2.1. Topsis evaluation model based on entropy weight method

The TOPSIS model is a method for ranking the superiority and inferiority of evaluation objects based on the proximity degree to the idealized target [17, 18]. Its essence is a distance comprehensive evaluation method. By assuming positive and negative ideal solutions, the distance between each evaluation indicator and the positive and negative ideal solutions are respectively calculated to determine the closeness between the evaluation object and the ideal sample, and thus judge the superiority and inferiority of each evaluation object. This method has good applicability in the evaluation of the resilience of the sports industry development involving a large number of indicators. The specific steps are as follows:

1. Step 1: Indicator normalization and standardization. Drawing on existing literature, the entropy weight method is used to assign weights to each indicator, which can avoid subjective factors affecting indicator preferences. Based on this, the weight vector W = (w₁, w₂, …, w_m) and the normalized matrix are obtained.
2. Step 2: Calculate the weighted normalized matrix.(1)
3. Step 3: Determine the positive and negative ideal solutions. The positive ideal solution refers to the sample with the highest resilience in the development of the sports industry, where all indicators have reached their optimal values. Similarly, the negative ideal solution refers to the sample with the lowest resilience in the development of the sports industry, where all indicators have the worst values.
4. Step 4: Calculate the distance between each evaluation object and the positive and negative ideal solutions, where i − 1, 2, …, n. (2) (3)
5. Step 5: Calculate the resilience index of the sports industry development for each city. The calculation result is in the range of [0,1], and the closer it is to 1, the closer the evaluation object is to the ideal solution. (4)

2.2 Exploratory spatial data analysis

Global spatial autocorrelation and local spatial autocorrelation are the two most commonly used methods in exploratory spatial data analysis. They are characterized by directly exploring hidden relationships, patterns, or trends in the data without the need for prior theoretical or hypothetical assumptions, while also revealing deviations from common models that are unpredictable [19].

(1) Global spatial autocorrelation. Global spatial autocorrelation is mainly used to determine the degree of spatial aggregation of the resilience index of the sports industry, which checks whether there is a spatial clustering trend [20, 21]. It is usually represented by Moran’s I. The formula is as follows: (5) (6) (7) where X_i represents the SIDRC of city i, n represents the sample size, and W_ij represents the inverse distance space weight matrix. The range of the global Moran’s I is [–1,1]. When moran’sI > 0, it indicates a positive spatial correlation of SIDRC, and the closer the value is to 1, the more areas tend to spatial clustering with similar SIDRC. When moran’sI < 0, it indicates a negative spatial correlation of SIDRC, and the closer the value is to -1, the more areas tend to diffuse with similar SIDRC. When moran’sI = 0, it means that SIDRC is randomly distributed in geographical space.

(2) Local spatial autocorrelation. The local spatial autocorrelation reveals the specific spatial correlation pattern of SIDRC, which focuses more on local changes compared to global spatial autocorrelation. The formula for calculating local Moran’s I is as follows: (8) Where L_i represents the local Moran’s I, and the other variables are the same as above.

2.3 Factors affecting enterprise innovation

The influencing factors of SIDRC are diverse, and this study mainly discusses from four aspects: policy support index (PSI), economic development level (GDP), sports industry structure diversity (SISD) and social participation index (SPI). Specifically, the policy support index (PSI) reflects the government’s support for the sports industry and is an important driving force to promote the development of the sports industry. This index is calculated by the entropy weight method from the number of sports laws and regulations, the number of non-governmental sports organizations, the number of sports advertisements and the number of texts related to the sports industry in government reports. The level of economic development (GDP) reflects the economic strength of a region and has an important impact on the consumption demand and investment willingness of the sports industry. The structural diversity of sports industry (SISD) measures the diversity and innovative development ability of sports industry, which is very important for dispersing external risks and improving industrial competitiveness. Social Participation Index (SPI) shows the public’s participation in sports, sports infrastructure coverage and sports culture atmosphere, and reflects the social support and demand for sports industry. Commonly used spatial econometric models include spatial lag model, spatial error model and spatial Dobbin model.

(1) The spatial lag model is a spatial autoregressive process, and its basic expression is: (9)

Among them, ln SIDRC_i,t is the logarithm of the toughness index of sports industry development, W is the spatial weight matrix, ρ is the spatial lag parameter, and μ is the white noise interference term.

(2) The spatial error model explains the spatial correlation and heteroscedasticity between variables, and the specific form is: (10) Where ε represents regression residual vector, λ is autoregressive coefficient, and other variables are consistent.

(3) The spatial dobbin model is a synthesis of spatial lag model and spatial error model, and its specific form is: (11)

Among them, γ is the coefficient of interaction between linear independent variable and spatial lag dependent variable, which reflects the spatial spillover effect.

2.4 Index system

Resilience theory has broad application in describing and explaining the coping abilities of complex systems, such as individuals, organizations, and societies, and can help decision-makers determine when to change operational modes or development strategies to cope with future uncertainties. This study borrows from resilience theory to propose the concept of a resilience index for the development of the sports industry, which mainly embodies three aspects: adaptive capacity, self-organizing ability, and self-recovery ability. Adaptive capacity reflects the ability of the sports industry to maintain stable development in the face of external shocks. For example, during the COVID-19 pandemic, the sports industry can expand its business scope through online marketing and events to maintain stable development. Self-organizing ability represents the macro manifestation of the market-oriented, commercialized, and standardized development of the sports industry, implying that the industry structure is reasonable, and the production chain, sales chain, and consumption chain are coupled and coordinated, forming a virtuous cycle of industry development. Self-recovery ability reveals the ability of industry development to gradually recover to a stable and orderly state after being affected by external influences and experiencing stagnation or setbacks. As the world begins to enter the post-pandemic era, the sports industry is also entering a period of revival and gradually recovering its vitality.

Based on the aforementioned analysis, it can be seen that the resilience index for the development of the sports industry involves a broader scope compared to indicators such as competitiveness and high-quality index, and its evaluation indicators also need to follow basic principles of comprehensiveness and scientific rigor. Therefore, this study constructs an evaluation index system for the resilience index of the sports industry development from four dimensions: input and output, structure and innovation, market and consumption, and society and policy (Table 1). Specifically, the input and output dimension includes the basic elements and fundamental goals of sports industry development, which directly impacts the industry’s development vitality and quality and reflects the operating status and market performance within the industry. The structure and innovation dimension reveals the key factors for achieving sustainable development in the sports industry, where industry structure rationality and technological innovation capability play a crucial role in enhancing future industry competitiveness. The market and consumption dimension are the most significant and basic characteristics of the sports industry, where indicators of consumption level and market size reflect the development potential of the sports consumption market, which plays an important role in enhancing industry self-organizing ability. The society and policy dimension represents the basic environment in which the sports industry develops and has a significant regulating effect on its development quality and effect, while providing institutional guarantees and material basis for enhancing the industry’s resilience.

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Table 1. SIDRC evaluation index system.

https://doi.org/10.1371/journal.pone.0295313.t001

2.5 Data source

Considering the availability of data and comparability of results, this study focuses on 285 cities in China from 2010 to 2022. During this period, the sports industry in China has developed rapidly and formed a good industrial structure, which not only provides valuable reference for the development of sports industry in other developing countries, but also provides empirical basis for guiding the future industrial layout and direction. The data used in this study are from the National Bureau of Statistics (http://www.stats.gov.cn.2023.04), China Sports Industry Development Report, China City Statistical Yearbook and Social Science Database (http://www.ppm anda.cn.2023.04). After obtaining the initial data set, SPSS software is used to clean the data, remove the abnormal values and supplement the missing values by linear interpolation. According to Formula 1–4, the development toughness index of sports industry is calculated, and the calculation results are statistically analyzed with the help of state software to master the data distribution structure. At the same time, the city-scale administrative divisions of China were obtained from the resource and environmental science data registration and publishing system (https://www.resdc.cn/DOI/), and the calculation results were visualized by ArcGIS software on the basis of the map, and whether there was spatial correlation was tested.

3.1 Temporal distribution characteristics analysis of IDRC

Based on Eqs 1–4, the resilience index of the sports industry development in China from 2010 to 2022 was calculated, and the sample structure was organized using PyCharm software. Fig 1 shows box plots of the resilience coefficients of the sports industry development in 285 Chinese cities for the years 2010, 2014, 2018, and 2022. The median line represents the median resilience coefficient of different years, while the box, consisting of the first quartile (Q1) and the third quartile (Q3), reveals the key part of the sample structure of the resilience coefficient. The whiskers represent the sample values outside Q1 and Q3, and their length reflects the sample structure’s degree of dispersion. Specifically, the median line was around 0.25 in 2010, and the box was relatively short, indicating that the resilience coefficients of the sports industry development in Chinese cities were at a generally low level, with no significant regional differences. With the passage of time, the median line slowly rose to around 0.5 in 2022, and the box gradually became higher and the whiskers extended to both sides. This change indicates that although the resilience coefficients of the sports industry development showed growth throughout the entire study period, the overall resilience level remained relatively low, and the gaps between cities were gradually widening. It is particularly noteworthy that there are still many outliers outside the whiskers, and their distances are gradually increasing, revealing the potential risk of unbalanced development in the sports industry. In other words, similar to the digital divide produced by the digital economy, China’s sports industry development may fall into the "Matthew Effect" trap, where high-resilience cities are more likely to obtain high-quality sports industry resources (facilities, technologies, talents, etc.) due to the siphon effect, leading to low-resilience cities losing competitive advantages and forming a vicious cycle of cumulative growth, resulting in increasingly significant gaps between cities.

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Fig 1. Box diagram of SIDRC in different years.

https://doi.org/10.1371/journal.pone.0295313.g001

In order to further explore the data distribution characteristics of SIDRC, this study makes descriptive statistics on the calculation results (Table 2). It can be found that the variance increased from 0.013 in 2010 to 0.082 in 2022, and the standard deviation increased from 0.116 in 2010 to 0.288 in 2022, which means that the interval SIDRC gap increased and the data dispersion characteristics began to strengthen. Although the growth rate is small, combined with Fig 1, it can be found that more and more cities begin to grow rapidly, that is, the gap between regions begins to increase gradually, which is unfavorable to the cross-regional flow of sports resources.

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Table 2. Descriptive statistics of SIDRC.

https://doi.org/10.1371/journal.pone.0295313.t002

3.2 Spatial distribution pattern analysis of SIDRC

The ArcGIS 10.2 software was utilized for the visualization of the SIDRCin China from 2010 to 2022. To facilitate comparability, the resilience coefficient was segmented into five categories. When SIDRC ∈ (0, 0.2], the sports industry is assigned to the Fragile group. This implies that the sector is vulnerable to external impacts, has limited adaptability, is small in scale, and is incapable of quickly resolving the external effects. When SIDRC ∈ (0.2, 0.4], the sports industry belongs to the Less Resilient group. Such industries are sensitive to external impacts but possess significant recovery and adaptability capabilities. A SIDRC ∈ (0.4, 0.6] is designated to the Resilient group, indicating that the sports industry can promptly adjust to external impacts, maintain basic operations, and reduce the impact of external pressures through risk management strategies and process optimization. A SIDRC ∈ (0.6, 0.8] denotes the Strongly Resilient group, in which the sports industry can maintain growth and competitive advantages through innovation and private enterprise and make progress during external impacts. A SIDRC ∈ (0.8, 1] places the industry under the Antifragile group, signifying that it can quickly adapt, grow, and enhance its adaptability in intricate and uncertain external environments. Additionally, the higher the external impact, the greater the industry’s innovation and growth capabilities. Fig 2 illustrates the spatial distribution of China’s SIDRC at different time intervals.

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Fig 2. Spatial distribution pattern of SIDRC (the administrative boundaries of prefecture-level city are republished from [16] under a CC BY license, with permission from the resource and environment data center, original copyright 2022).

https://doi.org/10.1371/journal.pone.0295313.g002

The SIDRC considerably improved during the study period. In 2010, 102 and 152 cities were classified as belonging to the Fragile and Less Resilient groups, respectively, accounting for 89.123% of the total sample. Additionally, only six cities, namely Beijing, Tianjin, Guangzhou, Shenzhen, Chongqing, and Shanghai, attained the Strongly Resilient level, and no city reached the Actifragile level. At this period, China’s sports industry had a weaker foundation for development, making it less adaptable to external impact. In terms of sports infrastructure investment, product innovation, and market construction, there remained a gap compared to highly developed countries such as the United States and Japan. By 2022, China’s sports industry SIDRC had improved impressively. The number of cities that belonged to the Less Resilient group decreased by 53.947% compared to 2010. Meanwhile, the number of cities in the Resilient and Strongly Resilient groups increased by 99 (a 396% rise) and 38 (a 633.333% rise), respectively. This implies that these two levels of cities will play a critical role in reducing the regional differences in SIDRC, becoming a powerful driving force. Furthermore, 40 cities progressed into the Antifragile group, indicating that they possess a more stable and robust sports industry and market. Nevertheless, despite the conspicuous increase in each level’s number of cities, the significant issue of sample structure imbalance displayed in Fig 1 still persisted. Specifically, many cities still carried highly fragile SIDRC in the sports industry, such as Jincheng, Qingyang, and Shangluo. These cities possess a disadvantage in terms of infrastructure investment, consumer market, and policy guidance, and, as such, risk becoming the periphery regions for balanced SIDRC development.

The uneven distribution of SIDRC in China is reflected in two aspects: sample structure and spatial pattern. The former was explained in the previous section, and here we focus on spatial unevenness. Cities ranked as Fragile and Less Resilient dominated the geographical space in 2010, with the former forming a "block-shaped" spatial pattern in regions such as northeastern Inner Mongolia, Gansu Province and Ningxia, southern Yunnan Province, and parts of Hunan Province and Jiangxi Province. By 2014, these "block-shaped" regions were further divided, and Less Resilient became the main distribution type, with cities such as Chongqing, Beijing, and Tianjin entering the Antifragile level. In 2018, the Resilient level began to appear heavily, indicating that the Chinese sports industry had entered a new stage, with significant improvements in industry structure, infrastructure layout, and sports consumer market, and an increase in the capacity for innovative development of the industry. The spatial pattern in the form of an interlocked distribution with Less Resilient was observed. Until 2022, Strongly Resilient and Antifragile began to appear heavily, and the Resilient level became dominant. Overall, the spatial evolution of SIDRC in China’s sports industry went through four stages: Fragile and Less Resilient interlocking distribution-Less Resilient balanced distribution-Less Resilient and Resilient interlocking distribution-Resilient and Antifragile interlocking distribution. However, there are still regional and urban disparities, with Eastern regions and provincial capital cities remaining superior.

3.3 Spatial correlation analysis of SIDRC

This study further investigates whether there is spatial correlation in the SIDRC at the local level. Fig 3 shows the scatter plot of the distribution of SIDRC under inverse distance weighting. H-H indicates that the SIDRC of a city and its surrounding cities are both at a higher level, which results in an anti-fragile region. H-L indicates that a city has a strong resilience while the SIDRC of adjacent cities is at a fragile level, resulting in a spill-over effect. Similarly, L-H indicates that a city has weak resilience while the SIDRC of surrounding cities is at an anti-fragile level, resulting in a chasing effect. L-L indicates that both a city and its surrounding cities are at a fragile level, resulting in a fragile region.

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Fig 3. Local spatial correlation of SIDRC.

https://doi.org/10.1371/journal.pone.0295313.g003

Calculated based on Eqs 4–5, the global Moran’s I index during the study period were 0.153, 0.159, 0.173, and 0.181, respectively, indicating a positive spatial correlation in the SIDRC of the sports industry. This means that the spatial distribution is not random, and cities with similar SIDRC are more likely to cluster. When the external environment changes, cities with similar or the same SIDRC are more likely to form complementary relationships in terms of resources, knowledge, and other factors. The local Moran’s I index decreased from 0.326635 to 0.299587, indicating a gradual decline in local correlation. This may be due to the development of information technology and digital economy, which compresses the spatial and temporal effects of sports industry resources and market size. The spill-over effect of highly resilient cities has a wider impact range.

Compared with the scatter plot distribution in 2010 and 2022, some cities have experienced quadrant changes, known as “leapfrogging,” at different times, revealing the local changes of the SIDRC. Fig 4 shows the spatiotemporal leapfrogging process of SIDRC. Specifically, Zunyi and Dazhou leapt from the L-H quadrant to H-H, known as “upstream leapfrogging,” reflecting the process of the city’s SIDRC changing from fragility to resilience. Zhaotong and Fushun, among others, leapt from L-H to L-L, while Huangshi and Xiaogan leapt from L-L to L-H, and Jixi leapt from H-H to L-L, known as “downstream leapfrogging,” describing the process of the city’s SIDRC transforming from resilience to fragility. Overall, downstream leapfrogging is dominant, and the number of leapfrogging instances is relatively small, indicating a relatively stable spatiotemporal evolution of the SIDRC.

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Fig 4. Time-space transition of SIDRC.

https://doi.org/10.1371/journal.pone.0295313.g004

3.4. Influence factors analysis of SIDRC

3.4.1. Result analysis.

Different types of spatial econometric models can be transformed into one another. To obtain a better fit, this study employs the Wald test and the likelihood ratio test to select the model. The results pass the 1% significance level, indicating that the spatial Durbin model does not suffer from degeneracy. Combining the adjusted R-squared, results show that the SDM model has the best fit. Therefore, this study analyzes the data based on this model. The specific regression results are shown in Table 3.

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Table 3. Spatial econometric regression results.

https://doi.org/10.1371/journal.pone.0295313.t003

The regression coefficient between the policy support index and the SIDRC is 0.643, which is significant at a 5% confidence level. Thus, policy support plays a significant role in promoting the resilience of the sports industry. On one hand, the government formulates corresponding policies that create a favorable business environment for sports enterprises, such as tax reductions, financial support, optimized market access mechanisms, and the reduction of production and operation costs. Additionally, the government’s industrial planning and development strategies provide direction for promoting the convergence and allocation efficiency of different types of sports resources, which promotes the transformation and upgrading of the industry’s structure. On the other hand, policy support stimulates the innovation capacity of the sports industry and the spread of sports culture. Sports enterprises realize digital transformation by developing new technologies, products, and services, enhancing the competitiveness, adaptability, and resilience of the sector. The popularization and spread of sports culture have also increased public awareness and understanding of the industry, promoting the public’s demand for sports market and spiritual demand of sports culture, resulting in improving the toughness of industrial development. Finally, the spatial lag coefficient of the policy support index is 0.890, which is not significant, demonstrating that the improvement of the policy support index in one city will not have a significant impact on the SIDRC of neighboring cities.

The regression coefficient of the level of economic development on SIDRC is 1.321, and it is significant at the 1% confidence level, indicating that economic development has a significant positive effect on enhancing the resilience of the sports industry. In other words, when the level of economic development increases by 1%, it can promote a 1.321% increase in SIDRC. Combining with the previous text, it can be found that the SIDRC in China’s eastern coastal areas and provincial capital cities is generally higher than that in other cities, which can be partially explained by the difference in the level of economic development. Cities with high levels of economic development usually have higher residents’ income levels and consumption capabilities, which also lead to the growth and expansion of the sports market demand for sports products, infrastructure, sports events, and services, etc. The benign cumulative effect of market demand and industry resilience enhancement helps to achieve sustainable development of the sports industry. In addition, regions with high levels of economic development often have richer educational resources and talent reserves, providing good resource supply for the development of the sports industry and enhancing its adaptability to external shocks. The spatial lag coefficient of the level of economic development is -0.031, and it is significant at the 10% confidence level, indicating that the level of economic development will have a negative effect on the promotion of SIDRC in surrounding cities. One possible reason is that developed cities generate a siphon effect, resulting in the loss of advantageous resources such as talents, technology, and enterprises in neighboring cities, thereby inhibiting the promotion of SIDRC.

The regression coefficient of the diversity of sports industry structures on SIDRC is 0.794, and it is significant at the 1% confidence level, indicating that the diversity of industry structures has a positive effect on strengthening the local external shocks of the sports industry. The diversity of sports industry structures means diversified development fields and formats, such as sports equipment manufacturing, sports event organization, sports venue construction, sports training, etc. These sub-industries can not only generate more new areas combined with the current digital transformation and green development but also help to disperse and avoid risks by changing the development mode when affected by external influences. Moreover, diversified industry structures also facilitate communication and cooperation between various fields, promote the generation of innovative thinking, and achieve the effect of 1+1>2. The spatial lag coefficient of the diversity of sports industry structures is 0.215, but it is not significant, indicating that it does not have a significant impact on the promotion of SIDRC in neighboring areas.

The regression coefficient of the social participation index on the SIDRC is 1.532, and it is significant at the 1% confidence level, indicating that it has a significant promoting effect on enhancing the resilience of the sports industry. On the one hand, areas with high social participation have higher attention and participation in the field of sports, making it easier to construct and disseminate sports culture and establish more branded sports products or organizations. Brand effects help to create higher visibility and occupy more market share in the sports industry. On the other hand, social participation brings more extensive financing channels. Due to people’s attention to the development of the sports industry, relevant enterprises are more likely to obtain financing and expand the market. The support of financial institutions, investors, and sponsors reduces the production costs of the sports industry. The spatial lag coefficient of the social participation index is 0.912, and it is significant at the 5% confidence level, indicating that it has a positive effect on the SIDRC in neighboring cities. This spillover effect may come from three aspects: resource sharing, market expansion, and extension of the industry chain. Urban agglomeration has become a new type of economic agglomeration, providing a foundation for sharing sports resources or facilities among cities. When the sports industry development resilience of a city is relatively high, its surrounding cities may benefit from resource or facility sharing, which has a positive effect on the development of their own sports industry. The growth of market demand may affect neighboring cities, bringing more market opportunities and helping to improve the SIDRC in neighboring areas. The location advantages between neighboring cities help to extend the sports industry chain, to some extent, promoting the improvement of the SIDRC in neighboring areas.

3.4.2. Robustness test.

The research chooses two methods to test the robustness of the SDM model: delaying the SIDRC by one period and shortening the time window. Table 4 describes the parameter changes of the model under the two test methods. It can be found that in both SDM-lag model and SDM-time model, the sign of each variable is changed, which shows that the original model is robust.

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Table 4. Robustness test result.

https://doi.org/10.1371/journal.pone.0295313.t004

5.1 Conclusion

This study evaluates and visualizes the resilience of the sports industry development in 285 cities in China using the Topsis model and exploratory spatial data analysis. We also construct a spatial econometric model to discuss the influencing factors of the sports industry SIDRC. The main conclusions are as follows:

1. The SIDRC of the Chinese sports industry has significantly improved, but the growth rate is relatively slow, and overall, it still remains at a low level of resilience. The Matthew effect has caused the gap between cities to widen further. Cities classified as Resilient or Strongly Resilient play a critical role in narrowing the regional SIDRC gap, while cities such as Jincheng, Qingyang, and Shangluo have consistently exhibited high vulnerability and serve as the outskirts of balanced development.
2. The Chinese sports industry SIDRC exhibits a significant spatial disequilibrium, with Fragile and Less Resilient cities dominating early research and presenting a "block-like" distribution pattern in space. With time, Resilient cities have dominated, but the distribution pattern has consistently favored the coastal eastern region over the central and western regions, and provincial capitals over other cities. The sports industry SIDRC displays strong spatial positive correlation, with relatively low local spatial variation rates.
3. The Policy Support Index, economic development level, diversity of sports industry structure, and social participation all have a significant promoting effect on the sports industry SIDRC. High economic development level cities cause obstacles to the development of the SIDRC of the sports industry in neighboring cities due to the "siphon effect’’ that causes talent and resource outflows. Social participation promotes the resilience enhancement of neighboring cities through resource sharing, market expansion, and the extension of the industry chain.

5.2 Discussion

The purpose of this study is to evaluate the resilience of sports industry development, identify its temporal and spatial differences, and explore its influencing factors. It is found that the development resilience of sports industry in China is rising continuously, and the growth rate is relatively slow, which is similar to the research conclusion of (Moretti et al., 2023). In addition, this study also found that there are significant spatial heterogeneity and spatial agglomeration in the development resilience of sports industry, and (Kin et al., 2023) also put forward similar views in the study, but in comparison, the index system of this study is more perfect. This study found that social participation index has a positive effect on the development resilience of sports industry, but some related studies put forward the opposite view, which may be due to the different variable sets selected by the regression model, and there is a regulatory effect between variables. Therefore, this study believes that there are still the following aspects that can be further improved in the follow-up work. (1) The spatial correlation of the sports industry SIDRC discussed in previous sections can be abstracted as a related network, or the development related network of the sports industry, which reveals the regional adaptability and resilience from the aspects of correlation and integrity, and has more connotation than the current study from the perspective of "flow space’’ theory; (2) The influencing factors of the sports industry SIDRC selection in this study mostly focus on social and economic aspects, which is clearly not sufficient and should be further explored in future research. These problems will be discussed further in our subsequent research.