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Wednesday, November 7, 2012

Combinatorics in College Football

I started with the assumption that there are currently four college football teams that have legitimate BCS title game resumes. Next, I ranked those teams based on where they might finish in the BCS if they stay unbeaten:

1) Alabama
2) Oregon
3) Kansas State
4) Notre Dame

(Sorry Louisville.) This list is open to debate, of course, but that isn't the focus of this analysis and it gives us something to work with.

Then I took the schedules of the four teams, attached to each game a probability based on the model, and simulated the rest of the season 1,000 times.

team (regular season %undefeated, post-champ game %undefeated)
1) Alabama (84%, 67%)
2) Oregon (61%, 47%)
3) Kansas State (62%, 62%)
4) Notre Dame (47%, 47%)

The results are illustrated in the table below. Red means the team lost at least once, green that the team did not. The number at the top of each column is the number of times that outcome occurred divided by 10 (or the percentage).


So, for example, in 84 or 8.4% of simulations all four teams stayed undefeated (all four teams are green in that first column). Three percent of the time they all lost. In 20.5% of simulations three teams lost, in 33.8% two teams lost at least once, and in 28.9% of simulations just one team bit the bullet.

That means we have  a one in three chance of avoiding the controversy that comes when a team with a similar resume and equal number of losses is left out (that's assuming, of course, that a one-loss SEC team doesn't refuse to concede to an undefeated Notre Dame).

The most probable individual scenario is that an undefeated Kansas State and undefeated Alabama play for the title after Oregon and Notre Dame lose (13.7%). If Oregon does really have the leg up on Kansas State, the most likely result is Oregon playing Alabama (30.1%). Oregon would also get in, I assume, if Kansas State, Notre Dame and Oregon all lose, and would play the winner of Alabama/Georgia (10%; sorry Louisville).

But if you are to take one thing away from analysis it should be this: the outcome of this season is by no means a foregone conclusion, and it's a bit silly to start worrying now about who will finish on top of the BCS until teams have had a few more chances to lose . . . because some of them will.

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