The top teams in college football seem almost invincible. Down south, Alabama started slowly in the first quarter but then romped over Mississippi 52-7 on the road. Meanwhile, LSU traveled to Knoxville to handily beat Tennessee 38-7. LSU ended the game by cramming the ball down Tennessee’s throat with 10 straight running plays that resulted in a touchdown. College football fans everywhere are ticking away the weeks until November 5, the day LSU goes to Tuscaloosa to play Alabama. Meanwhile, Wisconsin is breezing through the Big Ten with a 59-7 win over Indiana this weekend, a disappointing 52 point win after the Badgers beat the Hoosiers by 63 last year. Out west, Stanford completed its six game, get those three new offensive linemen some playing time, pre season with a 44-14 win over Washington State on the road.
All this dominance sets up an interesting scenario for the flawed college football national championship system. If Oklahoma and Oklahoma State both win all their games until they play their Bedlam rivalry game, the winner would most likely play the Alabama LSU winner in the national championship game. If Wisconsin and Stanford also go undefeated, the Big Ten and Pac 12 conferences would get snubbed in a system that only allows two teams to settle the championship on the field. The ultimate irony is that these two conferences have put up the most resistance to a college football playoff. SI.com’s Stewart Mandel has recently tantalized fans with news that these two conferences might be open to a four team playoff, the so called plus one system. Would having their conference champions shut out of the national championship game push this to happen?
Before we get too excited, let’s look at the likelihood of this scenario with our analytics. The Power Rank assigns each team not only a rank but also rating, and the difference in the rating of two teams (with a 3 point home field advantage) gives a predicted point spread. Moreover, we use standard statistical methods to translate this point spread into a win probability for both teams. For example, Oklahoma was predicted to beat Kansas by 31, which implied Kansas had a 5% chance of pulling the upset (Kansas lost by 30). To forecast the future, we assume that the outcome of any game has no bearing on the outcome of any other game. Then the likelihood that Stanford goes undefeated is simply the product of the probabilities that Stanford wins each of its remaining games. For the 10 remaining unbeaten teams, here are the probabilities they end the season without a loss.
1. Boise State: 60.6%
2. Stanford: 34.8%
3. Wisconsin: 33.9%
4. Alabama: 30.9%
5. LSU: 16.5%
6. Oklahoma: 14.4%
7. Oklahoma State: 13.5%
8. Clemson: 9.0%
9. Houston: 6.4%
10. Kansas State: 0.7%
If these probabilities seem low, consider the hypothetical team that has a 90% chance of winning each game. By our calculations, this is approximately Stanford’s chance of beating Washington State on the road. To determine the probability of an undefeated season, we take the product of 0.9 12 times. (Multiply 0.9 by 0.9, then multiply the product by 0.9, and then repeat the last step 9 more times.) The probability that this team goes undefeated is 28.2%, so perfect seasons are difficult even for dominant college football teams. For a 16 game season, this probability decreases to 18.5% while an 82 game season implies a 0.02% probability. There will never be an undefeated NBA team. A mathematician or physicist would say that the probability of going undefeated decreases exponentially with the number of games played. This exponential function shows up everywhere in statistical physics, the field that inspired the algorithm behind these rankings. Entropy man is a gentle, multimedia introduction to how this function appears in physics.
Our calculations give Boise State the highest likelihood of remaining undefeated. The Broncos are just that much better than their remaining Mountain West competition. Boise State’s odds of winning their remaining games range from 79.1% against TCU to 99.3% against New Mexico. Stanford has the next highest likelihood of going 13-0. The Cardinal get Oregon at home this year, and their 34.8% chance includes a home game against Arizona State in the inaugural Pac 12 championship game. Wisconsin, with difficult games remaining at Michigan State, at Illinois, and against Penn State, comes in 3rd. However, their probability of going undefeated, which includes a neutral site game with Michigan State in the Big Ten championship game, is most likely greater than 33.9% since our rankings overrate Ohio State (16). We use a one year window of games in the rankings, which overestimates the strength of teams like Ohio State and Auburn which underwent drastic changes in the off season.
Despite being 1st in The Power Rank, Alabama has only the 4th highest probability because they play LSU (3). Again, this 30.9% is low since Alabama plays an Auburn team that is most likely overrated at 11th. LSU, despite their position atop the standings used to determine the national championship, has the 5th highest probability of remaining undefeated. Our rankings have LSU behind Alabama due to their performance in big games against Oregon and Arkansas respectively, an issue we explored in depth last week. Oklahoma and Oklahoma State appear at 6th and 7th on this list since our algorithm rates these Big 12 leaders as at least 8 points worse than Alabama. These lower ratings and their game against each other make their likelihood of going undefeated small compared with other teams in the national title hunt.
Consider the chaos scenario in which Alabama, Oklahoma, Wisconsin and Stanford all go undefeated. We calculate that this situation has a 0.5% probability, about the same chance that New Mexico has of pulling an upset of Boise State on the smurf turf. Math sucks sometimes. The numbers are useful for calculating the probability of other scenarios. For example, Boise State has a 9.4% chance of being the only undefeated team, most likely the only situation that assures the Broncos a place in the national championship game. Of course, there are other situations with 2 undefeated in which Boise State plays for the national championship, but a one in ten chance seems promising for a team not from an automatic qualifying conference.
Have a scenario of which you’d like to have the probability? Leave us a comment, please. Thanks for reading.