If Alabama, Kansas State, Oregon and Notre Dame remain undefeated, there will be some angry college football fan in early December. The antiquated BCS can pick only 2 teams for its championship game. The four team playoff that will grace this sport in 2014 can’t come soon enough.
However, the likelihood that all 4 teams remain undefeated is small. To understand why, assume these teams have a 80% chance to win each of their remaining games. The 80% reflects the dominance of these teams, and the uniform win probability makes the math simple. Including the conference championship games, these teams have 14 games remaining. The probability that they all remain undefeated is 0.8 to the 14th power, or 4.4%.
Not very likely.
What Retirement Says About College Football
To understand why this probability is so small, consider a retirement account. If this investment returns 10% annually, then $10,000 becomes $11,000 next year but compounds to $174,494 in 30 years. In the opposite way, the chance these teams remain undefeated decreases rapidly with the number of remaining games. Your mathematician friends call this an exponential decrease. The 14 remaining games are the reasons we won’t likely see four undefeated teams at season’s end.
Again, the 80% win probability is a uniform number that simplifies the math in showing the exponential decrease. On the field, Alabama has a higher likelihood (81.1%) of beating Texas A&M on Saturday. With the more realistic win probabilities of The Power Rank, there is a 6.7% chance these 4 teams remain undefeated. This includes an Alabama versus Georgia SEC championship game. Also, it assumes UCLA, the most likely team to win the Pac-12 South, travels to Oregon for the Pac-12 championship game.
Detailed Breakdown of the Four Teams.
Here’s a more detailed breakdown of the remaining defeated teams. The team rank come from our college football rankings. The offense and defense rankings results from adjusting yards per play for strength of schedule.
Alabama. Either the Crimson Tide pass defense had an off night against LSU or Zack Mettenberger became Andrew Luck overnight. The former is more likely.
- Team rank: 1st.
- Probability of remaining undefeated: 58.7%.
- Toughest remaining game: 75.6% chance to beat Georgia.
- Offense rank: 1st.
- Defense rank: 2nd.
Kansas State. While Colin Klein’s arm motion isn’t pretty, he is leading the 4th best pass offense according to our numbers.
- Team rank: 3rd.
- Probability of remaining undefeated: 57.1%.
- Toughest remaining game: 82.2% chance to beat TCU.
- Offense rank: 7th.
- Defense rank: 30th.
Oregon. Can a team slow down Oregon’s rushing attack enough to make freshman quarterback Marcus Mariota beat them? While Stanford has the 3rd best rush defense, the Ducks have made them look silly the past two years.
- Team rank: 2nd.
- Probability of remaining undefeated: 48.2%.
- Toughest remaining game: 72.4% chance to beat Oregon State.
- Offense rank: 6th.
- Defense rank: 13th.
Notre Dame. The Fighting Irish were 5th in our rankings before their near death experience at home against Pitt.
- Team rank: 9th.
- Probability of remaining undefeated: 41.6%.
- Toughest remaining game: 49.7% chance to beat USC.
- Offense rank: 23rd.
- Defense rank: 11th.
What do you think?
Will these teams all remain undefeated? Who will go down first? Please leave us a comment.
Thanks for reading.
Fair enough. I’m curious about more specific predictions, though.
Let’s use TeamRankings’s predictions: Oregon has 90 & 95% win chances, plus unknown but probably at least 80% vs Oregon State. Alabama has 80% vs. Texas A&M and probably 95% vs. Auburn, plus 95%+ versus W Carolina. K-State has 87%, 91%, and probably over 80% versus Texas. Notre Dame gets 89%, 95% and probably over 80% versus USC. Finally, let’s give the two conference championship games 75% just to be safe.
.9*.95*.8*.8*.95*.95*.87*.91*.8*.89*.95*.80*.75*.75 = .119, or 11.9%. Almost three times the chance in your article, but still significantly low.
Ed Feng says
Alabama has a 81.1% chance to beat Texas A&M
Alabama has a 99.8% chance to beat Western Carolina
Alabama has a 95.6% chance to beat Auburn
Alabama has a 75.8% chance to beat Georgia
Kansas State has a 82.2% chance to beat TCU
Kansas State has a 83.9% chance to beat Baylor
Kansas State has a 82.7% chance to beat Texas
Notre Dame has a 89.8% chance to beat Boston College
Notre Dame has a 93.2% chance to beat Wake Forest
Notre Dame has a 49.7% chance to beat USC
Oregon has a 89.0% chance to beat California
Oregon has a 86.3% chance to beat Stanford
Oregon has a 72.4% chance to beat Oregon State
Oregon has a 86.7% chance to beat UCLA
Looks pretty similar except for 2 games: Notre Dame at USC and Kansas State at Baylor. I think most of the difference comes from the less than 50% chance for ND over USC. Also, note that our “real” numbers say 6.7%, not 4.4% with our simple model.
Bob Hebert says
You mean USC, not Oregon State, right?
Ed Feng says
Yes I do, Bob. Thank you. The post has been updated.
That gives following probabilities for # of unbeatens:
0 unbeatens: 5.3%
1 unbeaten: 23.3%
2 unbeatens: 38.3%
3 unbeatens: 26.3%
4 unbeatens: 6.7%
In other words, only about 23% chance of no controversy (exactly two unbeatens).