# The Scoring Mechanism of Players after Game Based on Cluster Regression Analysis Model

Authors: Jin Xu; Chao Yi
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

Cluster regression analysis model is an effective theory for a reasonable and fair player scoring game. It can roughly predict and evaluate the performance of athletes after the game with limited data and provide scientific predictions for the performance of athletes. The purpose of this research is to achieve the player’s postmatch scoring through the cluster regression model. Through the research and analysis of past ball games, the comparison and experiment of multiple objects based on different regression analysis theories, the following conclusions are drawn. Different regression models have different standard errors, but if the data in other model categories are put into the centroid model expression, the standard error and the error of the original model are within 0.3, which can replace other models for calculation. In the player’s postmatch scoring, although the expert’s prediction of the result is very accurate, within the error range of 1 copy, the player’s postmatch scoring mechanism based on the cluster regression analysis model is more accurate, and the error formula is in the 0.5 range. It is best to switch the data of the regression model twice to compare the scoring mechanism using different regression experiments.


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## Body

## 1. Introduction

With the development of computer technology, especially the development of artificial intelligence technology in recent years, computer technology is increasingly used in people’s study, work, and life [1]. Using machine learning to study the performance of basketball players is an interdisciplinary subject that combines comprehensive evaluation and machine learning. In real life and work, we often encounter the problem of evaluating or scoring various things or problems. Generally speaking, all types of scoring and evaluation problems are called comprehensive evaluation problems. In basketball, postgame scoring is always an essential part. Scoring can play a role in many aspects, such as promotion, team management, and competition prediction. Therefore, the postcompetition scoring system has great commercial value and can guarantee the fairness of the competition.A clustering algorithm based on fast search and density peak discovery is to quickly find the cluster center. Its accuracy is excessively dependent on the threshold, and no effective method is given to select the appropriate threshold. It is recommended to estimate the threshold based on experience. Li et al. proposed a new method to extract the threshold automatically by using the potential entropy of the original data field. For any dataset to be clustered, the threshold value can be calculated objectively from the dataset, rather than empirical estimation [2]. Although the existence of correlation in clusters (the tendency of similar response of items in clusters) is generally regarded as an obstacle to good reasoning, the complex structure of cluster data provides significant analysis advantages over independent data, but the focus is regression analysis of cluster data. A key advantage is the ability to separate effects at the individual (or project specific) and group (or cluster specific) levels. Begg and Parides reviewed different ways to separate the effects of individual level and cluster levels on response, their proper interpretation, and gave suggestions for model fitting according to the intention of data analysts. Different from many previous papers on this topic, Begg and Parides emphasized the explanation of cluster level covariate effect. The main idea is to analyze the relationship between birth weight and IQ through the data of brothers and sisters in a large birth cohort study [3]. When exposure variables are expensive or difficult to measure, two-stage design is a well-known and cost-effective method for biomedical research. Recent research advances further allow one or two phases of a two-phase design to depend on a continuous result variable. The sampling characteristics related to the results further improve the efficiency of parameter estimation and research the overall cost reduction. Among them, the research and design of cancer biomarkers include sampling of specimens and analysis of results. A semiparametric mixed effects regression model of two-stage design data was established. Xu’s method can explain the cluster or central effect of research objects [4].This research is an experimental analysis based on mathematical theory and cluster regression analysis method. The research process uses mathematical formulas, interview methods, control experiments, and other methods. There is a fierce discussion on the scoring mechanism of NBA and CBA. Based on the regression model, this study puts forward some ideas that can be improved, including the combination of clustering and regression. The experimental results also show that the combination of clustering and regression has the best effect. Finally, the idea of using expert scores after the game to predict the results of the game is proposed. Using the expert scores to compare with the method based on the cluster regression analysis model, you can judge whether the method is based on the theoretical model by looking at the error between the result and the actual is reference.


## 2. Cluster Regression Analysis Model

### 2.1. Cluster Analysis Method

Machine learning can be divided into two categories: supervised learning and unsupervised learning [5]. When all input and output variables in the learning situation are fully observed, we define the learning process as supervised learning [4]. In other words, in supervised learning problems, there are no missing or potential variables in the database. Therefore, supervised learning is more direct [6]. For some learning problems, in addition to being able to fully observe all variables, if we can fully observe the structure of the data production process, supervised learning can be regarded as a parameter evaluation problem. Like the maximum probability or least square estimation, if you do not know the data creation process, you must select a suitable model from many models to complete the learning problem [7].Because the model is not boundless and complex, for example, AIC, BIC, or cross-validation can find a “possibly correct” model to describe the data production process, which is Occam theory or PAC learning. In general, we do not know the process of data creation, but we also lack variables. When the output variable is lost, the learning problem becomes unsupervised [8, 9]. For unsupervised learning, the direct execution of AIC or BIC cannot reveal the distribution of potential variables and the information contained in potential variables. We must try to separate potential variables from the original data and evaluate them [10]. If the potential variables and other variables are independent of each other, the absence of such “offshore” variables will not have a great impact on the estimation. If the potential variable depends on other observed variables, we can use other observable variables to estimate the distribution or summary statistics of potential variables. In general, before evaluating potential variables, we need to determine the type of distribution, whether absolute or continuous [11]. In the case of continuous distribution, the best method is usually factor analysis or factor modeling, using all other variables to construct a new continuous distribution variable [12].Assuming that the potential variable is a polynomial, we can construct a Gaussian mixture model [13]. The above techniques are called cluster analysis. Cluster analysis collects infinite information in some limited set variables and uses these set variables to group the observed objects. In short, set analysis is a data processing method to classify a group of observation objects reasonably [14]. It is an important part of experimental machine learning and a common technology for analyzing statistical data. System analysis in machine learning is a part of unsupervised learning. Unlike supervised learning, the data in the dataset has no class label and is segmented by the similarity of feature data [15].


### 2.2. Cluster Regression Analysis Method

Clustering analysis is the process of dividing a group of physical or abstract objects into similar object classes. According to the survey object and purpose, regression analysis determines which is the independent variable (explanatory variable) and which is the dependent variable (explanatory variable), through the establishment of a regression model and control independent variables to evaluate and predict the dependence between research variables. For example, through correlation analysis, we can know that some variables are closely related, but which parts are the most important, and the degree of their interaction must be selected through cluster regression analysis [16, 17].Quantitative analysis is a method to determine the mathematical model based on statistical data and use the mathematical model to calculate the index and the value of the analysis object [18, 19]. It not only keeps the dependence on observation experiments and the collection of empirical data but also retains the characteristics of dependence on logical thinking and reasoning [20]. The application of the example combines the observation experiment method with the mathematical form [21]. Therefore, quantitative analysis often emphasizes the objectivity and observability of real objects, as well as the relationship and causality between phenomena and variables [10].Clustering refers to finding out the common characteristics of a group of objects in the database and classifying them into different categories according to different ways. Its purpose is to match the data elements in the database with the given category through the classification model [11]. It can be applied to application classification and trend prediction, and data groups can be divided into different categories according to the similarity and difference of data. The data belonging to the same category are very similar, but the data similarity between different categories is very small, and the data correlation between categories is very low [22].Regression analysis should reflect the characteristics of database eigenvalues, and use a function to express the relationship of data mapping to find the dependency between attribute values. It can be applied to the research of data series prediction and correlation. Let the dependent variabley and the independent variables x1, X2, XK be related to(1)v=b0+b1x1+⋯+bkbk+e,e∼N0,σ2.Through sampling,n groups of observation data are obtained:(2)y1;x11,x21,⋯,xk1,y2;x2n,x2n,⋯,xkn,⋯yn;x1n,x2n,⋯,xkn,where xij is the jth observation value of the independent variable xi and yj is the jth value of the dependent variable y, substituting the above formula to get the data structure of the model:(3)y1=b0+b1x11+b2x12+⋯+bkxk1+e1,y2=b0+b1x12+b2x12+⋯+bkxk2+en,⋯yn=b0+b1x1n+b2x1n+⋯+bkxkn+en.The above equation is a k-element normal linear regression model, in which b0, b1,…,bk andσ2 are unknown parameters to be estimated and ε1,ε2,…,εn are independent identically distributed N0,σ2.


### 2.3. Fitting of the Multiple Regression Model

From the perspective of correlation analysis, studying the linear correlation between one variable and multiple variables is called complex correlation analysis [23, 24]. There is no difference between dependent variables and independent variables in complex correlation, but in practical applications, complex correlation analysis is often associated with multiple linear regression analysis. Therefore, complex correlation analysis generally refers to the dependent variable y and k independent variables x1,x2, …,xk.Multivariate linear regression model is required to meet the Gauss hypothesis of multivariate regression. The least square method is used to estimate the regression coefficientsb0,b1,…,bk.(4)l11b1+l12b2+⋯+l1kbk=L1y,l21b1+l22b2+⋯+l2kbk=L2y,...lk1b1+lk2b2+⋯+lkkbk=Lky,b0=y¯−b1x¯+b2x¯2+⋯+bkxk.Calculate the distance between all known stations, use the calculus knowledge to solve the above equation group, and skip the random term to get the multiple linear regression equation. The residual analysis uses the outlier test, and the standard residuals of the test points fall in the space (−2, 2).


### 2.4. The Dilemma between Bias and Error

In any statistical model, the model error includes two parts: variance error and deviation error (frequency scientists believe that the error comes from the change sample, and Bayes believes that the change of parameters will also cause errors) [25]. If we use all data to estimate, the bias error will be very high; if the model contains very few features, compared to the rich functions, the variance error will be very large. This is the so-called “dilemma between bias and variance” [26].Look at this from another perspective: if too many variables are added to the model, it is almost certain that some non-existent possibilities will be added. It is also called overfitting, because the model contains not only the real possibilities, but also some unnecessary possibilities. If we collect data outside the sample and use the overload model to predict, the prediction error will be very large. On the contrary, insufficient fitting means that the model contains only part of the required information, not all of it [27]. In the underfitting model, using the data outside the sample to predict will also cause a lot of prediction errors.Overfitting and underfitting are just like the dilemma of bias and variance. If we match “nearly fair” data, it means that we find a good balance between “the dilemma of bias and variance.” Therefore, the following work mainly involves the minimization of “test error.” Ideally, we can collect more “out-of-sample” data as “test data.” However, as an ideal solution, we can collect more data samples and test some models in some fantasy scenarios.In most cases, data cannot be collected outside the sample for various reasons. As a pseudo solution, we divide the sample into two parts: one for evaluation, called “training sample,” and the other for testing, called “test sample.” The advantage of using this trick is that we can minimize “false errors” to ensure that the model has a good description of the data [28], to achieve the best balance between bias and variance.


## 2.1. Cluster Analysis Method

Machine learning can be divided into two categories: supervised learning and unsupervised learning [5]. When all input and output variables in the learning situation are fully observed, we define the learning process as supervised learning [4]. In other words, in supervised learning problems, there are no missing or potential variables in the database. Therefore, supervised learning is more direct [6]. For some learning problems, in addition to being able to fully observe all variables, if we can fully observe the structure of the data production process, supervised learning can be regarded as a parameter evaluation problem. Like the maximum probability or least square estimation, if you do not know the data creation process, you must select a suitable model from many models to complete the learning problem [7].Because the model is not boundless and complex, for example, AIC, BIC, or cross-validation can find a “possibly correct” model to describe the data production process, which is Occam theory or PAC learning. In general, we do not know the process of data creation, but we also lack variables. When the output variable is lost, the learning problem becomes unsupervised [8, 9]. For unsupervised learning, the direct execution of AIC or BIC cannot reveal the distribution of potential variables and the information contained in potential variables. We must try to separate potential variables from the original data and evaluate them [10]. If the potential variables and other variables are independent of each other, the absence of such “offshore” variables will not have a great impact on the estimation. If the potential variable depends on other observed variables, we can use other observable variables to estimate the distribution or summary statistics of potential variables. In general, before evaluating potential variables, we need to determine the type of distribution, whether absolute or continuous [11]. In the case of continuous distribution, the best method is usually factor analysis or factor modeling, using all other variables to construct a new continuous distribution variable [12].Assuming that the potential variable is a polynomial, we can construct a Gaussian mixture model [13]. The above techniques are called cluster analysis. Cluster analysis collects infinite information in some limited set variables and uses these set variables to group the observed objects. In short, set analysis is a data processing method to classify a group of observation objects reasonably [14]. It is an important part of experimental machine learning and a common technology for analyzing statistical data. System analysis in machine learning is a part of unsupervised learning. Unlike supervised learning, the data in the dataset has no class label and is segmented by the similarity of feature data [15].


## 2.2. Cluster Regression Analysis Method

Clustering analysis is the process of dividing a group of physical or abstract objects into similar object classes. According to the survey object and purpose, regression analysis determines which is the independent variable (explanatory variable) and which is the dependent variable (explanatory variable), through the establishment of a regression model and control independent variables to evaluate and predict the dependence between research variables. For example, through correlation analysis, we can know that some variables are closely related, but which parts are the most important, and the degree of their interaction must be selected through cluster regression analysis [16, 17].Quantitative analysis is a method to determine the mathematical model based on statistical data and use the mathematical model to calculate the index and the value of the analysis object [18, 19]. It not only keeps the dependence on observation experiments and the collection of empirical data but also retains the characteristics of dependence on logical thinking and reasoning [20]. The application of the example combines the observation experiment method with the mathematical form [21]. Therefore, quantitative analysis often emphasizes the objectivity and observability of real objects, as well as the relationship and causality between phenomena and variables [10].Clustering refers to finding out the common characteristics of a group of objects in the database and classifying them into different categories according to different ways. Its purpose is to match the data elements in the database with the given category through the classification model [11]. It can be applied to application classification and trend prediction, and data groups can be divided into different categories according to the similarity and difference of data. The data belonging to the same category are very similar, but the data similarity between different categories is very small, and the data correlation between categories is very low [22].Regression analysis should reflect the characteristics of database eigenvalues, and use a function to express the relationship of data mapping to find the dependency between attribute values. It can be applied to the research of data series prediction and correlation. Let the dependent variabley and the independent variables x1, X2, XK be related to(1)v=b0+b1x1+⋯+bkbk+e,e∼N0,σ2.Through sampling,n groups of observation data are obtained:(2)y1;x11,x21,⋯,xk1,y2;x2n,x2n,⋯,xkn,⋯yn;x1n,x2n,⋯,xkn,where xij is the jth observation value of the independent variable xi and yj is the jth value of the dependent variable y, substituting the above formula to get the data structure of the model:(3)y1=b0+b1x11+b2x12+⋯+bkxk1+e1,y2=b0+b1x12+b2x12+⋯+bkxk2+en,⋯yn=b0+b1x1n+b2x1n+⋯+bkxkn+en.The above equation is a k-element normal linear regression model, in which b0, b1,…,bk andσ2 are unknown parameters to be estimated and ε1,ε2,…,εn are independent identically distributed N0,σ2.


## 2.3. Fitting of the Multiple Regression Model

From the perspective of correlation analysis, studying the linear correlation between one variable and multiple variables is called complex correlation analysis [23, 24]. There is no difference between dependent variables and independent variables in complex correlation, but in practical applications, complex correlation analysis is often associated with multiple linear regression analysis. Therefore, complex correlation analysis generally refers to the dependent variable y and k independent variables x1,x2, …,xk.Multivariate linear regression model is required to meet the Gauss hypothesis of multivariate regression. The least square method is used to estimate the regression coefficientsb0,b1,…,bk.(4)l11b1+l12b2+⋯+l1kbk=L1y,l21b1+l22b2+⋯+l2kbk=L2y,...lk1b1+lk2b2+⋯+lkkbk=Lky,b0=y¯−b1x¯+b2x¯2+⋯+bkxk.Calculate the distance between all known stations, use the calculus knowledge to solve the above equation group, and skip the random term to get the multiple linear regression equation. The residual analysis uses the outlier test, and the standard residuals of the test points fall in the space (−2, 2).


## 2.4. The Dilemma between Bias and Error

In any statistical model, the model error includes two parts: variance error and deviation error (frequency scientists believe that the error comes from the change sample, and Bayes believes that the change of parameters will also cause errors) [25]. If we use all data to estimate, the bias error will be very high; if the model contains very few features, compared to the rich functions, the variance error will be very large. This is the so-called “dilemma between bias and variance” [26].Look at this from another perspective: if too many variables are added to the model, it is almost certain that some non-existent possibilities will be added. It is also called overfitting, because the model contains not only the real possibilities, but also some unnecessary possibilities. If we collect data outside the sample and use the overload model to predict, the prediction error will be very large. On the contrary, insufficient fitting means that the model contains only part of the required information, not all of it [27]. In the underfitting model, using the data outside the sample to predict will also cause a lot of prediction errors.Overfitting and underfitting are just like the dilemma of bias and variance. If we match “nearly fair” data, it means that we find a good balance between “the dilemma of bias and variance.” Therefore, the following work mainly involves the minimization of “test error.” Ideally, we can collect more “out-of-sample” data as “test data.” However, as an ideal solution, we can collect more data samples and test some models in some fantasy scenarios.In most cases, data cannot be collected outside the sample for various reasons. As a pseudo solution, we divide the sample into two parts: one for evaluation, called “training sample,” and the other for testing, called “test sample.” The advantage of using this trick is that we can minimize “false errors” to ensure that the model has a good description of the data [28], to achieve the best balance between bias and variance.


## 3. Experimental Design and Analysis

### 3.1. Dataset

The research object is 10 games of CBA playoffs semifinals and 4 games of finals in 2018-2019 season, 5 games of NBA Playoffs Southwest finals, 6 games of Northwest finals, and 5 games of finals. Among them, the CBA semifinal team includes Liaoning team, Sichuan team, Guangdong team, and Xinjiang team; the CBA final team includes Liaoning team and Guangdong team; the NBA semifinal team includes San Antonio Spurs, Memphis Grizzlies, Dallas Mavericks, and Denver Nuggets; the NBA final team includes Memphis Grizzlies and Dallas Mavericks.


### 3.2. Experiment Process

#### 3.2.1. Data Collection

Collect the player’s personal information, team information, and game videos, and learn about the game situation and other relevant information in recent years through the official websites of NBA and CBA. The interview outline is built around the relevant education elements of basketball players’ actual combat ability. It should be interviewed and negotiated with relevant experts and trainers, and the interview process and content should be organized. The specific interview content includes the scoring rules, mechanism, and system of competition. Provide accurate data support for the training of basketball team players and the scoring mechanism of this study, as shown in Table1.Table 1
Information gathering.
CategoryInformationPersonal informationName, height, weight, competition positionMember informationTeam profile, full-year game dataPersonal statisticsPlayer’s field average ranking and full-year competition dataTeam profileTeam field average data rankingTeam statisticsThe team’s performance ranking in recent yearsPerformance statisticsVideo of 10 games in the team’s rematch and final


#### 3.2.2. Experimental Steps

This paper introduces a system analysis method based on cluster regression analysis model. The process of calculating this algorithm is completely automatic. The analyst should only set a precision limitT according to the needs of the actual work, and the algorithm divides the objects whose distance is less than the limit into the same category. When performing the algorithm, T is also defined as the set centroid stop threshold of the model set. That is, when R > T sets the radius, the center of the model stops changing. Algorithm 1 is described as follows.Algorithm 1:For the set of multiple linear regression models A=M1,M2,…,MN, the accuracy of clustering is limited to T.
(1)
Fori = 1, 2,...,N, repeat the following steps (2)–(8);(2)
Select any model from the model set A and record it asMi;(3)
Ifi = 1, separate Mi into one category, and make A = A − M, and then perform step (2); otherwise, directly perform step (4);(4)
Calculate the distance betweenMi and the centroids of each clustering model set, select the model set with the minimum distance from Mi, and record the model set as Aj, and the distance between the two as Dij, and perform step (5);(5)
IfDij < T, classify Mi as model set Aj and make A = A-Mi; perform step (6); otherwise, perform step (8);(6)
If the mass center ofAj is not fixed, adjust the mass center and radius of Aj, record the new radius as R (Aj), and carry out step (7). Otherwise, perform step (2).(7)
IfR (Aj) > T, fix the Aj center of mass and carry out step (2). Otherwise, perform step (2) directly.(8)
SeparateMi into one group and make A = A-M. Perform step (2);(9)
Finally, the centroid of each model set is readjusted;(10)
The algorithm ends.


### 3.3. Mathematical Statistics

Input the collected competition information into the algorithm model, see the difference between the actual results and the results obtained by the algorithm model, collect the collected data for classification, and analyze, summarize, and sort out the statistical data by using Excel 2015 software. Exploratory and confirmatory factor analysis was used to test the validity of the scale, and reliability analysis was used to test the reliability of the scale. After the competition, single factor analysis and multiple comparative analysis were used to evaluate the accuracy of the system. The correlation analysis method was used to discuss the correlation of the scoring mechanism, and the multiple linear regression analysis method was used to explore the internal correlation of the rating mechanism.


## 3.1. Dataset

The research object is 10 games of CBA playoffs semifinals and 4 games of finals in 2018-2019 season, 5 games of NBA Playoffs Southwest finals, 6 games of Northwest finals, and 5 games of finals. Among them, the CBA semifinal team includes Liaoning team, Sichuan team, Guangdong team, and Xinjiang team; the CBA final team includes Liaoning team and Guangdong team; the NBA semifinal team includes San Antonio Spurs, Memphis Grizzlies, Dallas Mavericks, and Denver Nuggets; the NBA final team includes Memphis Grizzlies and Dallas Mavericks.


## 3.2. Experiment Process

### 3.2.1. Data Collection

Collect the player’s personal information, team information, and game videos, and learn about the game situation and other relevant information in recent years through the official websites of NBA and CBA. The interview outline is built around the relevant education elements of basketball players’ actual combat ability. It should be interviewed and negotiated with relevant experts and trainers, and the interview process and content should be organized. The specific interview content includes the scoring rules, mechanism, and system of competition. Provide accurate data support for the training of basketball team players and the scoring mechanism of this study, as shown in Table1.Table 1
Information gathering.
CategoryInformationPersonal informationName, height, weight, competition positionMember informationTeam profile, full-year game dataPersonal statisticsPlayer’s field average ranking and full-year competition dataTeam profileTeam field average data rankingTeam statisticsThe team’s performance ranking in recent yearsPerformance statisticsVideo of 10 games in the team’s rematch and final


### 3.2.2. Experimental Steps

This paper introduces a system analysis method based on cluster regression analysis model. The process of calculating this algorithm is completely automatic. The analyst should only set a precision limitT according to the needs of the actual work, and the algorithm divides the objects whose distance is less than the limit into the same category. When performing the algorithm, T is also defined as the set centroid stop threshold of the model set. That is, when R > T sets the radius, the center of the model stops changing. Algorithm 1 is described as follows.Algorithm 1:For the set of multiple linear regression models A=M1,M2,…,MN, the accuracy of clustering is limited to T.
(1)
Fori = 1, 2,...,N, repeat the following steps (2)–(8);(2)
Select any model from the model set A and record it asMi;(3)
Ifi = 1, separate Mi into one category, and make A = A − M, and then perform step (2); otherwise, directly perform step (4);(4)
Calculate the distance betweenMi and the centroids of each clustering model set, select the model set with the minimum distance from Mi, and record the model set as Aj, and the distance between the two as Dij, and perform step (5);(5)
IfDij < T, classify Mi as model set Aj and make A = A-Mi; perform step (6); otherwise, perform step (8);(6)
If the mass center ofAj is not fixed, adjust the mass center and radius of Aj, record the new radius as R (Aj), and carry out step (7). Otherwise, perform step (2).(7)
IfR (Aj) > T, fix the Aj center of mass and carry out step (2). Otherwise, perform step (2) directly.(8)
SeparateMi into one group and make A = A-M. Perform step (2);(9)
Finally, the centroid of each model set is readjusted;(10)
The algorithm ends.


## 3.2.1. Data Collection

Collect the player’s personal information, team information, and game videos, and learn about the game situation and other relevant information in recent years through the official websites of NBA and CBA. The interview outline is built around the relevant education elements of basketball players’ actual combat ability. It should be interviewed and negotiated with relevant experts and trainers, and the interview process and content should be organized. The specific interview content includes the scoring rules, mechanism, and system of competition. Provide accurate data support for the training of basketball team players and the scoring mechanism of this study, as shown in Table1.Table 1
Information gathering.
CategoryInformationPersonal informationName, height, weight, competition positionMember informationTeam profile, full-year game dataPersonal statisticsPlayer’s field average ranking and full-year competition dataTeam profileTeam field average data rankingTeam statisticsThe team’s performance ranking in recent yearsPerformance statisticsVideo of 10 games in the team’s rematch and final


## 3.2.2. Experimental Steps

This paper introduces a system analysis method based on cluster regression analysis model. The process of calculating this algorithm is completely automatic. The analyst should only set a precision limitT according to the needs of the actual work, and the algorithm divides the objects whose distance is less than the limit into the same category. When performing the algorithm, T is also defined as the set centroid stop threshold of the model set. That is, when R > T sets the radius, the center of the model stops changing. Algorithm 1 is described as follows.Algorithm 1:For the set of multiple linear regression models A=M1,M2,…,MN, the accuracy of clustering is limited to T.
(1)
Fori = 1, 2,...,N, repeat the following steps (2)–(8);(2)
Select any model from the model set A and record it asMi;(3)
Ifi = 1, separate Mi into one category, and make A = A − M, and then perform step (2); otherwise, directly perform step (4);(4)
Calculate the distance betweenMi and the centroids of each clustering model set, select the model set with the minimum distance from Mi, and record the model set as Aj, and the distance between the two as Dij, and perform step (5);(5)
IfDij < T, classify Mi as model set Aj and make A = A-Mi; perform step (6); otherwise, perform step (8);(6)
If the mass center ofAj is not fixed, adjust the mass center and radius of Aj, record the new radius as R (Aj), and carry out step (7). Otherwise, perform step (2).(7)
IfR (Aj) > T, fix the Aj center of mass and carry out step (2). Otherwise, perform step (2) directly.(8)
SeparateMi into one group and make A = A-M. Perform step (2);(9)
Finally, the centroid of each model set is readjusted;(10)
The algorithm ends.


## 3.3. Mathematical Statistics

Input the collected competition information into the algorithm model, see the difference between the actual results and the results obtained by the algorithm model, collect the collected data for classification, and analyze, summarize, and sort out the statistical data by using Excel 2015 software. Exploratory and confirmatory factor analysis was used to test the validity of the scale, and reliability analysis was used to test the reliability of the scale. After the competition, single factor analysis and multiple comparative analysis were used to evaluate the accuracy of the system. The correlation analysis method was used to discuss the correlation of the scoring mechanism, and the multiple linear regression analysis method was used to explore the internal correlation of the rating mechanism.


## 4. Research on the Cluster Regression Analysis Model

### 4.1. Regression Standard Error of Each Model

Regression analysis is only an estimate of players’ score after the game. There is a way out between it and the actual value, but the error is within a reasonable range. The errors between different models are different. Discuss and analyze the differences between different models, as shown in Figure1.Figure 1
Regression standard error of various models.Four different types of regression models are tested and compared with their centroid models. As can be seen from the figure, there is not a big way out between the data. If the first mock exam is the first mock exam, the model error is not the same as the original model, which means that, in the same model category, the centroid model can better represent other models in the model. Therefore, in the first mock exam of the same model category, it is not necessary to build regression models one by one. Only selecting the centroid model of this model type can represent this kind of class very well, greatly reducing the modeling work and improving modeling efficiency.


### 4.2. Dataset of the Quadratic Switching Regression Model

If the dataset of quadratic polynomial regression is adopted, the parameters are taken from Table1, the quadratic switching regression model is y=βi1+βi2x+βi3x2, and the distribution of the experimental dataset of quadratic switching is shown in Table 2.Table 2
Experimental dataset.
DatasetnX value intervalβ1β2A42[25, 29](20, −1, 0.0625)(−4, 2, −0.0625)B31[7, 22](20, −2, 0.0625)(−3, 1, −0.0625)C28[7, 11](16, −2, 0.03125)(−1, 1, −0.03125)D44[9, 19](165, −23, 1)(278, −42, 2)From the data in the table, it can be seen that the four different regression models present different results and shapes due to different constant values. As shown in Figure2, it is the secondary switching regression model presented by the dataset A.Figure 2
Quadratic switching regression model.The graph of the dataset A is two kinds of symmetric quadratic function graphs. Line 1 is opened downward, and the peak value is 11 when the independent variablex is 15. The opening of line 2 is upward, and the minimum value is 5.5 when the independent variable x is 15. The intersection of the two lines is 9.5 and 23.5, and the dependent variable values are 8 and 7, respectively.


### 4.3. Players’ Postgame Score Prediction

The construction of the scoring model is also the main work of scoring players after the game. A good scoring model can improve the accuracy and reliability of scoring, to improve the application value of scoring. To build the model, this study proposes a regression algorithm-based model. The model uses the statistical data of athletes in the competition to match the scores of experts in the competition. After the model is built, the player statistics in the test set are used for testing and compared with the expert scoring data in the test set, as shown in Figure3.Figure 3
Players’ postmatch scoring prediction.The experimental results show that although the error of expert scoring is very small, the scoring mechanism based on cluster regression analysis model is more accurate, the error range is within 0.5 points, and the error range of expert scoring is within 1 point. Expert score and regression analysis model score can well predict the ball game score.


### 4.4. Experimental Results of Different Regression Methods

The third-party library ofPython, scikit learn, contains a large number of commonly used regression methods. It only needs simple calls and parameter settings to test the effect of different regression methods. Therefore, using the regression method package provided by scikit learn, we try to call a lot of different regression methods to replace the BP neural network in the basic scoring model and carry out training and testing. The experimental effect of some regression methods is not ideal, so this study does not show and analyze the regression methods with poor effect; only three methods with better experimental results are screened for comparative analysis with BP neural network: linearSVR, RFR, and ridge, as shown in Figure 4.Figure 4
Experimental results of different regression methods.Through the analysis, we can see that the relationship between the input and output data tends to be linear, so the linear regression method is better. Among other things, ridge is particularly good at the accuracy of the game prediction results, but the performance of the test set is that generally there is a state of fitting. If we can get all the data of OPTA and increase the amount of data in the training set, we should be able to get better results. In many linear regressions, RFR is the best. Therefore, other improved methods in the future choose RFR regression as the training method in the model. The least deviation is BP regression method, the deviation range is 0.1, the more obvious deviation is RFR and linearSVR, and the deviation value is about 1.


## 4.1. Regression Standard Error of Each Model

Regression analysis is only an estimate of players’ score after the game. There is a way out between it and the actual value, but the error is within a reasonable range. The errors between different models are different. Discuss and analyze the differences between different models, as shown in Figure1.Figure 1
Regression standard error of various models.Four different types of regression models are tested and compared with their centroid models. As can be seen from the figure, there is not a big way out between the data. If the first mock exam is the first mock exam, the model error is not the same as the original model, which means that, in the same model category, the centroid model can better represent other models in the model. Therefore, in the first mock exam of the same model category, it is not necessary to build regression models one by one. Only selecting the centroid model of this model type can represent this kind of class very well, greatly reducing the modeling work and improving modeling efficiency.


## 4.2. Dataset of the Quadratic Switching Regression Model

If the dataset of quadratic polynomial regression is adopted, the parameters are taken from Table1, the quadratic switching regression model is y=βi1+βi2x+βi3x2, and the distribution of the experimental dataset of quadratic switching is shown in Table 2.Table 2
Experimental dataset.
DatasetnX value intervalβ1β2A42[25, 29](20, −1, 0.0625)(−4, 2, −0.0625)B31[7, 22](20, −2, 0.0625)(−3, 1, −0.0625)C28[7, 11](16, −2, 0.03125)(−1, 1, −0.03125)D44[9, 19](165, −23, 1)(278, −42, 2)From the data in the table, it can be seen that the four different regression models present different results and shapes due to different constant values. As shown in Figure2, it is the secondary switching regression model presented by the dataset A.Figure 2
Quadratic switching regression model.The graph of the dataset A is two kinds of symmetric quadratic function graphs. Line 1 is opened downward, and the peak value is 11 when the independent variablex is 15. The opening of line 2 is upward, and the minimum value is 5.5 when the independent variable x is 15. The intersection of the two lines is 9.5 and 23.5, and the dependent variable values are 8 and 7, respectively.


## 4.3. Players’ Postgame Score Prediction

The construction of the scoring model is also the main work of scoring players after the game. A good scoring model can improve the accuracy and reliability of scoring, to improve the application value of scoring. To build the model, this study proposes a regression algorithm-based model. The model uses the statistical data of athletes in the competition to match the scores of experts in the competition. After the model is built, the player statistics in the test set are used for testing and compared with the expert scoring data in the test set, as shown in Figure3.Figure 3
Players’ postmatch scoring prediction.The experimental results show that although the error of expert scoring is very small, the scoring mechanism based on cluster regression analysis model is more accurate, the error range is within 0.5 points, and the error range of expert scoring is within 1 point. Expert score and regression analysis model score can well predict the ball game score.


## 4.4. Experimental Results of Different Regression Methods

The third-party library ofPython, scikit learn, contains a large number of commonly used regression methods. It only needs simple calls and parameter settings to test the effect of different regression methods. Therefore, using the regression method package provided by scikit learn, we try to call a lot of different regression methods to replace the BP neural network in the basic scoring model and carry out training and testing. The experimental effect of some regression methods is not ideal, so this study does not show and analyze the regression methods with poor effect; only three methods with better experimental results are screened for comparative analysis with BP neural network: linearSVR, RFR, and ridge, as shown in Figure 4.Figure 4
Experimental results of different regression methods.Through the analysis, we can see that the relationship between the input and output data tends to be linear, so the linear regression method is better. Among other things, ridge is particularly good at the accuracy of the game prediction results, but the performance of the test set is that generally there is a state of fitting. If we can get all the data of OPTA and increase the amount of data in the training set, we should be able to get better results. In many linear regressions, RFR is the best. Therefore, other improved methods in the future choose RFR regression as the training method in the model. The least deviation is BP regression method, the deviation range is 0.1, the more obvious deviation is RFR and linearSVR, and the deviation value is about 1.


## 5. Conclusions

This research focuses on the scoring of basketball players, combined with different machine learning algorithms, in three aspects of data collection, model design and optimization, and the application of ratings. This research first introduces the research background, research status, and problems encountered. After that, data preparation was carried out for these problems, and experiments and results analysis were carried out on these problems. A regression-based ball scoring model is proposed, which uses player statistics to match expert data. Experimental results show that the degree of influence of this model is higher than the accuracy of expert ratings.Although many different data are used in the comparative experiment, in this study, there is a certain deviation between the experimental conclusion and the actual situation, because there are only a few 30 games as the reference object because of the less value of the game parameter. Moreover, the data characteristics are not rich enough, just for the study of the ball scoring mechanism of basketball; ball includes not only basketball, but also football and table tennis, and so on. Among them, for the polynomial form of the switching regression model, in this form, there is a linear relationship between the characteristics of the strain and the independent variable; therefore, for the nonlinear data space, we can find a transformation to divide the nonlinear space into some combination of linear subspaces, so that the polynomial regression exchange model can be applied to the nonlinear data set, and expand the scope of application of the model.Cluster analysis and regression analysis are the main methods in this study, and the common methods of system analysis should be summarized. When the data creation process is unknown and the variables are lost, to realize the distribution of latent variables and the information contained in the latent variables, it is necessary to try to separate and evaluate the latent variables from the original data. Clustering analysis is generally understood as clustering data. It is pointed out that both Gaussian mixture model and factor analysis model are the application of the maximum entropy principle, but only make different assumptions about the distribution of potential variables. The collected data is closer to the actual data production process than any classification. This is actually a preparation for the later grouping algorithm. On the whole, they all provide a good theoretical basis for the scoring mechanism after competition. With the development of information technology, increasingly advanced and complex mechanical learning methods have been put forward. How to learn from and use the advanced methods in other fields and optimize and improve the characteristics of ball games is the focus of the next work.



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*Source: 5524076-2021-03-13.xml*