I want to suggest first that the purpose of a playoff cannot be to determine the best team in the country. I say that for two reasons. First, there is no such thing as the best team in the country. Different teams have different strengths and weaknesses that will match up differently against different opponents. In any given game, anything can happen. In 2007, for example, Appalachian State beat Michigan who beat Florida who beat Kentucky who beat the supposed national champions LSU. So you’ve either got to declare Appalachian State the best team in the country, or drop your insistence on transitivity.
Second, if you do believe in such a thing as the (probabilistically) best team in the country, the more teams you put in the playoffs, the less likely it is that the best team ends up being declared the champion. Suppose for example that there’s a team that with 80% probability would win its game against any other team that might make the playoffs. With a single championship game, that superior team gets declared the champion with probability 80%. With a 4-team playoff, the best team must win both its games, the probability of which is (0.8)(0.8) = 0.64. With an 8-team playoff, the best team is only going to be declared the champion about half the time.
I therefore suggest that the primary purpose of the system is not so much to determine “the” best team as it is to bring enjoyment and satisfaction to the fans. Granted, the proposed playoff games themselves would do that very well for the handful of teams and games that get included in the playoffs, but at the cost of subtracting from the excitement of the 30 or so other post-season games that would have to be diminished as a result. Of course, the parties with a vested financial stake in those other games are for that precise reason opposed to the playoff idea, and that opposition is the main reason it hasn’t yet happened. But if you took the objective to be to maximize the economic surplus of all the post-season games combined, I say you’d want to stick with a system like the present one. The lobbying power of those vested interests is precisely a lobby on behalf of maximizing total economic surplus.
But whatever you may think of the merits of a college football playoff, doesn’t it bother you to see the U.S. Congress acting as if it’s the nation’s ruler on this matter?
It does me. Which is why I wrote this.