Although there are several opinions on the breadth of growth that publicly funded stadiums create, there is no question that the immediate district benefits. Increased traffic in the localized stadium district supports businesses such as restaurants and bars. Public transportation and other city infrastructure requirements for the stadium also boost local growth and profitability. Stadium supporters should focus on localized growth initially and then support the transportation infrastructure to widen the scope of growth.
Having a stadium that holds a lot of people will bring others into a city. If they have a small stadium then they can't fit as many people, and therefore, will bring less people into the city. The people who come from other places to watch the games might like the city they are visiting and decide to move there.
For any cities to grow and maintain that growth, the common people should be uplifted. No doubt that building new stadium is a sign of economic growth but in order to sustain such growth, the common people's living standard must be uplifted. Common people should be able to pay ticket prices to enjoy the game in the stadium.
There isn't any empirical evidence that building sports stadiums help cities at all. Team owners receive subsidies, grants, tax incentives, and free land, and the argument always is that it will help revitalize the area and help the city grow. It never, every works out that way. The only entity that benefits is the team owner, not the city.