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Wednesday, May 11, 2005
I am mucking around with some data describing Division IA NCAA football conferences, and asking some questions about optimal conference size. Here are two interesting graphs. First, the relationship between the competitive balance and the number of teams in a conference. The general empirical result that more teams tends to lead to a more even distribution of wins seems confirmed. In this sense, if fans like competitive balance (which we think they do), then bigger conferences are better (ceteris paribus)
However, having a conference with thirty teams might make it difficult to keep up the intense rivalries that are unique to college football. Schools and conferences take advantage of these intense rivalries to make money (gasp!) and therefore there is likely a limit to the size of the conference.
Taking per-attendee average football expenditures and per-attendee average football revenues (at the conference level) and estimating quadratic forms for both average revenue and average cost, we find the following two relationships. The quadratic form of average revenue is a bit weird, but might indicate that up to a point more teams increases fan interest and hence their willingness-to-pay and after that point there are too many teams and fan interest drops.
The upshot? The "profit" maximizing number of teams is approximately 11.3, which introduces an integer problem. Profit maximization at the conference level occurs at 11 or 12 teams, which is exactly the trend we have seen in college football. The Big 12 and the SEC are both twelve team conferences. The Big 10 is really 11 teams and when Notre Dame's television contract isn't worth much, they will beg to join the Big 10. The ACC is heading to twelve teams with the addition of Miami, Va Tech and BC. The Big East will eventually be twelve teams and the Pac 10 needs two more to get to twelve, perhaps BYU and Utah?
It would seem that the movement towards twelve team conferences does have some rhyme and reason to it, although most athletic directors and university presidents are loathe to use the word "profit" and "football" in the same sentence or paragraph.
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