Analysis of the results of the comprehensive efficiency of competitive sports inputs
The comprehensive efficiency (also known as technical efficiency, TE value of DEA-CCR) analyzed in this paper refers to whether the structure of competitive sports resources in each province in China can meet the development goals and overall requirements of competitive sports and give full play to the maximum efficiency of the resources. The comprehensive efficiency results of China’s competitive sports resource inputs are analyzed in Table 2. Results verify: 1) There are five provinces (cities and districts), including Tianjin, where the comprehensive efficiency of competitive sports training benefits is 1, i.e., the DEA effective state, reaching the Pareto optimization with the highest resource input and output benefits. 2) The mean value of the comprehensive efficiency of the other 24 regions is 0.571, which is in the ineffective state of DEA. In order to make it as close as possible to the Pareto-optimal state, the above provinces need to make balanced adjustments to the quantity and configuration of the resources invested in 42.9% of the competitive sports. 3) The standard deviation of the efficiency of national competitive sports training is 0.277, which indicates that the input efficiency of local competitive sports in China is generally low and there are serious regional efficiency differences. 4) The combined efficiency of training benefits is below the national average in 15 provinces, accounting for more than half of the total, requiring deeper improvements in resource structure and optimization direction. At the region-wide level, the overall efficiency of China’s competitive sports training benefits generally shows a developmental trend of eastern region (0.868) > central region (0.554) > western region (0.472). And the eastern region is much higher than the other two regions, and presents the provinces of Beijing, Tianjin, Hebei, Shandong, Jiangsu, Zhejiang, Shanghai, Yunnan, Guizhou, Chongqing and other provinces presenting similar phenomena of efficiency, which precisely reflects the regional agglomeration effect. Speculate on the reasons that led to this phenomenon: 1) Under the trend of digitization of the sports economy, the effect of spatial distance makes neighboring regions have similar levels of economic development, and the positive correlation between the comprehensive economic strength of cities and the level of development of the digital economy leads to the convergence of the comprehensive efficiency of resource inputs in different geographical areas. 2) China’s digital construction has reached the world’s leading level, but the economy is more backward in the central and western regions to strengthen the construction of sports digital intelligence there is still much room for improvement, compared with the eastern provinces of resources, talents and other competitive advantages are not obvious, resulting in a convergence of inputs of the overall efficiency of the lower. 3) The Beijing-Tianjin-Hebei and Yangtze River Delta regions, with their steadily growing digital economic strength, clustering of scientific and technological innovation centers, and the city’s leading effect, are becoming the key forces supporting the high-quality development of competitive sports, leading to the unique competitive advantages generated by these provinces in terms of management mechanisms, scientific and technological innovations, and technological breakthroughs.
Analysis of results for pure technical and scale efficiency of competitive sport inputs
Pure technical efficiency analysis
Pure Technical Efficiency (PTE) is the efficiency result calculated by Variable Returns to Scale (VRS) model, which is used to measure the input factor production efficiency of the Decision Making Units (DMU), i.e., each province, under the condition of optimal scale, and it can respond to the level of allocation of the input resources in the development of competitive sports in each province (city and district)23. In this study, pure technical efficiency mainly refers to the management quality of Chinese provinces in the process of developing competitive sports, i.e., whether the resources for the five input indicators constructed (coaches, athletes, program expenditures, scientific research funds, and sports institutions) can be systematized and institutionalized to form a complete sports operation and management mechanism, and to achieve optimal efficiency. As can be seen from Table 2, the national average value of pure technical efficiency of competitive sports inputs is 0.750, with 10 provinces (municipalities and districts) reaching a pure technical efficiency of 1, and 65.5% of the regions having an efficiency value of less than 1, indicating that the level of allocation of competitive sports resources and the quality of management in most of the provinces at the current stage of development is not of high quality, i.e., under the conditions of the established input factors in order to achieve the optimal scale of production.
Same as the comprehensive efficiency, the pure technical efficiency of competitive sports training effectiveness in the eastern region of China is still far ahead of the other two regions, but unlike it, the pure technical efficiency in the western region is better than that in the central region (0.663 > 0.573), and the provinces that are lower than the national average are evenly distributed in the central and western regions. This illustrates that the efficiency of competitive sports training in most Chinese provinces is strongly influenced by pure technical efficiency, while also encompassing the combined effects of other indicators such as scale efficiency. To that end, the following substantive recommendations are made: first, deepen the development strategy of the digital economy, improve the digitization of competitive sports, and strengthen the quality of inputs and the direction of the use of competitive sports resources. For regions such as Anhui, Jilin, and Gansu, where the investment of competitive sports resources is much lower than the national efficiency average, more countermeasures should be made in various aspects such as human resource structure, talent management ability, and innovative management mechanisms to improve the overall training efficiency. Second, to expand the influence of the regional agglomeration effect and to utilize the exemplary role of the eastern provinces with higher efficiency values. The mean value of the efficiency of competitive sports training in the eastern region is as high as 0.959, which fully indicates that they have a strong sports control capacity and a high level of resource management, while other regions with lower efficiency values should further strengthen cooperation with the eastern region in terms of talent exchange and policy learning while strengthening the digitalization of their own sports in order to scale down the efficiency differences between them and the developed regions. Third, in the flourishing stage of the digital economy, it is still necessary to strengthen the coordinated development of the quantity and utilization rate of the input of competitive sports resources, and to empower the cause of competitive sports by means of digital science and technology, so as to improve the quality of the management of the resources of competitive sports and realize the synergistic development of “quality” and “quantity”.
Scale efficiency analysis
Scale efficiency (SE) refers to the gap between the actual scale of resource input and the optimal scale of production in each region, which can be used to indicate the agglomeration level of the scale of resource input in competitive sports in each province, i.e., when increasing the proportion of input of resource elements, the value of the increase in the output of benefits is greater than the scale of the actual input, which can be used as a reference for the regulation of the “quantity” of the financial input of the competitive sports business to reach the optimal scale of efficiency24. The scale efficiency discussed in this paper specifically refers to the optimization of competitive sports training efficiency through the rational regulation of the amount of resources invested in the five competitive sports. Table 2 shows the results: 1) The average value of scale efficiency of China’s competitive sports training effectiveness is 0.880, and only six provinces have reached scale efficiency, accounting for 20.69% of the total, indicating that most provinces are in scale ineffectiveness, and there exists a certain degree and scale of resource waste phenomenon, that is, there exists a problem of in-coordination between the scale of financial input and the level of resource allocation and quality of management in the development of competitive sports undertakings. 2) Comparison of the data in Table 2 shows that there is a consistency between the scale efficiency of competitive sports training efficiency and the provinces where the combined efficiency is effective. It can be hypothesized that the non-efficiency of the comprehensive efficiency of competitive sports inputs may be due to the non-efficiency of scale efficiency. The three provinces (regions) of Hainan, Ningxia and Guizhou have a pure technical efficiency of 1, while the comprehensive efficiency does not reach the Pareto optimum, and it is inferred that the quantity of resource inputs, the scale and the quality of management are the important reasons for the non-efficiency of their input and output efficiencies. 3) Anhui, Jiangxi, Henan, Inner Mongolia and other provinces (municipalities and districts) whose pure technical efficiency is lower than the value of scale efficiency, the reason for their non-effective comprehensive efficiency stems more from the fact that it is caused by lower pure technical efficiency, and that there are greater problems in the operating mechanism, talent training system, resource allocation and management level, and so on. 4) The pure technical efficiency of Jiangsu, Zhejiang, Ningxia and Guizhou is 1, but the scale efficiency and comprehensive efficiency are not to reach the effective state, it can be inferred that the scale and quantity of resource inputs are the main reasons leading to the non-effective training efficiency of the four provinces (regions).
In summary, it can be seen that the lack of competitive sports training effectiveness in most provinces is related to the quality of management, while such provinces (regions) as Ningxia, Hainan and Guizhou are more closely related to the scale and quantity of resources invested in competitive sports. In view of this, at the national level, most of China’s provinces, while expanding the proportion of resources invested, are paying more attention to the utilization of the “quality” of resources and the rational distribution of the structural system. Dissecting the intrinsic structure of provincial input resources to see, the provinces in the central and western regions should invest steadily from the scale and quantity of resource inputs, grasp the quality of resources, realize the two-way-driven coupling and optimization mechanism and leaps and bounds, improve the efficiency of competitive sports training, and shrink the efficiency differences between regions.
Rewards of scale
A change in the returns to scale refers to the fact that, given a particular premise, an increase in resource inputs and an increase in scale will increase the efficiency of output25. Changes in returns to scale corroborate the law of diminishing marginal utility in economics, which states that the returns to scale of production technology in each industry go through three stages: increasing, constant, and decreasing26. In this study, changes in returns to scale are assumed to be based on a constant level of technology, and the scale and quantity of resource inputs to competitive sport will expand the output benefits, but if a certain range is exceeded, the increase in benefits will be much less than the scale and value of the resource inputs, and may even result in an absolute reduction in the benefits of training. As can be seen from Table 2, Beijing, Hebei, Jiangsu, Zhejiang and other 8 provinces (municipalities and districts) show the development trend of diminishing returns to scale; Hainan, Anhui, Xinjiang, Guizhou, Inner Mongolia and other 14 provinces are in the stage of increasing returns to scale. Namely, China’s management and optimization of the quantity, scale and quality of input resources for the development of competitive sports programs in a new phase of digital economy-enabled sports development can increase the training benefits of competitive sports. However, for the provinces with efficient scale efficiency and fixed returns to scale except Fujian, which has increasing returns to scale, they are on the production frontier of the DEA model, and have the characteristic that increasing or decreasing the scale of resource inputs results in increasing or decreasing returns in the same proportion. To this end, it is recommended that managers and policy makers in the above provinces pay attention to innovations in resource management systems and mechanisms and rationalize the resource structure. It is recommended that regions in central and western China that are lagging behind in economic development and slow in the construction of the digital economy should, within the scope of conditions, expand the scale of resource input as much as possible, while focusing on the quality of resource management and the level of allocation, and strengthen exchanges and cooperation with the eastern region, so as to enhance the overall level of development and narrow the differences between regions. Provinces in the Beijing-Tianjin-Hebei and Yangtze River Delta regions have implemented support policies for central and western provinces, accelerated the construction of sports numbers and intelligence, and strengthened inter-provincial resource sharing and talent flow, laying the foundation for the realization of a balanced regional development of the benefits of competitive sports training.
Table 2
Results of DEA evaluation of training benefits of competitive sports in China’s provincial areas
Regional Division | Regional | Technical Efficiency(TE) | Pure Technical Efficiency(PTE) | Scale Efficiency(SE) | Return on Scale |
Eastern Region | Beijing | 0.907 | 0.983 | 0.923 | drs |
Tianjin | 1 | 1 | 1 | — |
Hebei | 0.836 | 0.849 | 0.984 | drs |
Liaoning | 1 | 1 | 1 | — |
Shanghai | 1 | 1 | 1 | — |
Jiangsu | 0.968 | 1 | 0.968 | drs |
Zhejiang | 0.905 | 1 | 0.905 | drs |
Fujian | 0.814 | 0.814 | 1 | irs |
Shandong | 1 | 1 | 1 | — |
Guangdong | 0.667 | 0.902 | 0.740 | drs |
Hainan | 0.453 | 1 | 0.453 | irs |
East Section | 0.868 | 0.959 | 0.906 | |
Central Region | Anhui | 0.350 | 0.356 | 0.982 | irs |
Jiangxi | 0.410 | 0.445 | 0.921 | irs |
Henan | 0.444 | 0.459 | 0.968 | irs |
Hubei | 0.685 | 0.733 | 0.934 | drs |
Hunan | 0.857 | 0.887 | 0.966 | drs |
Jilin | 0.298 | 0.299 | 0.997 | |
Shanxi | 0.396 | 0.404 | 0.982 | irs |
Heilongjiang | 0.994 | 0.998 | 0.997 | — |
Central Section | 0.554 | 0.573 | 0.968 | |
Western Region | Gansu | 0.281 | 0.282 | 0.995 | irs |
Xinjiang | 0.363 | 0.552 | 0.658 | irs |
Shaanxi | 0.436 | 0.437 | 0.999 | irs |
Sichuan | 0.628 | 0.654 | 0.959 | drs |
Chongqing | 0.523 | 0.610 | 0.857 | irs |
Guizhou | 0.467 | 1 | 0.467 | irs |
Yunnan | 0.535 | 0.819 | 0.653 | irs |
Inner Mongolia | 0.272 | 0.275 | 0.987 | irs |
Xizang | 1 | 1 | 1 | — |
Ningxia | 0.218 | 1 | 0.218 | irs |
Western Section | 0.472 | 0.663 | 0.779 | |
| National Average | 0.645 | 0.750 | 0.880 | |
| SD | 0.277 | 0.272 | 0.201 | |
Note: 1)TE refers to Technical Efficiency; PTE refers to Pure Technical Efficiency; SE refers to Scale Efficiency (SE = CCR-TE/BCC-TE); 2)In the column of Rewards of Scale, “—” in the column of returns to scale means that the returns to scale in the province are constant, irs (increasing) means that the returns to scale in the province are increasing, and drs (decreasing) means that the returns to scale in the province are decreasing. |
Analysis of target value results
Input redundancy rate
In this paper, the input redundancy rate refers to the ratio of the improved target value and the original value of the input of competitive sports resources in each province (city and district), and the larger the value is, it means that there are excessive inputs on this indicator, which leads to the lower comprehensive efficiency of the input of competitive sports resources27, and the results of the analysis are shown in Table 3.
In terms of input indicators for sports organizations, athletes, coaches, project expenditures and scientific research funds, 19 provinces (municipalities and districts) have redundancy in resource input, indicating that there is a general phenomenon of wastefulness in the input of resources for competitive sports undertakings in these provinces, and the input indicator of X5 (scientific research funds) has the highest redundancy of up to 66.54%, with Hebei, Shanxi and other regions having up to 90% or more. This is in line with the analytical results of Yuan Lingfeng in his article, “Research on the Benefits of China’s Provincial Sports Public Finance Inputs in the Context of the Construction of a ‘Sports Powerful Country’”. Analyzed at the data level alone, most provinces (cities and districts) can improve the effectiveness of competitive sports training by reducing research funding by more than 60%. However, from the point of view of the special case of scientific research funding and in conjunction with the reality of China, the following reasons may exist behind the high redundancy rate of scientific research funding: first, China’s competitive sports research is disconnected from practice, making it difficult to connect research results with actual training; second, the scientific research results only stay in the stage of theoretical foundation, lack of real data support materials, and with the deep development of the digital economy, the actual training data elements, the level of sports intelligence, etc. to make higher requirements, resulting in the scientific research results and the practice of competitive sports “fork in the road”, difficult to serve in the practice of athleticism. In order to improve the effectiveness of the outputs of the provinces, it is recommended that future innovations in scientific research results take more advantage of digital intelligence to support the ability of scientific research workers to innovate in their research on the subject matter and to truly realize the transformation of textual content into sports practice.
In Table 3, Heilongjiang, Jilin, and Fujian have three indicators that exceed the mean redundancy rate in the input of resources for competitive sports, and Fujian, Guangdong, and Hebei have higher input redundancy rates. The reason for this is mainly due to the fact that the eastern provinces have a strong resource base in terms of “people, money and materials”, and the overall strength of the economy is stronger, resulting in the faster development of the digital economy, leading to the current output of pursuing athletic performance in terms of the scale and quantity of resources. Shaanxi, Inner Mongolia, and Jilin are related to their own regional characteristics and advantageous programs, such as ice and snow programs in Jilin, and traditional sports (horse racing, wrestling, and archery) in Inner Mongolia and Shaanxi, and it is hypothesized that the redundancy rate may be higher than the national average due to the large-volume investments made by these provinces in their characteristic advantageous programs. To this end, it is recommended from the perspective of indicator resource inputs: first, to optimize the number of coaches and to improve the coaching level of coaches, we can learn from the salary reward mechanism of the 13th National Games to motivate coaches to improve their coaching ability; second, the system of training athletes should be perfected, and athletic talents should be cultivated with the help of multiple forces, so as to absorb and cultivate excellent reserve talents at multiple levels; third, science and technology is a powerful engine to promote the rapid improvement of sports performance and training level, fully utilizing the digital economy to empower the scientific training system of competitive sports28; fourth, improve the system of project declaration and fund management of scientific research topics, and truly implement them into training practice, so as to comprehensively improve the success rate of athletes. To sum up, each province (city and district) should optimize the allocation of resources in an all-round and multi-level manner according to its own redundancy rate and the current status quo of the development of competitive sports undertakings, so as to improve the effectiveness of competitive sports training.
Table 3
Input redundancy rate and output insufficiency rate of competitive sports training effectiveness in China’s provincial areas
Eastern Region | | Input Redundancy Rate | Output Shortfall Rate |
Provinces | X1 | X2 | X3 | X4 | X5 | Y1 |
Beijing | — | — | — | 22.48 | 25.35 | 1.73 |
Tianjin | — | — | — | — | — | — |
Hebei | 24.77 | — | 46.68 | — | 95.75 | 17.76 |
Liaoning | — | — | — | — | — | — |
Shanghai | — | — | — | — | — | — |
Jiangsu | — | — | — | — | — | — |
Zhejiang | — | — | — | — | — | — |
Fujian | 38.68 | — | — | 39.72 | 99.86 | 22.80 |
Shandong | — | — | — | — | — | — |
Guangdong | 26.04 | — | 15.14 | 48.45 | — | 10.89 |
Hainan | — | — | — | — | — | — |
Central Region | Anhui | 7.55 | — | 24.46 | — | 56.07 | 180.78 |
Jiangxi | 69.50 | — | 14.05 | — | — | 124.49 |
Henan | — | — | 34.61 | — | 52.69 | 117.93 |
Hubei | 48.83 | — | — | — | 94.95 | 36.50 |
Hunan | 53.10 | — | 0.66 | — | 57.74 | 12.70 |
Jilin | 45.83 | 0.92 | — | 27.94 | 85.68 | 234.10 |
Shanxi | 35.36 | — | 26.30 | — | 65.28 | 147.80 |
Heilongjiang | 58.97 | 31.36 | — | 30.30 | 38.49 | 0.25 |
Western Region | Gansu | 19.26 | — | — | 25.82 | 40.16 | 254.80 |
Xinjiang | 58.96 | 30.18 | — | 15.85 | — | 81.08 |
Shaanxi | 35.19 | — | — | 32.10 | 94.69 | 128.94 |
Sichuan | 54.27 | — | — | 17.99 | — | 52.83 |
Chongqing | 54.25 | — | 69.16 | — | — | 64.01 |
Guizhou | — | — | — | — | — | — |
Yunnan | 60.91 | 55.07 | — | 1.14 | — | 22.03 |
Inner Mongolia | 48.35 | — | 23.58 | — | 58.28 | 263.59 |
Xizang | — | — | — | — | — | — |
Ningxia | — | — | — | — | — | — |
National Average | 43.52 | 29.38 | 28.29 | 26.18 | 66.54 | 93.42 |
Number of Provinces Improved | 17 | 4 | 9 | 10 | 13 | 19 |
Note: 1) Input redundancy rate = target value for improvement of input indicator/original value; 2) Output deficiency rate = target value for improvement of output indicator/original value; 3) Input redundancy rate and output deficiency rate of “—” means that the value of this unit is 0, i.e., there is no redundancy on this item. |
Output shortfall rate
The output insufficiency rate is the ratio of the improved value to the original value of the output index of competitive sports undertakings in each province. By analyzing the target value of DMU, the effective state of decision-making unit can be further distinguished, which can provide theoretical basis for the improvement of the efficiency of competitive sports training in each province and city, and then improve the overall comprehensive efficiency through the new initiatives and means of resource optimization, and strive to achieve the effective state of DEA. The output shortfall rate in this paper mainly reflects the fact that after optimizing the five input indicators, adjustments still need to be made in the medal performance point outputs in order for the DEA to be effective. As can be seen from Table 3, most provinces in China have widespread output deficits in competitive sports, with the national average value of output deficits being as high as 90% or more. Among them, Anhui, Jiangxi, Henan, Jilin, Shanxi, Gansu, Shaanxi and Inner Mongolia have high competitive sports output deficiencies of more than 100 percent, exceeding the national average of output deficiencies. As can be seen from the above data, there is a serious lack of output in terms of race points from China’s ethnic minority autonomous regions and some inland areas, which may be due to the following reasons: 1) It is related to the relatively backward economic conditions. The comprehensive strength of the economy affects the development of the digital economy. In the relatively backward training environment, the lack of scientific training system and technical support, the mismatch between the number of training bases and venues and the number of athletes, as well as the lack of high-quality coaching team, the lagging management concept, and the decline of the overall governance capacity, it is difficult to train athletes with a competitive advantage in the competition. 2) The lack of a reserve training system. Due to economic constraints, ethnic minorities and remote areas have limited resources and financial input into the development of their own competitive sports, making it difficult to form a competitive advantage in talent attraction compared to other provinces, and with the loss of athletes, the reserve talent force is gradually weakening. In view of these reasons, the relevant provinces should strengthen their own advantageous programs according to their own economic conditions and resource advantages, develop the potential advantageous programs, and issue relevant policies to guide and encourage the development of key sports and cultivate high-level athletes according to the characteristics of regional features and advantages. Developing the digital economy, creating sports digital intelligence to help the development of competitive sports, learning from the new advanced governance concepts and management models of other provinces, strengthening the communication of scientific and technological information in competitive sports, strengthening the scientific and technological means of training, and improving the scientific training system; Actively participating in major domestic and international sports events, using competitions as a means of training, obtaining more opportunities for athletes to compete, and developing high-level athletes capable of winning medals at national and international events, thereby narrowing the differences between provinces with high rates of output shortfalls.