Efficiency evaluation of Chinese Yunnan Province County Area Public Service for sports and fitness based on three-stage DEA model

County areas hold critical strategic significance in terms of population, gross domestic product, and their role within the National Fitness Strategy and National Fitness Public Service System.Analyzing the efficiency of county areas National Fitness public services in Yunnan Province can provide evidence-based support for advancing the development of a higher-level public service system for national fitness across Southwest China. Using a three-stage Data envelopment analysis (DEA) method, this study evaluates the efficiency of public fitness services at the county-level administrative division in Yunnan Province for the year 2023. The analysis encompasses 129 county-level administrative divisions, comprising 17 municipal districts and 112 county areas within Yunnan Province. Research indicates that environmental factors such as regional GDP, sports and fitness infrastructure, local industrial structure, and population density significantly influence the efficiency of national fitness services. After excluding these variables in the second-stage stochastic frontier analysis (SFA) regression analysis, the Technical Efficiency (TE) of national fitness services in Yunnan Province's municipal districts and county areas reached 0.919 and 0.824 respectively in 2023. Adjusted Scale Efficiency (SE) for municipal districts and county area generally exceeded Pure Technical Efficiency (PTE), with significant PTE disparities between the municipal districts and county area. Additionally, 47.06% of municipal districts and 72.32% of county area exhibited Increasing Returns to Scale (IRS). Accordingly, efforts should be made to continuously improve the county area supervision management system and investment mechanisms, broaden service types to achieve integrated development, and fully leverage IRS to promote the dissemination of regional and ethnic traditional cultures.