By John Ezekowitz and Chris Bruce
Over the past few weeks, we have been predicting the college football polls. We were surprised by how predictable moves in these polls turned out to be. This got us thinking: what if we could predict the BCS formula itself? Could we know with some confidence who will be in the National Championship game before it is even announced?
As you may know, the BCS is composed of two human polls, the Harris and the Coaches’, and six different computer rankings of dubious quality. We obviously do not know the inner workings of these systems, but the fact is we do not need to know them in order to successfully predict the BCS. Using a dataset we compiled of every BCS ranking since 2006, we were able to build a model that predicts moves in the BCS amazingly well. It turns out that the BCS is an extremely predictable process.
We will first detail the model, then use it to run through the various scenarios still possible in this year’s college football season. The model we built, summarized in the table below, has an R^2 of 0.86. That means it explains 86 percent of the variation of week-to-week moves in the BCS formula, which ranges from 0 to 1 at the upper limit. The model is very simple: it includes terms for the team’s previous BCS standing, its opponent’s standing, the result of the game (win or loss), the margin of the result, and some interactions between these terms.
Because we used interaction terms, the coefficients on Margin and Win*Margin are extremely small, but still significant predictors at the 99 percent level. To check for overfitting, we ran numerous out of sample tests and the model performed very well in all of them. As you can see from the graph below, the actual and predicted values for the BCS Standings are almost identical.
Ironically, although BCS computers are not allowed to take margin of victory into account in their formulas, we found that it is a significant predictor of the overall BCS itself. Clearly the voters are using margin of victory in their assessment of teams.
We now turn to the season at hand. As it stands before this weekend’s games, LSU and Alabama are on course for a rematch in the National Championship game. This is the most likely outcome, but if either Arkansas or Auburn win this weekend, chaos will reign. For the purposes of this analysis, we are assuming that the only teams that can catch the top two are Arkansas, Oklahoma State, Virginia Tech, and Stanford. Also, because Oklahoma State has a bye this week before their game against Oklahoma, we are going to treat that game as if it happens the same week as these games and assume that Oklahoma will beat Iowa State (they are 28.5 point favorites, so this seems like a reasonable assumption, but who knows after ISU beat Oklahoma State last week). We also assume that both Virginia Tech and Stanford will win their games this weekend. Both are large favorites. Without further ado, the scenarios:
Scenario 1: LSU and Alabama win, LSU wins SEC Title Game
This scenario is straight forward. LSU and Alabama will play each other in the National Championship Game. A victory by Oklahoma State has no bearing on this, as Alabama (predicted BCS ranking of 0.98) and LSU (predicted BCS ranking of 1.00) are too far ahead.
Scenario 2: Arkansas and Alabama win, Alabama wins SEC Title Game
The table on the right shows our model’s predictions. The 95% Low and 95% High columns represent the 95% Confidence Interval for the data. As you can see, even if Oklahoma State wins, their confidence interval is well below that of Alabama’s or Arkansas’. It would be tough to imagine voters leap-frogging the Cowboys over the Razorbacks or Crimson Tide.
It may be that voters won’t drop LSU as far as the model thinks because, frankly, this scenario would be unique in the last five years. What is clear, however, is that teams that beat the number one team in the BCS, as Arkansas would have done, get large boosts.
The interesting wrinkle here is that in this scenario, Alabama would actually go to the SEC Title Game over Arkansas, despite the Razorbacks being the top ranked team in the BCS. This is because there would be a three-way tie in the SEC West, which would go to the 8th and last tiebreaker. That tiebreaker states that because the top teams are within fuve spots in the BCS rankings, they would take the top 2 teams according the BCS standings and take their head to head record to determine who goes to the championship. Alabama will go to the Title Game because they beat Arkansas. Ironically, if the two teams were ranked #1 and #6 instead of #1 and #2, then Arkansas would go.
Scenario 3: LSU and Oklahoma State win, Alabama loses, LSU wins SEC Title Game
This is the only scenario where Oklahoma State gets in to the National Title Game. As you can see from the table below, in this case the Pokes are a clear second choice with both Arkansas and Alabama losing. What pushes them above Virginia Tech and Stanford is the quality of their win over Oklahoma.
Scenario 4: LSU and Virginia Tech win out, Alabama and Oklahoma State lose.
Head spinning yet? These last two scenarios go into murky territory. This scenario is the same as before, except Oklahoma State loses to Oklahoma. Our model does not see a two-loss Oklahoma team gaining enough ground to be in the picture. Additionally, because this requires Alabama losing to Auburn, our model sees the Crimson Tide being eliminated in this scenario. This leaves 1-loss, ACC Champ Virginia Tech as the likely backdoor BCS crasher. Virginia Tech leapfrogs Stanford mainly on the strength of the win over Clemson in the ACC Title Game.
Of course, this relies on a series of assumptions and guesses. If Clemson loses to South Carolina this week, the Hokies may not get such a boost by beating them. We also don’t know how far voters will drop Arkansas if they lose a very close game at LSU. It seems that in this scenario, however improbably, the Hokies have the inside track.
Scenario 4: LSU and Alabama lose, Oklahoma State and Virginia Tech win.
This one is the most speculative, and the most unlikely. TeamRankings’ models put the odds of both LSU and Alabama losing this weekend at less than 1 percent. Nevertheless, if this were to happen, Arkansas would almost certainly be in the National Title Game. Who they would face is a much trickier question. Assuming both Oklahoma State and Virginia Tech win, our models give the edge to OSU. The hard factor here is LSU. It is hard to predict how much the Tigers would drop in the human polls if they lose a tight game to Arkansas. They may stay above Oklahoma State. Our model suggests the Cowboys would play the Razorbacks in this scenario (can you imagine the points scored in that game?), but it is far from certain.