Digital Model Innovation of Leisure Sports Development in the Convergence Perspective of Culture, Sports and Tourism

“Sports-tourism integration” is becoming an important way and trend for the development of leisure sports and cultural tourism industry, and is also an important pillar for pulling local economic development. The research focus of the article is to measure the coupling and coordination level between leisure sports and cultural and tourism integration using the entropy weight method and to discover the factors affecting the coupling of the two. With the data related to the development of leisure sports and cultural and tourism integration in City A in the 10 years from 2014 to 2023, the comprehensive development level of leisure sports and cultural and tourism integration in City A in the past 10 years, as well as the coupling and coordination level of the two, are obtained. In 2014-2023, the 10 districts in the tourism demonstration county of city A can be roughly divided into three levels, and the district with the best level of development of recreational sports is district E, with an average composite index of 0.521. The level of development of the integration of culture and tourism in the 10 districts is also markedly different, and the district with the best level of development is the district I, with an average composite index of 0.606. The analysis leads to the coupling and coordination degree of leisure, sports, culture, and tourism industries in the tourism demonstration county of city A. The average value of the coupling and coordination degree of the culture and tourism industry is between 0.3 and 0.6, and the gray correlation degree is X6>X2>X3>X9>X4>X1>X5>X8>X7 in descending order.