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Mac Mirabile’s BCS Simulator Stimulator

Mac's workstation.

With the first BCS standings announced Sunday, the real fun can now begin. Auburn, LSU and Alabama are all still in the hunt for a BCS title game appearance. But which teams in the SEC and outside the conference will still be in the hunt by the time the regular season ends and after all conference championship games are decided?

Each year a non-BCS school or two seems to creep into the BCS championship game conversation. Fans of college football know that on any given Saturday, any of these top BCS contenders could probably beat any other. Certainly on occasions such wins are big upsets, but they happen all the time. We are now halfway through the season and are beginning to separate the pretenders from the contenders, but we have a long way to go.

Anyone who professes to know how things will shake out will almost certainly be wrong. I will attempt to explain the likelihood of different scenarios that we will encounter using a statistical technique called “Monte Carlo experiments.” As I’ve setup this system, Monte Carlo simulation basically examines thousands of potential variations in game outcomes and how they affect our BCS outcome of interest: How many undefeated teams will remain when the BCS championship game pairing is decided.

Let me underscore this point: I am only simulating how many undefeated teams will remain, not which two will be chosen or what the final BCS standings will be. Although these alternate outcomes are in many ways more interesting than the one I’ve chosen to examine, they rely on too many moving pieces, having to forecast changes in both the polls and the computer rankings to do a proper treatment.

So, getting back to the Monte Carlo simulations. I am going to examine the top 11 teams, from Oklahoma to Missouri, to simulate the likelihoods of different outcomes. Remember that all of these teams have five, six or even seven games remaining. Each of these teams has some likelihood to win (or lose) each game. The chance that a team will lose may be exceedingly small (Oregon, as a 24-point favorite, should win more than 99 percent of the time), but it can happen. This is where Monte Carlo simulation comes into play — by looking at how each team is expected to perform and the likelihood that they will win, we can begin to quantify how all these uncertainties (individual game outcomes) will likely play out in reality.

The most important step in setting up this simulation is also the trickiest — predicting how likely each team is to win each of the remaining games on its schedule. To achieve this, I am using a probability model where each team’s ranking, season-to-date statistics, game location, etc. are factored in. It is important to note that the data I am using for these predictions in the future are all season to date through Oct. 16. This is important to note because, for example, if Missouri absolutely destroys Oklahoma, everyone’s opinions of each of these teams will be revised and we would all consider Missouri much more likely to win their remaining games than before we had observed the Oklahoma game’s outcome. The model, however, can only forecast these remaining games with what it knows now about Missouri. The solution to this issue is to revise the model after this week’s slate of games and rerun the simulation. (For more information on the exact variables used in this model, please see this week’s forthcoming Predict-O-Nomics column.) This model will forecast a probability of winning (and losing) that is used in the second step of the process.

The second step involves setting up the random parameters that will drive the process. Each random parameter can take a value anywhere between zero and one. It has a uniform distribution, meaning that no one value is more likely to be drawn than another. To reinforce this statement, that means that the random parameter could have a value of 0.1, 0.24, 0.74, 0.9983129, or any fractional number between zero and one. So let us look at an example of a game where the home team had exactly a 50 percent chance of winning. If my random parameter associated with that game was greater than 0.5, I would call this a win for the team. If it were less than 0.5, I’d call it a loss for the team. With repeated sampling run thousands of times, we would see that the team should end up with approximately the same number of wins and losses in the game. That’s the goal since we know the model projected the team had a 50 percent chance of winning. By now, it should be clear that the greater the probability the model believes a team will win the game, the more times the Monte Carlo simulation will indeed observe that team winning the game.

Once both the model has predicted a probability of winning each game the random parameters have been established, running the actual simulation is as easy as clicking the “start simulation” button. One minute later, the computer has simulated the entire rest of the season for these teams 10,000 times. The results I share below cannot predict what scenario will actually occur, only what scenarios are most likely to occur.

Predicting the rest of the season

The graphs below shows, in order of current BCS ranking, how many wins each team should average and each team’s likelihood of finishing undefeated. The simulation and model reveal a couple of things right away. Oklahoma will probably lose and Boise, Oregon and TCU all have great chances of going undefeated. Let’s dig into each team in a little more detail. I’ll begin with an analysis of just the top 11 ranked teams in the current BCS standings (with apologies to temporarily unbeaten Oklahoma State).

Oklahoma has probably been more lucky than good. A couple of embarrassingly close wins at home against Utah State and Air Force and on the road against Cincinnati have the model predicting bad things for the Sooners in the second half of the year.

Oregon, who has yet to be challenged in the Pac-10, looks better right now (in the model’s eyes) than they probably are. The Ducks have beaten one quality opponent in Stanford but have Top 25 games remaining at Southern Cal, Oregon State and at home against Arizona. I wouldn’t put too much stock in Oregon until we say how they play on the road in two weeks against the Trojans.

Boise State should go undefeated. They really should. There is a 59 percent chance that they finish the season undefeated. They will be big favorites in every game with the possible exception when the Broncos go on the road to Nevada on Nov. 26.

Auburn is in remarkably good position right now to make it to the BCS title game. With two Top 10 opponents remaining, the Tigers strength of schedule will only improve if they can win out. That is a big IF, however, as the Tigers have an 11.2 percent chance of running through the remaining gauntlet of the SEC unscathed. The first test comes this week against LSU, then to the road for the Iron Bowl.

TCU has looked dominant all year, but that may not be good enough to make it to the title game. Even if TCU runs the table (and they have a 43.3 percent chance of doing so), the Horned Frogs’ best win would be over fellow non-automatically qualified Utah.

LSU is in the same situation as Auburn — win out and the Bengals will probably leapfrog the teams ahead based on strength of schedule. To do so, they’ll need to beat both Alabama and Auburn. If they can accomplish that and finish the season undefeated (something the model suggests will only occur 4.9 percent of the time), they deserve to represent the SEC in the championship game.

Michigan State is undefeated in the Big Ten, but as Ohio State has shown time and time again, that doesn’t mean much. Michigan State’s favorable schedule this year rotated out Ohio State, so the Spartans’ marquee win of the season is a 34-24 victory at home against Wisconsin, with an Oct. 30 trip to Iowa looming large on the horizon. Even if Michigan State wins out (and they have a 26 percent chance of winning their remaining five games), they are unlikely to get a shot at the title.

Alabama, preseason No. 1 and defending national champion, could make things very interesting if they run the table in the SEC. I think most voters might be hard-pressed to keep them out of the BCS title game if it comes to displacing an undefeated Boise State, TCU or Utah team. Alabama would have to beat four Top 25 teams (including the SEC East champion) to do get there, so it is going to be an uphill climb to the title game for the Tide.

Ohio State is all but out of the hunt this week after being an overwhelming favorite to make it to the title game just a week ago. Even if Ohio State wins out, the Buckeyes best win might be against a mediocre Miami team. Even SEC fans who love facing Ohio State in the BCS championship game would probably enjoy a change of pace.

Utah again finds itself in the unenviable position of possibly going undefeated but not going to the title game. The Utes, however, have made an honest effort to improve their scheduling, facing both Pittsburgh and Notre Dame out of conference. Unfortunately for Utah, neither of these teams lived up to their preseason billing. Utah has a relatively tricky remaining schedule with road games remaining against Air Force, Notre Dame and San Diego State, and home games against TCU and BYU. Utah would need to count on there only being one other undefeated team before they’d have much of a chance on making a title game appearance.

Missouri finds itself at 6-0 after opening the season on a five-game home stand. The second half of the Tigers’ scheduling is not so friendly with four of their last six games on the road with the option of a conference championship game if things go well. Things will have to go exceedingly well for Missouri to go undefeated through the remainder of the season, something the model and simulation forecast will occur 1.2 percent of the time.

The undefeated

This year is going to be a mess, in all likelihood. OK, all math puns aside, things could/should shake out to put the BCS in a bit of a pickle again this year. Using the same 10,000-run simulation, I’ve put together a chart below on the probability of different outcomes. The first bar shows that there is a 6.3 percent chance that no team goes undefeated. The last bar reveals that there is a 1.7 percent chance that five or more teams remain undefeated at the end of the year.

No undefeated teams is probably the best-case scenario for proponents of the BCS as it means Boise State, TCU and Utah can all be immediately discarded from real consideration. However, it introduces just as many problems as now one-loss teams like Alabama, Ohio State are back in the mix.

One undefeated team (most likely a Boise State or TCU) scenario could be a mixed blessing for the BCS. Sure they have to sort through who the other team is (but that’s what the system was designed to do, right?), but more importantly, the BCS could finally be forced into giving these perennial underdogs a chance at the crown.

A scenario of two undefeated teams could make for a great game and lots of fan interest, unless of course the two undefeated teams hail from non-BCS conferences. I wonder if the BCS would even recognize the winner of this game as the best team in the country. To be certain, most voters would have a difficult time giving a Boise State-TCU/Utah winner the top final ballot spot come January over a one-loss SEC, Big 12, Big Ten or Pac-10 team.

In the remaining scenarios, some undefeated team is going to be left out of the title game. So, it looks like there is a 34 percent chance that someone is going to get snubbed. You can bet that it is not going to be an undefeated SEC team, however, given the conference’s 5-0 mark in BCS title games. More than likely, the odd man (men) out is going to come from the conference the polls and voters respect the least.

Now is actually a good time to introduce some findings from a paper my co-author Mark Witte from the College of Charleston and I published last fall. We found evidence of voters in both polls that consistently voted higher members of their own conference and also voted lower teams from non-BCS conferences. As you might expect, the voters from these polls are over-represented by the BCS conferences based on the location of the media voter or the coach voting in the poll. The only real way for non-AQ (automatic qualifier) teams to keep pace in the polls was to run up the score and consistently cover the point spread. Essentially, non-AQ teams have to exceed the expectations of the voters week in and week out if they are to be treated like their peers from the BCS conference. Keep that in mind next time you see Boise State beating a WAC opponent by 50-points — it is the only way voters will give them any respect. Ironically, it is also the biggest reason no one respects their strength of schedule.

Mac Mirabile is a 2002 graduate of Auburn’s economics and journalism departments. During his time at Auburn, he was a copy and photo editor with The Auburn Plainsman. He has a master’s in economics from UNC-Chapel Hill and has written numerous academic publications on college football, the NFL, and gambling markets. His previous columns can be found here. He can be reached at [email protected]

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