij=πj not πj≥∀j all πj zero; then, π is called an invariant measure of P. And if ∑iπi=1, then it is called an invariant probability measure.It can be seen that the core problem of the Markov model is to determine the transfer probability matrixP. In this paper, we take unit year (one year) as the scale and investigate and count the different ways of sports training and the frequency of common risks occurring since the last decade, use it to construct the Markov model to predict the frequency of risks occurring in sports training in the next few years, and propose training improvement methods for each of these risks.


## 3.1.1. Markov Process

LetX=X1,X2,X3,⋯,Xt be a sequence of random variables, where each random variable takes values in a finite set S=s1,s2,s3,⋯,sn, called the state space. Markov is characterized by the following.
(1)
Finite history assumption(1)PXt+1=sk∣X1,⋯,Xt=PXt+1=skXt.(2)
Time invariance assumption(2)∀i∈1,2,3,⋯,T∀x,y∈S,PXi=y∣Xi−1=x=py∣x.IfX has these characteristics above, then this sequence of X is called a Markov process (chain).If this sequence is a Markov chain, it has then≫0 following i,j∈I, properties for all pijn integers and n-step transfer probabilities.
(3)pijn=∑kϵIpik1pkjn−1,PXn1=i1,Xn2=i2,⋯Xnm=im=∑ipi0pii1nipi1pi2n2−n1⋯pim−1pimnm−nm−1,Pn=Pn−1P.


## 3.1.2. Markov Analysis Method

The basic model of Markov analysis is(4)XK+1=XK×P,where XK+1 denotes the state vector of the trend T=K analysis and prediction object at P the moment, denotes the one-step transfer probability XK+1 matrix, and denotes the state vector of the T=K+1 trend analysis and prediction object at the moment.Letpij=PXi=j∣X0=i,i,j∈I, and then pij be called transfer probability, which denotes the transfer probability from state i to state j. The transfer pij probability matrix thought of as an element is shown as follows.
(5)P=p11⋯p1m⋮⋱⋮pm1⋯pmm=pijm×n.If the Markov model is to be used to make a prediction about something, it is a very important prerequisite that such a thing must have Markovianity. Therefore, the thing needs to be tested first, and the test result is judged usingχ2. Assuming that the index series is divided into m states, the frequency of transformation of state i to state j is noted as fij, the transfer probability is pij, and the conditional probability of the state transfer frequency matrix is taken as the marginal probability. According fiji,j∈I to the calculation of each column of the matrix, calculate all the elements and, finally, the division operation. The calculation formula is as follows.
(6)Pj=∑i=1mfij∑j=1m∑i=1mfij,The formula for calculating theχ2 statistic is as follows.
(7)χ2=2∑j=1m∑i=1mfijlogpijPj.It should be noted here that the log in the equation is becauselnx is often written as logx in programming.The degrees of freedom are obtained by checking the table given the significantχα2m−12 level α. So χ2>χα2m−12, if then the test is passed.


## 3.1.3. Constructing the Multistep Transfer Probability Matrix

The calculation of the multistep transfer probability matrix requires the use of the C-K equation (Chapman-Kolmogorov equation), which is calculated as follows.(8)Pu+v=PuPv.In the equation, if we makeu=1 and v=n−1, then we can get the following recurrence Pn=P1Pn−1=PPn−1=⋯=Pn relation, so for the chi-square Markov chain, the n-step transfer probability matrix is equal to the nth power of the one-step transfer probability.


## 3.1.4. Calculating the Invariant Probability Measure

ForP, we can obtain a vector π such that ∑iπipij=πj not πj≥∀j all πj zero; then, π is called an invariant measure of P. And if ∑iπi=1, then it is called an invariant probability measure.It can be seen that the core problem of the Markov model is to determine the transfer probability matrixP. In this paper, we take unit year (one year) as the scale and investigate and count the different ways of sports training and the frequency of common risks occurring since the last decade, use it to construct the Markov model to predict the frequency of risks occurring in sports training in the next few years, and propose training improvement methods for each of these risks.


## 3.2. Analysis of Sports Training and Its Common Risks

### 3.2.1. The Necessity of Sports Training

With the improvement of people’s living standard, people pay more attention to the health and shape of their bodies, and sports training has been paid more and more attention, and sports training becomes an indispensable basic sports ability for people after work and life. As shown in Figure1, the number of people who participated in sports training in the twenty-year period from 2002 to 2022 has been increasing year by year and more and more rapidly.Figure 1
Statistical chart of the change of the number of people participating in sports training in the past 20 years.First of all, the muscles in people’s body are responsible for some basic functions of the body, such as walking, jumping, and weight-bearing; people rely on muscles to send food into the digestive system, and the movement of muscles helps people digest, absorb, and excrete; muscles through the mouth breathe in fresh air into the body and expel carbon dioxide gas; muscles throughout the body move to send blood to the vascular system from the head to the feet and expand and contract according to the demand. It can be said that all the basic functions of the human body need to rely on muscles to complete; therefore, to keep yourself healthy, you should first make all of your own muscles energetic; otherwise, the body will not be able to afford the basic daily needs; people need cardiovascular endurance and muscular endurance to work for a long time; to move heavy objects or fight against resistance, muscle strength is needed; to do a large range of activities in order to perform movements with a large range of motion, it is necessary to have flexible joints and strong stretching of muscles and ligaments.Secondly, sports training helps people to master complex training movements, and the right sports training makes people get twice the result with half the effort. A very important feature of sports is that the sportsman needs to master the correct way of movement and skills, so that the results of sports can be shown on the human body. Different sports training programs have different degrees of requirements for trainers, and only when the trainer’s training ability is improved in sports can the effect of sports training be improved.Third, into the field for sports training which can improve the human body’s ability to withstand large loads of training and high-intensity sports, for athletes such as the high physical requirements of the population, it is necessary to constantly improve their sports, and only frequent sports training exists to ensure the human body’s ability to withstand the super-high requirements of training intensity; otherwise, the fatigue after training will be very serious, and the body’s soreness is also unbearable. The body may even cause serious damage to internal organs, joints, etc.Finally, sports training can help people maintain a stable and good mental state in daily training and competition. A large number of facts have shown that athletes with a stable and good mental quality in sports training competition is an important factor in achieving success and winning, because correct and safe sports training is a great way to form a stable and good mental state.In general, sports training has a very significant meaning and role in comprehensively improving the quality of the nation, improving the health and sports level of all people, and cultivating good spiritual qualities of the people, and with the development of the times, strengthening sports training for all people has become an urgent task.


### 3.2.2. Analysis of the Common Ways of Sports Training and the Common Risks Caused

There are many types of sports training methods, which can be classified into the following categories from different exercise perspectives: endurance training programs, strength training programs, relaxation training programs, and corrective therapy programs.Among them, endurance training programs are good for improving immunity and increasing the body’s metabolism. This type of exercise includes medical walking, fitness running, bicycling, hiking, rope skipping, stair climbing, and other items that belong to the periodic, rhythmic repetitive exercise. Strength training program exercises are good for muscle building and fat loss, slimming, and shaping and can target different body parts for different muscle training. Relaxation program exercise is mainly to relax the body and to reduce the busy or irregular work and rest bringing harm to the body and mind; you can choose to walk and do tai chi, health exercises, qigong, and massage. Corrective treatment programs are mainly targeted treatment; the main audience is some patients with physical diseases or disabilities, such as medical gymnastics and massage, such as breathing gymnastics for the treatment of asthma and emphysema, gymnastics for the treatment of sagging internal organs to exercise the abdominal muscles, and spinal correction gymnastics for the correction of scoliosis.These different training methods also bring different risks, mainly divided into the following categories: training management risk, facility management risk, competition management risk, and trainer management risk.Training management risk is the existence of various types of accidental risks in sports training, such as physical function damage, dangerous hazards, fainting, and sudden death. Once these risks occur, they will produce both physical and psychological trauma to the trainer and will also affect the development and progress of the economy. Facility management risk, as the name implies, is the safety risks in the construction of hardware facilities used for sports training, such as the construction of sports venues not meeting national quality standards, unreasonable design of sports tracks, which can cause sports injuries to trainers, and sports equipment quality being not up to scratch, causing injury to trainers. Competition management risk is the existence of various types of risks in sports competition, such as the lack of sportsmanship in the competition, the lack of awareness of rules, the lack of means to win the game, malicious fouls against opponents, increasing the athletes’ sports injuries, and even intensifying the conflict between competitors. The risk of trainer management is that in sports management, trainers and coaches pay too much attention to the cultivation of ability and training results, ignoring the development of trainers’ psychological health; in addition, some competitive sports training management has “secret operation,” which is against fairness and causes athletes’ resistance and questioning to competition. This increases the risk of sports management.The probability of occurrence of the above-mentioned common sports training risks is shown in Figure2.Figure 2
Probability of occurrence of several common sports training risks.From Figure2, it can be seen that training management risk is the most probable risk in sports training, and this study will also focus on predicting and making recommendations for training management risk.The steps for prediction of training management risk in sports training using the Markov model are shown in Figure3. Firstly, the Markov transfer matrix needs to be established; secondly, the Markov transfer matrix is initially solved by using a statistical method, quadratic programming method, and other mathematical calculation methods; then, the results are normalized to obtain the transfer probability matrix, and finally, the probability matrix is analyzed and summarized.Figure 3
Steps to predict sports training risks using the Markov model.The most common training management risk is the sports injuries that may occur during sports training. According to Sports Weekly, the types of sports injuries due to improper sports training from 2012 to 2021 were investigated, and there are four main types: muscle and tendon strains, joint injuries, heart injuries, and fractures. The trend graph of the changes in the risk due to the above four types of sports injuries since the last decade is shown in Figure4.Figure 4
The trend of the change of risk caused by four kinds of sports injuries in the past ten years.In particular, it should be noted that since the total number of sports training people counted varies from year to year, the calculation of the impact caused by the risk of sports injuries is normalized.Based on the preliminary understanding and regular analysis of the changes in the above sports injuries, the following assumptions can be made about the Markov model for predicting the risk of sports training.(1)
The four injury states are set as 1, 2, 3, and 4, respectively, for modeling(2)
The four sports injury states are transferred to each other in order, where the time of transferring one state to the adjacent state is set as unit year (data are counted by years)(3)
The transfer order was transferred from state 1 to state 2, state 2 to state 3, state 3 to state 4, and state 4 to state 1, respectivelyFor the analysis of the statistical graph of the risk caused by sports injuries during the last ten years, the number of transfers of the four sports injuries can be calculated, and the transfer probability matrix can be calculated by the formula. Using this transfer matrix, the risk of sports training in the latter three years, especially the risk of sports injury in training management risk, can be predicted, and the results obtained are shown in Figures5–8, respectively.Figure 5
Prediction curve of the risk of muscle tendon strain in the next three years.Figure 6
Predicted risk curve for joint injuries over the next three years.Figure 7
Predicted risk of heart injury over the next three years.Figure 8
Fracture risk prediction curve for the next three years.


## 3.2.1. The Necessity of Sports Training

With the improvement of people’s living standard, people pay more attention to the health and shape of their bodies, and sports training has been paid more and more attention, and sports training becomes an indispensable basic sports ability for people after work and life. As shown in Figure1, the number of people who participated in sports training in the twenty-year period from 2002 to 2022 has been increasing year by year and more and more rapidly.Figure 1
Statistical chart of the change of the number of people participating in sports training in the past 20 years.First of all, the muscles in people’s body are responsible for some basic functions of the body, such as walking, jumping, and weight-bearing; people rely on muscles to send food into the digestive system, and the movement of muscles helps people digest, absorb, and excrete; muscles through the mouth breathe in fresh air into the body and expel carbon dioxide gas; muscles throughout the body move to send blood to the vascular system from the head to the feet and expand and contract according to the demand. It can be said that all the basic functions of the human body need to rely on muscles to complete; therefore, to keep yourself healthy, you should first make all of your own muscles energetic; otherwise, the body will not be able to afford the basic daily needs; people need cardiovascular endurance and muscular endurance to work for a long time; to move heavy objects or fight against resistance, muscle strength is needed; to do a large range of activities in order to perform movements with a large range of motion, it is necessary to have flexible joints and strong stretching of muscles and ligaments.Secondly, sports training helps people to master complex training movements, and the right sports training makes people get twice the result with half the effort. A very important feature of sports is that the sportsman needs to master the correct way of movement and skills, so that the results of sports can be shown on the human body. Different sports training programs have different degrees of requirements for trainers, and only when the trainer’s training ability is improved in sports can the effect of sports training be improved.Third, into the field for sports training which can improve the human body’s ability to withstand large loads of training and high-intensity sports, for athletes such as the high physical requirements of the population, it is necessary to constantly improve their sports, and only frequent sports training exists to ensure the human body’s ability to withstand the super-high requirements of training intensity; otherwise, the fatigue after training will be very serious, and the body’s soreness is also unbearable. The body may even cause serious damage to internal organs, joints, etc.Finally, sports training can help people maintain a stable and good mental state in daily training and competition. A large number of facts have shown that athletes with a stable and good mental quality in sports training competition is an important factor in achieving success and winning, because correct and safe sports training is a great way to form a stable and good mental state.In general, sports training has a very significant meaning and role in comprehensively improving the quality of the nation, improving the health and sports level of all people, and cultivating good spiritual qualities of the people, and with the development of the times, strengthening sports training for all people has become an urgent task.


## 3.2.2. Analysis of the Common Ways of Sports Training and the Common Risks Caused

There are many types of sports training methods, which can be classified into the following categories from different exercise perspectives: endurance training programs, strength training programs, relaxation training programs, and corrective therapy programs.Among them, endurance training programs are good for improving immunity and increasing the body’s metabolism. This type of exercise includes medical walking, fitness running, bicycling, hiking, rope skipping, stair climbing, and other items that belong to the periodic, rhythmic repetitive exercise. Strength training program exercises are good for muscle building and fat loss, slimming, and shaping and can target different body parts for different muscle training. Relaxation program exercise is mainly to relax the body and to reduce the busy or irregular work and rest bringing harm to the body and mind; you can choose to walk and do tai chi, health exercises, qigong, and massage. Corrective treatment programs are mainly targeted treatment; the main audience is some patients with physical diseases or disabilities, such as medical gymnastics and massage, such as breathing gymnastics for the treatment of asthma and emphysema, gymnastics for the treatment of sagging internal organs to exercise the abdominal muscles, and spinal correction gymnastics for the correction of scoliosis.These different training methods also bring different risks, mainly divided into the following categories: training management risk, facility management risk, competition management risk, and trainer management risk.Training management risk is the existence of various types of accidental risks in sports training, such as physical function damage, dangerous hazards, fainting, and sudden death. Once these risks occur, they will produce both physical and psychological trauma to the trainer and will also affect the development and progress of the economy. Facility management risk, as the name implies, is the safety risks in the construction of hardware facilities used for sports training, such as the construction of sports venues not meeting national quality standards, unreasonable design of sports tracks, which can cause sports injuries to trainers, and sports equipment quality being not up to scratch, causing injury to trainers. Competition management risk is the existence of various types of risks in sports competition, such as the lack of sportsmanship in the competition, the lack of awareness of rules, the lack of means to win the game, malicious fouls against opponents, increasing the athletes’ sports injuries, and even intensifying the conflict between competitors. The risk of trainer management is that in sports management, trainers and coaches pay too much attention to the cultivation of ability and training results, ignoring the development of trainers’ psychological health; in addition, some competitive sports training management has “secret operation,” which is against fairness and causes athletes’ resistance and questioning to competition. This increases the risk of sports management.The probability of occurrence of the above-mentioned common sports training risks is shown in Figure2.Figure 2
Probability of occurrence of several common sports training risks.From Figure2, it can be seen that training management risk is the most probable risk in sports training, and this study will also focus on predicting and making recommendations for training management risk.The steps for prediction of training management risk in sports training using the Markov model are shown in Figure3. Firstly, the Markov transfer matrix needs to be established; secondly, the Markov transfer matrix is initially solved by using a statistical method, quadratic programming method, and other mathematical calculation methods; then, the results are normalized to obtain the transfer probability matrix, and finally, the probability matrix is analyzed and summarized.Figure 3
Steps to predict sports training risks using the Markov model.The most common training management risk is the sports injuries that may occur during sports training. According to Sports Weekly, the types of sports injuries due to improper sports training from 2012 to 2021 were investigated, and there are four main types: muscle and tendon strains, joint injuries, heart injuries, and fractures. The trend graph of the changes in the risk due to the above four types of sports injuries since the last decade is shown in Figure4.Figure 4
The trend of the change of risk caused by four kinds of sports injuries in the past ten years.In particular, it should be noted that since the total number of sports training people counted varies from year to year, the calculation of the impact caused by the risk of sports injuries is normalized.Based on the preliminary understanding and regular analysis of the changes in the above sports injuries, the following assumptions can be made about the Markov model for predicting the risk of sports training.(1)
The four injury states are set as 1, 2, 3, and 4, respectively, for modeling(2)
The four sports injury states are transferred to each other in order, where the time of transferring one state to the adjacent state is set as unit year (data are counted by years)(3)
The transfer order was transferred from state 1 to state 2, state 2 to state 3, state 3 to state 4, and state 4 to state 1, respectivelyFor the analysis of the statistical graph of the risk caused by sports injuries during the last ten years, the number of transfers of the four sports injuries can be calculated, and the transfer probability matrix can be calculated by the formula. Using this transfer matrix, the risk of sports training in the latter three years, especially the risk of sports injury in training management risk, can be predicted, and the results obtained are shown in Figures5–8, respectively.Figure 5
Prediction curve of the risk of muscle tendon strain in the next three years.Figure 6
Predicted risk curve for joint injuries over the next three years.Figure 7
Predicted risk of heart injury over the next three years.Figure 8
Fracture risk prediction curve for the next three years.


## 4. Results and Discussion

From the above results, it can be seen that the risk of sports injury in sports training is decreasing year by year, among which the two injuries, joint injury and fracture, are decreasing faster, and the muscle tendon strain and heart injury are decreasing more slowly. The reasons for this are as follows.(1)
Joint injuries and fractures of these two types of injuries in addition to improper sports and sports training venues, the use of sports training equipment, and other aspects also have a great relationship. With the popularity of sports training and the increase in the number of participants in sports training, sports training venues are becoming more and more in line with the standards, equipment has also undergone various inspections and tests, and now more and more people choose to train with the coach, which significantly reduces the risk caused by external factors(2)
With the development of science, the knowledge of sports training has become more abundant and the technology has become more mature; people pay more and more attention to the maintenance problems before and after sports training, which is why the risk of muscle tendon strain and heart injury is gradually decreasing. For example, warming up before formal training, stretching after training, and proper diet during sports training have greatly reduced the damage caused to the internal body by improper sports trainingBased on the above theory and analysis, the following suggestions and plans are made for the control of sports training risks.First, we should focus on the management of hardware facilities and improve the infrastructure of sports training. Hardware facilities are the material basis for carrying out sports training activities; therefore, when organizing sports training, it is necessary to check the degree of perfection of sports training facilities, whether there is a greater risk of injury to the human body, and in the design of new sports training equipment, it is also necessary to consider the human body structure, sports training methods and methods, endurance, and other aspects and strive to design both in line with human mechanics but also to ensure the long-term use of training equipment.Second, to focus on the repair of sports injuries, the need for timely treatment and therapy is necessary. Generally speaking, the main recovery measures used only after sports injuries are four: Chinese medicine treatment, sports therapy, physical therapy, and massage therapy. Chinese medicine has significant efficacy and economic price, can cure the symptoms and other characteristics, and has a long history in China; in the specific treatment process, according to the specific condition of the sports injury site, the degree of injury reasonably selected Chinese medicine preparations, which do a good job of pain treatment and anti-inflammatory treatment, to speed up the trainer sports injury recovery speed, to help it return to normal status faster; sports therapy is mainly for the trainer rehabilitation training; when the trainer sports injury occurs, the trainer sports injury recovery measures. When the trainer experiences sports injury, the use of rehabilitation training can maintain its normal cardiovascular and cerebrovascular function and prevent muscle atrophy, to avoid adverse changes in the joints; physical therapy is a common medical treatment method, mainly including cold therapy and heat therapy; cold therapy can quickly reduce the current temperature of the local skin, contract the local skin capillaries, effectively control the amount of bleeding, and reduce the sensitivity of the central nervous system, thus playing a pain relief, hemostasis, and anti-inflammatory effects; more commonly used is thermal therapy, such as repairing sports injury parts of the tissue using an infrared irradiation method to help trainers recover from sports injuries; the massage recovery method for the treatment of soft tissue injuries has significant efficacy, the recovery speed of the injured parts is faster, this method has no side effects on the human body and can accelerate the recovery speed of sports injury tissue, but want to use the massage recovery method correctly, must have a systematic understanding of the body’s physiological structure, familiar with different acupuncture points, need further study.Not only that but also to strengthen the rules and regulations of sports and athletics. In athletic competitions, everyone will play their best sports to fight, the probability of risk becomes higher. Therefore, in sports competition, managers must strengthen the rules management of the competition, uphold the principle of fairness, justice and openness, promote the orderly development of sports competition, for violations of fairness must be severely punished but also to strengthen the sportsmanship of participants, control the order of sports competition.Finally, when trainers train, coaches must pay attention to the issue of mental health. A big role of sports training is to promote the development of people’s psychological health, so in the process of sports training, great attention must be paid to the psychological problems of trainers, especially if trainers vent through training, more correct guidance, so as not to over-train because of psychological problems, causing harm to the body, to help trainers properly deal with mental health problems, to exclude negative emotional pressure, to maintain positive mindset.


## 5. Conclusion

The main purpose of this paper is to analyze the risks generated by athletic training since the last decade and predict the risks of athletic training in the next three years by building a Markov model and also to make some recommendations for the risks of athletic training. The main work carried out is shown below.(1)
The importance of studying sports training and the types of common risks in sports training are introduced(2)
The concept, meaning, and establishment method of the Markov model were introduced, and the development history and application scenarios of the Markov model were investigated through literature(3)
A Markov model for prediction of sports training risks was established, and the frequency of sports training risks in the next three years was predicted based on the unit year, and it was found that with the progress and development of technology, the risks generated by sports training would be reduced year by year and the reduction would become larger(4)
Suggestions are made for the possible risks arising from sports training, and it is hoped that the increasing level of awareness and improving sports knowledge will lead to better risk avoidanceIn addition, the Markov model is a very practical probabilistic statistical model with strong and high application value in speech recognition, risk prediction, accident handling, engineering design, etc. In the future, it will definitely be more widely used in various different fields.In the future, with the continuous development of science and technology, sports training will certainly be more perfect and humanized, and with the introduction of artificial intelligence and automatic control, sports training will definitely be more safe and reliable, and as long as everyone insists on reasonable physical training, the body will definitely be healthier.The Markov model-based sports training risk prediction model proposed in this paper has some imperfections and needs further improvement.First, the analysis is not comprehensive enough, only for the most common training risks in sports training among sports injuries, but in fact, there are many risks in sports training, and they affect each other, and because of this, it brings more difficulties to the establishment of the model and also affects the accuracy.Secondly, in making predictions only through data analysis modeling predictions, and the future with the continuous development of artificial intelligence technology, sports training will certainly continue to develop in the direction of diversification, which does not take into account the impact of sports injuries; the model needs to be further improved and optimized.



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*Source: 9368686-2022-07-16.xml*