Based on the factors affecting sports performance, from a more comprehensive and broad perspective, after consulting the literature, 52 factors that affect the outcome of football matches are selected, including technology, tactics, physical fitness and referees’ penalties. By watching the video of the game, 52 influencing factors of 200 games and 400 teams were counted. The original data was statistically processed with correlation analysis and multiple linear regression analysis, and the statistics of the 26 European Cup games were substituted into the winning formula. To verify the scientific nature and objectivity of the formula, we aim to ascertain the core factors in the winning factors of a football game and the quantitative relationship between these factors and the result of the game, so as to provide a certain reference for football training, game analysis and scientific research. The technical and tactical ability of individuals and teams is the core competitive ability factor that affects the result of the game; from a single factor, 15 factor indicators have a significant impact on the result of a football match; on the whole, 10 factor indicators have a significant effect on the result of a football match. In addition, there is a certain quantitative relationship between these influencing factors and the results of the game; empirical evidence shows that the football game winning formula has a certain degree of science and objectivity.

#### Keywords

- football match
- winning factors
- winning formula
- multiple linear regression equation

#### MSC 2010

- 90C08

Training theory research and football competition practice show that factors such as the competitive ability of their own players and the team's group competitive ability, the opponent's competitive ability and the team's group competitive ability, and the referee's law enforcement ability and moral quality determine the football competition results. The contradictory analysis method provided by the law of the unity of opposites of materialist dialectics enlightens us: Among the many complex factors that determine the result of a football match, some factors have a decisive influence on the result of a football match. These factors are a football team's training and guarantee work. The areas that need to be addressed are identified and improved. Therefore, this study collected 52 indicators reflecting the football team's technical ability, tactical ability, physical fitness and referee's enforcement by watching videos. The original data was statistically processed using correlation analysis and multiple linear regression analysis, and the European Cup was used as the source. The statistical data of 26 games is substituted into the winning formula to verify the scientific nature and objectivity of the formula. It aims to find out the decisive factors that affect the results of football matches and the inherent quantitative relationships between these factors, and is the focus of training for all types of football teams. The determination of football as the target of our analysis and the analysis of player and team performance provide certain theoretical guidance, and also provide new ideas for the research of football researchers [1].

The research object is the core winning factors and winning formulas of football matches.

This study mainly used ‘football training’, ‘football match’, ‘World Cup’ and ‘European Cup’ as keywords to retrieve relevant documents in the CNKI full-text database. After screening, we read 50 new documents in the past 5 years, and at the same time consulted 8 The Ministry's monographs on football training provide documentary support for the determination of factor indicators and statistical scales and the analysis and discussion of statistical results.

Watched 200 games of 4 levels of games, and counted 52 factor indicators for 400 teams. These 52 factor indicators reflect the technical ability, tactical ability, physical ability and referee's enforcement in football matches. Among the five elements that reflect the players’ competitive ability and the team's competitive ability, psychological and sports intelligence indicators are difficult to measure and are reflected in the technical ability, tactical ability and physical performance of the players and the team, so they are not included in the statistics. The indicators used in the analysis are as follows: The statistics of the game are divided into 4 levels: the first level is the world competition, that is, the 2014 World Cup final stage 16 knockout games; the second level is the intercontinental competition, that is, the 2016 European Cup final stage 15 knockout games and the Americas. There are 8 knockout matches in the final stage of the Cup; the third level is the intercontinental club league, that is, the 2015–2016 season UEFA Champions League 29 knockout matches and the 2016 season Asian Champions League 29 knockout matches; the fourth level is the national league, including 2015 – the top five European leagues in 2016 (15 games each, 75 games in total) and the 2016 Chinese Super League (28 games). Some indicators are calculated using team twelve's football technical statistical software, and some indicators are calculated by watching videos according to statistical standards by dedicated personnel. All competitions only count the number of indicators in the regular game time, and the extra time part is not counted [2].

The SPSS20.0 software package was used to carry out correlation analysis and multiple linear regression analysis on the obtained data. Especially on the basis of the correlation analysis between each factor index and the competition result, the quantitative relationship between each factor index and the competition result is explored by using multiple linear regression analysis. And the statistical data of 26 European Cup matches were substituted into the winning formula to verify the scientific nature and objectivity of the formula.

On the basis of using statistical methods to process the original data, the logical methods of analysis, comparison, induction, deduction and reasoning are used to analyse the factors that play a decisive role in the results of football matches. At the same time, the relationship between factor indicators and football results is discussed, which is a quantitative relationship.

These indicators include team possession rate (X1), number of goals (X2), number of shots (X3), number of shots (X4), number of free kicks (X5), number of free kicks (X6), number of free kicks (X7), the number of corner kicks (X8), the number of crosses (X8), the success rate of crosses (X9), the successful entry into the 30 m area of the front field (X10), the successful entry into the penalty area (X11), the number of assists (X12), the number of counterattacks (X13), the number of passes (X14), pass success rate (X15), total number of short passes (X16), total number of mid-range passes (X17), total number of long passes (X18), total number of forward passes (X19), the total number of cross passes (X20), the total number of return passes (X21), the total number of breakthroughs (X22) and the number of offsides (X23).

These indicators include the number of goals conceded (X25), the number of shots (X26), the number of shots (X27), the number of steals (X28), the success rate of steals (X29), the number of steals (X30), the number of fights (X31), the success rate of the top (X32), the number of clearances (X33), the number of sieges (X34), the number of blocked shots (X35), the number of blocked shots (X36), the number of blocked passes (X37), the number of yellow cards (X38)), number of red cards (X39), number of saves (X40), number of fouls (X41), number of tackles (X42) and success rate of tackles (X43).

These indicators include full-court running distance (X44), ball control running distance (X45), non-ball running distance (X46), low-intensity running distance (X47), medium-intensity running distance (X48), high intensity running distance (X49) and extreme intensity running distance (X50).

These include the number of favourable penalties (X51) and the number of unfavourable penalties (X52).

The independent variable _{1} − _{27} in the regression model corresponds to each secondary index, and the detailed definition is shown in Table 1. The dependent variable _{1}, _{2}, . . . , _{k}_{0} is the constant term of the regression equation, also called the intercept, _{1}, _{2}, . . . , _{k}_{j}_{j}_{j}

Stepwise regression process

1 | X6 | 1 | 0.7855 | 0.7855 | 354.351 | 183.10 | <0.0001 |

2 | X13 | 2 | 0.0971 | 0.8826 | 174.172 | 40.54 | <0.0001 |

3 | X2 | 3 | 0.0342 | 0.9168 | 111.994 | 19.75 | <0.0001 |

4 | X20 | 4 | 0.0269 | 0.9437 | 63.5307 | 22.47 | <0.0001 |

5 | X11 | 5 | 0.0174 | 0.9611 | 32.8756 | 20.61 | <0.0001 |

6 | X21 | 6 | 0.0072 | 0.9684 | 21.3579 | 10.25 | 0.0025 |

7 | X23 | 7 | 0.0044 | 0.9728 | 15.0255 | 7.19 | 0.0103 |

8 | X19 | 8 | 0.0043 | 0.9771 | 9.0000 | 8.03 | 0.0070 |

In multiple linear regression analysis, it is necessary to study how many independent variables should be introduced into the model. If fewer independent variables are introduced, the regression equation will not be able to explain the changes of dependent variables well; but it is not that the more independent variables are the better, so it is necessary to adopt some strategies to control and filter the independent variables into the regression equation. We adopt the stepwise regression method, which is to test the import threshold of the P value according to the set regression coefficient significance, introduce independent variables into the model one by one, recalculate the P values of all coefficients in the model and screen variables according to the set elimination threshold. When selecting independent variables, we first select the variable with the highest linear correlation coefficient with the dependent variable into the equation, and perform various tests of the regression equation; then, we find the variable with the highest partial correlation coefficient with the dependent variable and pass the test among the remaining variables [3]. Regression equation, and various tests, are performed on the newly established regression equation; this process is repeated until there are no more variables that can enter the equation. Data processing is performed in SAS 8.01 for Windows software, the significance level of entering the model is set to 0.05 and the significance level of the excluded or retained variables is also set to 0.05. The analysis process of selecting variables and performing regression is shown in Table 1, the statistical results of model regression are shown in Table 2 and the regression coefficients are shown in Table 3.

Regression statistics results

Regression analysis | 8 | 0.14009 | 0.01751 | 229.10 | <0.0001 |

Residual | 43 | 0.00329 | 0.00007644 | ||

Total | 51 | 0.14338 |

DF, degree of freedom; MS, mean square; SS, total square.

Regression coefficient table

Intercept | 0.07407 | 0.01719 | 0.00142 | 18.57 | <0.0001 |

X6 | 0.27741 | 0.02728 | 0.00790 | 103.40 | <0.0001 |

X13 | 0.09219 | 0.01663 | 0.00235 | 30.72 | <0.0001 |

X2 | 0.13100 | 0.02305 | 0.00247 | 32.30 | <0.0001 |

X20 | 0.07443 | 0.01342 | 0.00235 | 30.74 | <.0001 |

X11 | 0.12904 | 0.02254 | 0.00250 | 32.77 | <0.0001 |

X21 | 0.04669 | 0.01905 | 0.00046 | 6.01 | 0.0184 |

X23 | 0.06296 | 0.02080 | 0.00070 | 9.17 | 0.0042 |

X19 | 0.06853 | 0.02419 | 0.00061 | 8.03 | 0.0070 |

SS, total square.

The regression equation is:

The coefficient of determination R2 = 0.9771, which is very close to 1, indicating that the regression equation is highly significant. _{2}, _{6}, _{11}, _{13}, _{19}, _{20}, _{21}, _{23} has a highly significant linear effect on

The F test value involves ascertaining whether the independent variable has a significant effect on the dependent variable as a whole. The F test value is 229.10, and the significance (Pr > F) is <0.0001, indicating that _{2}, _{6}, _{11}, _{13}, _{19}, _{20}, _{21}, _{23} has a significant influence on

Table 4 shows the estimated value, standard error and other data of the regression coefficient, indicating _{2}, _{6}, _{11}, _{13}, _{19}, _{20}, _{21}, _{23}. All eight independent variables passed the regression coefficient significance test.

The correlation between the outcome of the game and the indicators

X1 | 400 | 0.475 | 0.047 | X27 | 400 | −0.683 | 0.002 |

X2 | 400 | 0.976 | 0 | X28 | 400 | −0.183 | 0.469 |

X3 | 400 | 0.535 | 0.022 | X29 | 400 | 0.304 | 0.22 |

X4 | 400 | 0.683 | 0.002 | X30 | 400 | 0.122 | 0.63 |

X5 | 400 | 0.545 | 0.019 | X31 | 400 | 0.011 | 0.913 |

X6 | 400 | 0.416 | 0.086 | X32 | 400 | 0.34 | 0.167 |

X7 | 400 | 0.131 | 0.604 | X33 | 400 | 0.452 | 0.06 |

X8 | 400 | 0.098 | 0.7 | X34 | 400 | 0.657 | 0.003 |

X9 | 400 | 0.024 | 0.924 | X35 | 400 | 0.354 | 0.15 |

X10 | 400 | 0.085 | 0.737 | X36 | 400 | −0.219 | 0.383 |

X11 | 400 | 0.438 | 0.069 | X37 | 400 | −0.280 | 0.261 |

X12 | 400 | 0.523 | 0.026 | X38 | 400 | −0.173 | 0.493 |

X13 | 400 | 0.401 | 0.099 | X39 | 400 | 0.427 | 0.077 |

X14 | 400 | 0.617 | 0.006 | X40 | 400 | −0.527 | 0.025 |

X15 | 400 | 0.377 | 0.123 | X41 | 400 | −0.401 | 0.099 |

X16 | 400 | 0.295 | 0.235 | X42 | 400 | −0.450 | 0.061 |

X17 | 400 | 0.413 | 0.088 | X43 | 400 | 0.225 | 0.369 |

X18 | 400 | 0.402 | 0.098 | X44 | 400 | 0.228 | 0.363 |

X19 | 400 | 0.061 | 0.809 | X45 | 400 | −0.085 | 0.737 |

X20 | 400 | 0.511 | 0.03 | X46 | 400 | 0.182 | 0.469 |

X21 | 400 | 0.547 | 0.019 | X47 | 400 | 0.267 | 0.284 |

X22 | 400 | 0.206 | 0.411 | X48 | 400 | 0.383 | 0.117 |

X23 | 400 | 0.802 | 0 | X49 | 400 | 0.389 | 0.111 |

X24 | 400 | −0.012 | 0.962 | X50 | 400 | 0.073 | 0.774 |

X25 | 400 | −0.976 | 0 | X51 | 400 | 0.152 | 0.548 |

X26 | 400 | −0.559 | 0.016 | X52 | 400 | −0.152 | 0.548 |

Residual error refers to the difference between the actual observation value and the regression estimated value. Residual error analysis refers to analysing the reliability, periodicity or other interference of the data through the information provided by the residual error. The calculation formulas for residual and relative error are the following:

Front court 30 m area and side road area, FIFA's standard for field division has been adopted (Figure 1). For running intensity, we are adopting the China Super League running intensity level standard, that is, extreme intensity running for speeds >21 km per hour; high intensity running for speeds of 17–21 km per hour; medium intensity running for speeds of 14–17 km per hour; and 11–14 km per hour run for low intensity. Other indicators refer to the 2016/2017 FIFA competition rules.

Correlation analysis is used to obtain the correlation coefficients between 52 factor indicators and the results of the game (Table 4): total possession rate, number of goals, number of shots, number of shots, number of free kicks, number of successful attempts into the penalty area and number of counterattacks; forward 10 factors that reflect offensive skills and tactics, including: the number of straight passes, the number of cross passes and the number of breakthroughs; as well as 5 factors that reflect defensive skills and tactics, including: the number of goals conceded, the number of shots, the number of shots and the number of sieges and saves. The indicators have a significant relationship with the result of the game. This shows that these 15 technical and tactical factors have a significant impact on the results of football matches, and it also supports the theory that the level of skills and tactics is the core winning factor in determining the results of football matches.

Owning the ball is one of the fundamental ways to score goals in a football game. Therefore, long-term possession of the ball indicates an expansion of the chance of scoring goals. In addition, long-term possession of the ball can not only reduce the player's physical consumption but also increase the opponent's psychological pressure, which creates good conditions for winning the final game. The number of goals scored, the number of shots and the number of shots on target are all indicators that reflect a team's shooting ability and shooting efficiency. The only way to win a football game is to score more goals than the opponent. Therefore, if the team wants to win the game, it must improve the accuracy of the shot while strengthening the shot. Only in this way can the chance of scoring be increased and the game won. Therefore, these three indicators are the fundamental factors that determine the outcome of the game [4].

Under the guidance of the concept of ‘defines first, win first’, the coach puts the improvement of players and the team's defensive ability at the top of training. Through daily targeted training, the players’ personal defensive ability and the team's overall defensive ability have undergone significant improvement, resulting in the time and space available for the use of offensive players to become narrower and more difficult. In this case, as a method of set-kick offence, free-kick offence can use the advantageous conditions of set-kick to complete the shot and get the chance to score. Therefore, the implication is that free kick is also important for the team to win the game in modern football matches.

According to the sports classification method, football belongs to the hit category. Only by approaching the opponent's goal in the game can the goal rate be increased. Therefore, the restricted area has become key for both the offensive players and the defenders to compete in. Successfully scoring the opponent's penalty area means the threat of shooting, shooting accuracy and the improvement of the scoring rate, which largely determines the probability of the team winning. Therefore, the number of instances of successfully scoring the opponent's penalty area has become one of the important indicators that affect the outcome of football matches.

As the coaches of each team attach great importance to defensive capabilities, the individual defensive capabilities of the players of each team have been continuously improved, the team's partial and overall defensive organisation has become more rigorous, and coupled with the qualitative improvement of the players’ physical level, the offensive team is fighting in position. The time and space available in China is narrower and more difficult. In this case, taking advantage of the defensive team's loose defensive formation and the unformed defensive organisation, at the moment of the offensive and defensive transition, to launch a quick counterattack has become one of the important methods of each team's offensive, and it has also become the main attack method for scoring goals. Therefore, counterattack tactics are the main offensive means for teams to win games in modern football matches.

One of the outstanding features of modern football games is the high level of integrity. Therefore, the continuous improvement of the overall defensive ability of each team has made it more and more difficult for individual offences. Relying on the overall offence of the team is an important means to win the game. Therefore, passing has become the main means of connecting players and completing team offences. In the passing direction, a forward pass can break through the opponent's defines line and create a chance to score a goal; while a cross pass can shift the offensive direction, mobilise the opponent's defines line, create vertical penetration space and form a local number advantage. Therefore, these two types of passes greatly affect the outcome of the game.

Under the situation that each team attaches great importance to defines, the players’ personal defensive ability and the team's local and overall defensive organisation ability have been greatly improved. In this case, only the player's personal breakthrough ability can be continuously improved. Only in the confrontation with the defensive players can the victory be won, by breaking through the opponent's defines, thereby forming an advantage in the number of offensives in a local area, creating favourable conditions for finally breaking through the opponent's defines line, facilitating availability of optimal shooting opportunities and completing the goal. Therefore, personal breakthrough ability also has an important impact on the outcome of the game [5].

The number of goals conceded, the number of shots and the number of shots taken together reflect the final effect of the team's defines. In the course of the game, the team can only rely on the excellent personal defensive ability of the players and the local and overall tight defensive formation to make it difficult for the offensive team to complete the shot. In particular, to ensure that the goal is not lost, the team can win the game on this basis. Therefore, the number of goals conceded, the number of shots and the number of shots are important indicators that affect the outcome of the game.

Encirclement is the main indicator reflecting the local defines organisation. In the game, through the first defender's frontal delay or close pressing against the team player, combined with the partial coordination, orderly cooperation and rapid movement of the second and third defenders, they form an organisation with the first defender. Strict and well-defined local defensive formations form an encirclement to the team members, thereby improving the team's defensive quality and ensuring that the team concedes fewer or no goals. Therefore, the level of siege directly affects the quality of the team's defines, and to a large extent determines the outcome of the game.

As the last defender of the team, ‘a good goalkeeper is equal to half a team’ has become a consensus in football. A save is an important indicator that reflects the goalkeeper's defensive ability. The strength of this ability to save plays a very important role in ensuring that the team does not concede a goal. Therefore, improving the goalkeeper's ability to save has an important impact on the result of the game.

The high correlation between the above 15 offensive and defensive technical and tactical factors and the results of the game enlighten us to the following inference: deep understanding of modern football concepts, following modern football development trends, strengthening the players’ ball control and breakthrough capabilities, improving the quality of the team's direct and cross passes, making full use of the advantages of counterattacks and free kicks to launch an offence and a good grasp of shooting opportunities is where coaches need to focus on improving offensive training in the future. At the same time, it is necessary to improve the team's partial and overall defensive organisation ability, reduce the offensive team's shots and try to avoid the team's conceding. In addition, the importance of goalkeepers has become increasingly prominent, and goal-keeper training should be strengthened [6].

Through correlation analysis, we only understand the correlation between each factor index and the game result, but it cannot reflect the relationship between each factor index and the game result as a whole. In order to grasp and understand the impact of various factors on the results of the game as a whole, and to explore the quantitative relationship between the two, a multiple linear regression analysis was carried out with the game results as the dependent variable and each factor index as the independent variable.

The regression analysis adopts the full entry method. The correlation coefficient value (R) is 0.882, the determination coefficient R^{2} (Square) is 0.778 and the adjusted R^{2} (Adjusted Square) is 0.578, indicating that the regression model has a high degree of fit, and 10 selected independent variables: the number of goals, the number of free kicks, the number of successful attempts into the penalty area, the number of counterattacks, the number of forward passes, the number of cross passes, the number of breakthroughs, the number of goals conceded, the number of sieges and the number of saves explain 57.8 of the variance in the total score percentage, and the Durbin–Watson test value is 2.270, indicating that the residuals are independent of each other. The Durbin arson test is passed, and the regression equation can be used. The results of the analysis of variance calculated by the multiple linear regression analysis show (Table 5) that, in this multiple linear regression model, F is 3.888, P < 0.01 and there is a very significant difference, indicating that the regression analysis is meaningful [7].

Regression analysis variance of game winning factors and game performance

1 | Regression | 129.495 | 2.878 | 3.8880.000 |

Residual | 37.005 | 0.74 | ||

Total | 160.5 |

Given the significance level

What needs further explanation is that of the 15 factor indicators that are highly correlated with the game results through correlation analysis, only 10 indicators in the multiple linear regression model have high correlation with the game results. The reason is the unselected shots. There is a high correlation between the number of shots and the number of goals scored, so the most representative number of goals is selected; the number of goals shot and the number of shots are highly correlated with the number of goals conceded, so the most representative conceded goals were incorporated in the number selected; and the ball possession rate was not selected, mainly because the ball control is mainly reflected by the passing of the team's offence and the breakthrough of the individual offence, so there is a high correlation with the passing and the breakthrough, forward passes and cross passes. The selection of the ball and breakthrough largely reflects and represents the ball possession rate.

In order to verify whether the winning formula has a certain degree of scientific and objectivity, we take the 26 games in which the win–loss relationship is determined within 90 min of the group stage of the 2016 European Cup finals as an example, the 26 games and 52 team goals etc. The core winning factor indicators are substituted into the winning formula. Among the 22 games, the team with the larger Y value calculated by the winning formula won, and the winning rate reached 85%, which shows that the winning formula has a certain degree of scientific temperament and objectivity [8].

In terms of specific competition cases, the two matches of Wales

The technical and tactical capabilities of individuals and teams are the core competitive ability factors that affect the outcome of the game. The number of goals scored, the number of free kicks, the number of successful attempts into the penalty area, the number of counterattacks, the number of forward passes, the number of cross passes and the number of breakthroughs are indicators of offensive factors; the number of goals conceded, the number of sieges and saves are indicators of defensive factors that affect the core winning factor of football match results. There is a certain quantitative relationship between the 10 core winning factors and the results of football matches. The quantitative relationship in this research is only intended to provide a formula model to reflect the quantitative law between them. Empirical evidence shows that the winning formula of football matches is scientific and objective.

#### The correlation between the outcome of the game and the indicators

X1 | 400 | 0.475 | 0.047 | X27 | 400 | −0.683 | 0.002 |

X2 | 400 | 0.976 | 0 | X28 | 400 | −0.183 | 0.469 |

X3 | 400 | 0.535 | 0.022 | X29 | 400 | 0.304 | 0.22 |

X4 | 400 | 0.683 | 0.002 | X30 | 400 | 0.122 | 0.63 |

X5 | 400 | 0.545 | 0.019 | X31 | 400 | 0.011 | 0.913 |

X6 | 400 | 0.416 | 0.086 | X32 | 400 | 0.34 | 0.167 |

X7 | 400 | 0.131 | 0.604 | X33 | 400 | 0.452 | 0.06 |

X8 | 400 | 0.098 | 0.7 | X34 | 400 | 0.657 | 0.003 |

X9 | 400 | 0.024 | 0.924 | X35 | 400 | 0.354 | 0.15 |

X10 | 400 | 0.085 | 0.737 | X36 | 400 | −0.219 | 0.383 |

X11 | 400 | 0.438 | 0.069 | X37 | 400 | −0.280 | 0.261 |

X12 | 400 | 0.523 | 0.026 | X38 | 400 | −0.173 | 0.493 |

X13 | 400 | 0.401 | 0.099 | X39 | 400 | 0.427 | 0.077 |

X14 | 400 | 0.617 | 0.006 | X40 | 400 | −0.527 | 0.025 |

X15 | 400 | 0.377 | 0.123 | X41 | 400 | −0.401 | 0.099 |

X16 | 400 | 0.295 | 0.235 | X42 | 400 | −0.450 | 0.061 |

X17 | 400 | 0.413 | 0.088 | X43 | 400 | 0.225 | 0.369 |

X18 | 400 | 0.402 | 0.098 | X44 | 400 | 0.228 | 0.363 |

X19 | 400 | 0.061 | 0.809 | X45 | 400 | −0.085 | 0.737 |

X20 | 400 | 0.511 | 0.03 | X46 | 400 | 0.182 | 0.469 |

X21 | 400 | 0.547 | 0.019 | X47 | 400 | 0.267 | 0.284 |

X22 | 400 | 0.206 | 0.411 | X48 | 400 | 0.383 | 0.117 |

X23 | 400 | 0.802 | 0 | X49 | 400 | 0.389 | 0.111 |

X24 | 400 | −0.012 | 0.962 | X50 | 400 | 0.073 | 0.774 |

X25 | 400 | −0.976 | 0 | X51 | 400 | 0.152 | 0.548 |

X26 | 400 | −0.559 | 0.016 | X52 | 400 | −0.152 | 0.548 |

#### Regression coefficient table

Intercept | 0.07407 | 0.01719 | 0.00142 | 18.57 | <0.0001 |

X6 | 0.27741 | 0.02728 | 0.00790 | 103.40 | <0.0001 |

X13 | 0.09219 | 0.01663 | 0.00235 | 30.72 | <0.0001 |

X2 | 0.13100 | 0.02305 | 0.00247 | 32.30 | <0.0001 |

X20 | 0.07443 | 0.01342 | 0.00235 | 30.74 | <.0001 |

X11 | 0.12904 | 0.02254 | 0.00250 | 32.77 | <0.0001 |

X21 | 0.04669 | 0.01905 | 0.00046 | 6.01 | 0.0184 |

X23 | 0.06296 | 0.02080 | 0.00070 | 9.17 | 0.0042 |

X19 | 0.06853 | 0.02419 | 0.00061 | 8.03 | 0.0070 |

#### Regression analysis variance of game winning factors and game performance

1 | Regression | 129.495 | 2.878 | 3.8880.000 |

Residual | 37.005 | 0.74 | ||

Total | 160.5 |

#### Stepwise regression process

1 | X6 | 1 | 0.7855 | 0.7855 | 354.351 | 183.10 | <0.0001 |

2 | X13 | 2 | 0.0971 | 0.8826 | 174.172 | 40.54 | <0.0001 |

3 | X2 | 3 | 0.0342 | 0.9168 | 111.994 | 19.75 | <0.0001 |

4 | X20 | 4 | 0.0269 | 0.9437 | 63.5307 | 22.47 | <0.0001 |

5 | X11 | 5 | 0.0174 | 0.9611 | 32.8756 | 20.61 | <0.0001 |

6 | X21 | 6 | 0.0072 | 0.9684 | 21.3579 | 10.25 | 0.0025 |

7 | X23 | 7 | 0.0044 | 0.9728 | 15.0255 | 7.19 | 0.0103 |

8 | X19 | 8 | 0.0043 | 0.9771 | 9.0000 | 8.03 | 0.0070 |

#### Regression statistics results

Regression analysis | 8 | 0.14009 | 0.01751 | 229.10 | <0.0001 |

Residual | 43 | 0.00329 | 0.00007644 | ||

Total | 51 | 0.14338 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Response model for the psychological education of college students based on non-linear finite element equations Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Nonlinear Differential Equations in the Teaching Model of Educational Informatisation The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Research on tourism income index based on ordinary differential mathematical equation Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Sports Science Teaching of Athletics Based on Nonlinear Mathematical Equation Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Translog function in government development of low-carbon economy Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on the Psychological Distribution Delay of Artificial Neural Network Based on the Analysis of Differential Equation by Inequality Expansion and Contraction Method Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode The Model of Sugar Metabolism and Exercise Energy Expenditure Based on Fractional Linear Regression Equation Constructing Artistic Surface Modeling Design Based on Nonlinear Over-limit Interpolation Equation Numerical Simulation Analysis Mathematics of Fluid Mechanics for Semiconductor Circuit Breaker Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Human Body Movement Coupling Model in Physical Education Class in the Educational Mathematical Equation of Reasonable Exercise Course The contribution of structural equation model analysis to higher education agglomeration and innovation and entrepreneurship Study on the evolutionary game theory of the psychological choice for online purchase of fresh produce under replicator dynamics formula The influence of X fuzzy mathematics method in basketball tactics scoring Mathematical statistics algorithm in the bending performance test of corroded reinforced concrete beams under fatigue load Nonlinear strategic human resource management based on organisational mathematical model Back propagation mathematical model for stock price prediction Evolutionary game research on the psychological choice of online shopping of fresh agricultural products based on dynamic simulation model Differential equation model of financial market stability based on big data Multi-attribute decision-making methods based on normal random variables in supply chain risk management Linear fractional differential equations in bank resource allocation and financial risk management model Construction and reform of art design teaching mode under the background of the integration of non-linear equations and the internet Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Financial accounting measurement model based on numerical analysis of rigid normal differential equation and rigid generalised functional equation Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory College students’ innovation and entrepreneurship ability based on nonlinear model Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Mathematical simulation analysis of optimal testing of shot puter's throwing path Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings The term structure of economic management rate under the parameter analysis of the estimation model based on common differential equation Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data The improvement of museum information flow based on paste functional mapping method The art design of industrialised manufacturing furniture products based on the simulation of mathematical curves TOPSIS missile target selection method supported by the posterior probability of target recognition Research on Evaluation of Intercultural Competence of Civil Aviation College Students Based on Language Operator The incentive contract of subject librarians in university library under the non-linear task importance Modelling and Simulation of Collaborative Innovation System in Colleges and Universities Based on Interpreted Structural Equation Model Small amplitude periodic solution of Hopf Bifurcation Theorem for fractional differential equations of balance point in group competitive martial arts The Optimal Solution of Feature Decomposition Based on the Mathematical Model of Nonlinear Landscape Garden Features Composite mechanical performance of prefabricated concrete based on hysteresis curve equation Higher education innovation and reform model based on hierarchical probit Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot The teaching of sports science of track and field-based on nonlinear mathematical equations Visual error correction of continuous aerobics action images based on graph difference function Ecological balance model of effective utilization of agricultural water resources based on fractional differential equations Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Precision algorithms in second-order fractional differential equations Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Fractional differential equations in National Sports Training in Colleges and Universities Radioactive source search problem and optimisation model based on meta-heuristic algorithm Visualized calculation of regional power grid power data based on multiple linear regression equation Application of mathematical probabilistic statistical model of base – FFCA financial data processing Least-squares method and deep learning in the identification and analysis of name-plates of power equipment Research on a method of completeness index based on complex model Distribution network monitoring and management system based on intelligent recognition and judgement Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Topological optimisation technology of gravity dam section structure based on ANSYS partial differential equation operation Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control Analysing the action techniques of basketball players’ shooting training using calculus method Engineering project management based on multiple regression equation and building information modelling technology Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology