While watching West Virginia outscore Pittsburg last night, a heated discussion over the best way to determine a NCAA division one football national champion erupted between my friends. Now I’m not going to argue that the current system, the Bowl Championship Series (BCS), is perfect, but I do think that even some of the preferred methods (such as a playoff system) offer only marginal improvements and are still very flawed systems of determining a champion.
Now I think it’s important to make a clear distinction between the “best” team, and a team that is revealed to be the “best” team. For instance, let’s look at a horse race. If we ran two horses (lets call them C.J. and James) around a track 1,000 times and recorded their times, we could get a pretty good idea of how fast each one is. Now let’s suppose that on average C.J. is faster than James. Then we would expect that if we ran the two around the track at the same time, C.J. would cross the finish line first. Such is the way we use a system (in this case a race) to try and estimate a true characteristic (speed). But as centuries of horseracing (or one horse at Keenland) have shown, the fastest horse doesn’t always win the race, just as the “best” team doesn’t always win a football game.
So the question becomes, what’s the best way to determine the best team each year? Even more interesting, in my mind, is how can we rank teams from best to worst? Well I am about to settle the debate and present the Dispassionate Rationality system for ranking college football teams.
First, we must decide what we consider the “best” team to be. Imagine we’re back in the Cold War. Russia calls up Regan and says let’s play some football. We have to pick one team in the NCAA to play against the Russian team, whose players are yet to be determined. That is how I will define the “best” team in college football: the team that has the best chance of all division one teams to beat a randomly selected opponent. So how do we determine such a team? Well let’s look at one opponent, say…Georgia Tech. How would we determine which team has the best chance of beating Georgia Tech on any given day? We have each team play them 1,000 times and see which one beats them the most times. We could also rank the teams, because we would have a reasonable determination of how much more likely one team is to beat Georgia Tech than another. Next, we could do this for all the teams; have every team play every other team 1,000 times. The rankings would be different for each opponent, because some people are better at shutting down Calvin Johnson than others, but on average we could then determine who is most likely to beat a randomly selected opponent. Now this would be almost perfect, and it would only take 7 million games to determine, or 2,308 years if every team played every weekend. We'll all be dead by then so 20 games with each opponent would probably suffice, but that would still be 141,610 games or 46 years. If we threw the law of large numbers out the window and each team only played every other team once, it would still take over two years.
The point is that it is impractical to play all these games to try and reveal a true “best” team. In fact, it is impossible to do so. So the best we can do is create a system designed to reveal the “best” team and then see who is the best at winning the “game” comprised of games. The current game is the BCS, the rules are not very clear and some teams start off with an advantage. One alternate proposal is a playoff. In the playoff system, the game is well defined, but some teams still have an advantage and rankings are useless. Each has its advantages over the other, but neither is as iron clad as our 7 million game season. Let’s face it; we will always have a flawed system. I think the game of football is much more interesting than the game of winning a championship. So let’s stop worrying so much about who is going to win the BCS (or worse, who should have won the BCS), and start worrying more about why Clemson is going to beat South Carolina on November 25th.
