In an earlier post I mentioned that there aren't too many treatments in the formal sports economics literature that examine fans as inputs. One notable exception is that from David Boyd and Laura Boyd that appeared in the Journal of Economics and Finance in 1998 (issue 2/3 pp 169 - 179). They develop a model where fans are an input in winning and they use it to give an explanation as to why the common finding of inelastic ticket pricing is not inconsistent with profit maximization.
Here's the conclusion to their article.
Increasingly, economists are utilizing standard microeconomic analysis in an attempt to better understand the world of professional sports. However, since most of microeconomic theory is based on profit-maximizing behavior, the assumption of profit maximization in the sporting world must first be justified before microeconomists can legitimately apply their tools. In this paper, we have shown that some existing empirical evidence regarding the elasticity of demand for tickets to professional sporting events which, on the surface, seems to raise questions about profit-maximizing ticket pricing policy is not necessarily inconsistent with team profit maximization.We have offered here a theory of team sports ticket pricing, based on the home field advantage, which implies that the traditional price elasticity of demand, measuring the ceteris paribus effect of changing ticket prices on attendance, is less elastic than is the elasticity of demand relevant for team profit maximization. The results of the theoretical analysis generated the prediction that accounting for simultaneity between attendance and team performance would result in a more elastic point estimate of the elasticity of demand for tickets. This hypothesis was supported using data from professional baseball. Moreover, the model generated predictions about how traditional, ceteris paribus elasticities of demand for tickets are likely to vary across different professional team sports. Again, these predictions were consistent with the results of existing empirical work on professional baseball and basketball. Although the assumption of profit-maximization as applied to professional athletics is far from fully vindicated, the results of this work can certainly be used as one piece of evidence for those who continue to use microeconomic theory to better understand the world of professional sport.
There are other reasons which were put forth by previous researchers (and mentioned by Boyd and Boyd) as well as others since this paper was published in 1998, but I won't go into them here. Here is the other part to this little series of posts.
Thank's to commenter Peter G. for his Super Bowl comment that spurred me to remember the Boyd and Boyd paper.