THE POWER RANK

Forecasting the College Football National Championship Game

By 5 Comments

And then there were six
Who will play in the big game?
Behold their chances

The Power Rank, College Football, Week 9, 2011

On the last Saturday in October, college football offered some huge conference match ups. In the Big Ten, Wisconsin traveled to Ohio State to face the Buckeyes at The Horseshoe. Down south, the SEC pitted Georgia against Florida amidst The World’s Largest Outdoor Cocktail Party. But the most important game on Saturday, as validated by the presence of ESPN’s College Gameday, was Stanford at USC. It wouldn’t be surprising if USC were attracting all the media attention given their success this decade. But times have changed. Gameday showed up in Los Angeles because of an undefeated Stanford team. The Cardinal are one of a few teams in contention to play the SEC champion in the national championship game.

Before the game, USC coach Lane Kiffin won the media BS award of the week by calling Stanford quarterback Andrew Luck perfect and asking his interviewer for any ideas about how to stop Stanford’s offense. Kiffin didn’t need to consult his dad, USC’s defensive coordinator, to know that slowing down Stanford’s running game and getting pressure on Luck would mitigate Stanford’s offense. Or maybe he did. Either way, USC held Stanford to 3.9 yards per carry (186 total), much lower than their 5.6 yard average for the season. USC also sacked Luck twice. While this sack total might not sound impressive, Stanford’s offensive line, which features 2 potential first round picks, has allowed only 2 sacks all season. Despite this defensive performance, Stanford escaped with a 56-48 win when Ben Gardner’s right arm swatted the ball away from USC’s Curtis McNeal to end the third overtime.

Stanford remains undefeated with the win, but Kansas State and Clemson dropped out of the national championship picture with losses to Oklahoma and Georgia Tech respectively. With only 6 undefeated teams remaining, The Power Rank can update the projections that each of these teams remain undefeated. However, this week, we make the transition to rankings that only use games from this year. Up to this point, the rankings included all games in a one year window, with this year’s games counted twice. This drastically overrated teams like Auburn, who had a huge 56-17 win over South Carolina (19) and a 3 point win over Oregon (5) at the end of last year. With the loss of key players, coach Gene Chizik has found this season much more difficult. This change drops Auburn’s rating by 8 points, moving them from 12th to 38th. Perhaps this lower ranking isn’t a surprise given Chizik’s 5-19 record at Iowa State before becoming Auburn’s coach. Moreover, this change also improves Oregon’s rating by 2 points. These changes affect our forecast since Alabama plays Auburn while Oregon travels to Stanford. Here are the chances that each of 6 teams remains undefeated.

Boise State: 66.6%
Stanford: 41.7%
Alabama: 39.8%
Oklahoma State: 39.7%
LSU: 34.3%
Houston: 32.2%

With these changes, Alabama’s likelihood of going undefeated gets closer to Stanford’s than in our previous analysis. Alabama has the toughest remaining game, a 58.7% chance of beating LSU, but Stanford still faces Oregon with a 67.6% chance of winning. The changes in the rankings also recognize Houston as a completely different team with the return of quarterback Case Keenum this year. The Cougars move from 45th to 23rd and have a 32.2% chance to remain undefeated, much higher than the 8.7% we predicted earlier. This analysis includes a Conference USA championship game against Southern Miss.

The Power Rank can also estimate the likelihood that LSU and Alabama have a rematch in the national championship game. For this to happen, the remaining 4 unbeaten teams must each lose at least one gamen and the winner of the Tuscaloosa Tussle must go undefeated while the loser ends the season with only that one loss. The new rankings give this a 15.3% chance, quite a bit higher than the 4.9% chance we forecasted last week. Of course, these conditions do not ensure a rematch, since Oklahoma reenters the picture if they beat Oklahoma State and finish the season with one loss.

A more interesting scenario arises if we tweak the last situation so that Boise State goes undefeated. The winner of Alabama LSU and Boise State would be the only unbeaten teams, while the loser of the Tuscaloosa Tussle finishes the season with one loss. This is my personal favorite scenario since the SEC would secede from college football if an undefeated Boise State made the national championship game over a one loss Alabama or LSU team. The Power Rank gives this a 10.1% likelihood, about a one in ten chance for chaos.

Our analysis also produces some surprising numbers. As dominant as Alabama and LSU have been all season, there is a 30.4% chance that they both lose at least one game. While this number might seem absurdly high, consider that one of these two teams will lose on Saturday when they play each other. So 30.4% is the probability that the winner loses one of three remaining regular season games or the SEC championship game. The Power Rank suggests taking up a friend who will pay 10 to 1 if LSU and Alabama will both lose at least one game. Of course, no undefeated SEC teams greatly helps Boise State make the national championship game. The chance that Boise State remains the only undefeated team at the end of the regular season is 5.5%. They might make the championship game in other scenarios, but the system won’t lock them out as the only undefeated team.

Have a scenario of which you’d like to have the probability? Leave us a comment, please. Thanks for reading.

More National Championship chaos and Boise State

By Leave a Comment

James writes “Even better for chaos would be for Georgia to win the SEC……….. now how would that work out? Could you put one loss Alabama or LSU back in……oh the possibilities are just great for the ultimate chaos.” Ah yes, it would be fascinating if Alabama/LSU both had one loss but neither ended up winning the SEC. Do you put a one loss, dominant team in the National Championship game if they don’t win their conference? So, here’s the situation. First, Alabama and LSU win all their remaining regular season games after the Tuscaloosa Tussle. Second, the winner of the Alabama LSU game loses to Georgia in the SEC championship game. Third, every other team has at least one loss. The Power Rank gives this a 0.67% probability, so it’s not that likely. Even if the higher ranked South Carolina wins the SEC championship game, the likelihood only goes up to 0.77%.

Last week, we calculated the probability that Boise State ends the season as the only undefeated team. Unfortunately, we made an error since we assumed the remaining undefeated teams did not play each other. Of course, this isn’t true, as Kansas State faces Oklahoma State while Alabama and LSU will command everyone’s attention next Saturday. When we work out the likelihood that Alabama and LSU both end the season with at least one loss, we get 44.2%, most likely a number higher than most people expect. With the correct math, Boise State has a 9.1% chance of being the only undefeated team at the end of the season. It’s still about the 1 in 10 chance we stated previously.

Alabama and LSU have a 4.9% chance of meeting in the National Championship game

By 7 Comments

LSU, Bama
Rematch, championship game?
Four point nine percent

LSU and Alabama continue to storm through their schedules with little resistance. On Saturday, LSU beat up on National Champion Auburn 45-10. The LSU defensive line dominated, allowing only 2.6 yards per carry (87 total) to an Auburn offense that has averaged 4.4 yards per carry this season. This followed last week’s 31 point win over Tennessee on the road. Last year, LSU needed a late game miracle to squeak by Tennessee at home and lost by 7 to Auburn. LSU’s vast improvement this year has bumped their rating from 15.6 at the end of last year to 28.8 now. Alabama started slowly the last two weeks against Mississippi and Tennessee but dominated the opposition in the second half. They outscored Tennessee 31-0 by not allowing a single first down in the second half on Saturday. Alabama and LSU, along with Stanford, have gained separation atop The Power Rank with Wisconsin’s loss to Michigan State and Boise State’s poor showing at home against Air Force. These 3 teams are 6 points clear of 4th ranked Oregon.

LSU and Alabama have the week off before they play in the Tuscaloosa Super Bowl on November 5. Many have argued that these two teams should play again in the National Championship game. While politics will play a huge role in determining who plays in this game, we can say something quantitative about an Alabama LSU rematch with The Power Rank. Our rankings imply a win probability for each team in every game. Last week, we gave the probability that each of 10 teams would remain undefeated and predicted a 0.5% likelihood that Alabama, Oklahoma, Wisconsin and Stanford all end the season undefeated. Losses by Wisconsin and Oklahoma late Saturday night validated this prediction. Here are updated probabilities for the remaining undefeated teams.

Boise State: 60.4%
Stanford: 40.0%
Alabama: 33.5%
Oklahoma State: 29.6%
LSU: 26.1%
Clemson: 10.8%
Houston: 8.7%
Kansas State: 0.7%

Many things must happen for LSU and Alabama to both reach the National Championship game. First, every other undefeated team must lose at least one game. It is incredibly unlikely that an undefeated Stanford team with a quarterback who gave up being the first pick in the NFL draft to finish his degree would get shut out of the championship as one of two undefeated teams. The same goes for an Oklahoma State team led by a 28 year old quarterback who found college football after not making the major leagues as a pitcher. The Power Rank gives a 13.5% chance that Boise State, Stanford, Oklahoma State, Clemson, Houston and Kansas State all lose at least one game. Then, LSU and Alabama must both win all their remaining regular season games. We give this a 42.1% chance. While less than even odds might seem strange, LSU has a game with Arkansas while Alabama goes on the road to Mississippi State and Auburn. Last week, we discussed how the probability of winning all games goes down rapidly with the number of games. Last, the winner of the Tuscaloosa Super Bowl must win the SEC championship game. Assuming that South Carolina emerges from the East, there is a 86.5% chance that LSU or Alabama clear this hurdle. With these assumptions, there is 4.9% chance that LSU and Alabama play in the National Championship game. One in 20 is not a high likelihood.

The biggest barrier to a championship rematch is the need for the 6 remaining undefeated teams to lose at least once, a scenario with a 13.5% chance. Of course, with all the murkiness of two human polls and a set of computer rankings not allowed to use margin of victory, there are other scenarios that allow for an LSU Alabama rematch. Suppose Boise State goes undefeated but needs a Hail Mary to beat TCU at home and a officiating blunder to win at San Diego State. What would happen if Boise State and Alabama were the only two undefeated teams but LSU loses to Alabama by 1, crushes Arkansas by 49 and clearly stands out as the best one loss team? Chaos. No one from the south would accept Boise State in the championship game, while the rest of the country would riot or vomit with 2 SEC teams in the championship game. On the more rational side, consider the following possibility. First, Boise State goes undefeated. Second, the SEC champion, either Alabama or LSU, goes undefeated. Third, the loser of the Alabama LSU game only loses once. Last, every other team loses at least one game. The Power Rank gives this scenario a 7.4% chance. For all the haters of the system, this is your best bet for chaos.

Have a scenario of which you’d like to have the probability? Leave us a comment, please. Thanks for reading.

BCS chaos, undefeated teams, and Boise State in the championship game

By 3 Comments

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.

How can LSU not be number one in your rankings?

By 1 Comment

Strength of schedule
LSU has two big wins
What? Not number one?

When Wisconsin’s 31 point win over Nebraska moved them to second in The Power Rank last week, Brian Hammer shared a link on Facebook. Brian is engaged to Val, a very close friend who was the maid of honor at our wedding. They live in Madison and have gotten swept up in Badger fever this fall. Brian’s friend Parker Anderson saw the link and commented, “I’m having trouble wrapping my head around an algorithm that rewards wins over ranked opponents and doesn’t put LSU #1.” Now, Parker clearly cares about college football, as his profile picture shows him with ESPN’s Kirk Herbstreit, presumably from when College Game Day visited Madison last week. Moreover, he must have clicked on the “About” page of this site to get an idea about our analytic methods. Teams earn their rank by beating other highly ranked teams. So how do we explain why LSU, who has beaten Oregon (7) by 13 and West Virginia (23) by 26, lingers at 4th in our rankings, behind Alabama, Stanford and Boise State?

Good question. In our early season rankings, we use a one year window of games, with this year’s games counted twice. For LSU, this set of games includes last year’s loss to Auburn and every game since then. Of course, we could also use only games from this year, which gives us different rankings.

1. Alabama, 6-0, 34.20
2. LSU, 6-0, 31.35
3. Wisconsin, 5-0, 31.17
4. Stanford, 5-0, 27.58
5. Boise State, 5-0, 25.37
6. Oklahoma, 5-0, 24.03
7. Oregon, 4-1, 23.89
8. Oklahoma State, 5-0, 22.21
9. Michigan, 6-0, 18.34
10. Texas A&M, 3-2, 16.88
11. Arkansas, 5-1, 16.05
12. Clemson, 6-0, 14.04
13. Notre Dame, 4-2, 13.81
14. Arizona State, 5-1, 13.10
15. Rutgers, 4-1, 12.93
16. Penn State, 5-1, 12.79
17. Georgia, 4-2, 11.42
18. Missouri, 2-3, 10.80
19. Baylor, 4-1, 9.78
20. Florida State, 2-3, 9.58

Since these rankings reflect what teams have earned on the field this year, they more closely correspond conventional wisdom and the AP poll. However, LSU still comes in 2nd behind Alabama. The algorithm thinks more highly of Alabama’s 24 point home win over Arkansas (9) than LSU’s 13 point win in Dallas over Oregon (7), the toughest games played by either team this year. In the AP poll, Alabama didn’t get the credit they deserved for this Arkansas win because LSU went on the road to beat West Virginia that same week.

The rankings with games from last year make better predictions, and these predictions are more important than evaluating teams on their play this year. In this year’s college football games, the rankings that use a one window of games predicts the correct winner in 73.6% of 638 games played between two Division I teams. The rankings that only use games from this year can only make predictions after week 4 and predict winners in 69.1% of 217 games. While football will always have a limited number of games, the algorithm can contemplate 82 regular season games per team in the NBA. With all this data, it predicts the winner in 70.0% of 2330 late season games over the last 4 years. For comparison, the line picked 70.8% winners in this same set of games.

Also, we can already see how more games tends to depress the ratings of top teams like Alabama and LSU. For example, LSU has a 31.4 rating using only this year’s games but a 24.2 rating in the actual rankings. LSU enjoyed a 4-1 and 4-0 turnover edge against Oregon and West Virginia, respectively, which padded the margin of victory in both games. LSU cornerback Tyrann Mathieu forced a fumble and scored a touchdown against Oregon, but we don’t consider this lucky as our Heisman frontrunner continues to create turnovers in other games. However, LSU benefitted from 2 fumbles by Oregon true freshman De’Anthony Thomas in his first college game, a performance unlikely to be repeated if Oregon played LSU again. Considering more games in our rankings averages out this luck.

Of course, there are problems with using games from last year. Auburn shows up at 10th in the rankings based on their incredible late season performance last year. However, quarterback Cam Newton and defensive tackle Nick Fairley are gone, casting doubt on this high ranking. Their 38th ranking in our results using only games this year is probably a more accurate assessment. Ohio State still lingers at 18th on the strength of last year’s games. Without coach Jim Tressel this year, Ohio State is painful to watch and comes in 53rd in our rankings with only this year’s games.

So thanks, Parker, for caring enough about college football to make a stink about LSU. And while we’re addressing the concerns of fans from Madison, we should explain why Wisconsin dropped to 5th without playing a game. Stanford (+41 over Colorado), Boise State (+50 on the road at Fresno State) and LSU (+30 against Florida) all scored huge wins over the weekend that boosted their ratings significantly. Still, all four of these teams remain within 1.3 points of each other. Let’s play some more football.