Declarations of the "economic impact" of sports stadiums never touch on the fundamental question of resource allocation that should be at the heart of the debate over stadium finance. One virtue of leaving the financing of such projects to the teams themselves is that, should customers be willing to pay sufficiently through ticket prices and the like, we can be confident that the resources used to build stadiums are flowing to their highest-valued use. Once the state gets involved, all bets are off.
An example of the opportunity costs of diverting resources to state-supported projects comes from a new manuscript written by Ekelund, Hebert, and Tollison. In Economics and Christianity, they offer a supply-side analysis of the link between the Protestant Reformation and the subsequent development of capitalism in Europe. This addresses the famous thesis of Max Weber, whose explanation for the link is preference-based (crudely put, Calvin promoted thrift, and so on, which made savings available for capital investment). In contrast, the essence of Ekelund, Hebert, and Tollison's theory is that the Reformation reduced the cost of religious services in Europe below that offered under the Catholic monopoly. Reduced spending on cathedrals and bishops allowed more resources to be directed towards transport, education, and technology. You need not read very far to find the analogy to sports stadiums:
Competition, in medieval times and our own, almost always has a locational component. Urban centers with cathedrals vied fiercely for relics and works of art to adorn their churches. Somewhat in the manner of modern sports stadiums, medieval cities engaged in a kind of spatial competition for ever grander cathedrals that inflated the costs of providing religious services of all kinds...
In this as in all matters economic, the true cost of the cathedral was the opportunity cost of resources used in its construction and maintenance: the opportunity cost of stone masons, artists and saver-investors whose human and physical capital resources were directed to the provision of religious services.
...The precise amount of resource use generated by cathedral building cannot be directly calculated, but a good deal of anecdotal evidence suggests that the opportunity costs were massive. According to Scott, more stone was cut between 1050 and 1350 in France than in the entire history of Egypt. Scott and Morris also note that almost 9,500 ecclesiastical buildings, such as abbeys, cathedrals, parish churches, were constructed in England and Wales over the medieval period. While capital markets were rudimentary, the actual building of cathedrals on these scales meant that resources were in fact responsive to a kind of "spiritual" investment demand and therefore allocated away from additional infrastructure, such as roads and bridges, or from greater investments in education and technology.
...Scott estimates that each Gothic cathedral or other type of great church would cost hundreds of millions of pounds in contemporary currency. Such estimates, while anecdotal, provide indirect evidence of an enormous opportunity cost of building cathedrals and other church structures. Indeed, if Weber is correct, economic growth set in after the spate of cathedral building stopped, which is a corollary of our argument.
...It is clear that medieval Catholicism emphasized large-scale, extravagant structures over small-scale, simple ones. Economic resources have alternative uses. Therefore, by rejecting the extravagance of church buildings - however they were financed - Protestantism made it possible for such resources to be directed toward more secular, market-oriented activities.
We are wealthier these days, and can afford some degree of state-sponsored extravagance when it comes to building stadiums. But I find the cathedral cost story compelling. And the principle remains the same centuries down the road -- the opportunity costs to resource mis-allocation are real, and potentially quite large.