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College Football Mathematical Preview 2021: The Big Ten

I simulated the results of the Big Ten race 100,000 times.

Ohio State v Michigan State
Can anyone in the Big Ten catch the Buckeye this year?
Photo by Gregory Shamus/Getty Images

This summer, as is my annual tradition, I have been applying a set of mathematical tools to try to better understand how the coming college football season may play out. In part one of this series, I presented the first set of data from my simulation of the full season, and completed a full breakdown of Michigan State’s schedule. Today, it is time to take a broader look at the Big Ten.

The basic method that I utilize involves generating an average preseason power ranking of all 130 FBS college football teams using the consensus of the rankings from various magazines and websites. I can then project point spread and victory probabilities for every game in the upcoming season, including possible College Football Playoff matchups.

As an additional input to my model, I also add the historical uncertainty in the preseason rankings themselves. Finally, I perform 100,000 Monte Carlo simulations of the season in order to generate odds for various season outcomes.

Let’s take a look at the results of this simulation for the Big Ten conference.

Big Ten Overview

Table 1 below gives the full results of my simulation for the Big Ten.

Table 1: Monte Carlo simulation results for the Big Ten conference

The table highlights the consensus preseason ranking of each team (the main input to the simulation), the total number of expected wins for each team, my calculated strengths of schedule, and the odds for each team to win their division, the conference, make the playoffs or win the national title.

As we can see, both Big Ten divisions have a clear favorite: Ohio State in the East and Wisconsin in the West. Both teams have 50-50 odds to return to Indianapolis. Naturally, the Buckeyes and Badgers have the best odds to make the playoffs (27 and 18 percent) and to win the national championship (eight and four percent).

As for potential dark horse candidates, Penn State in the East and Iowa in the West are the teams that are most likely. Both teams have a one-in-four chance to advance to the Big Ten Championship game. Indiana is the only other team with over a 10 percent chance to reach Indianapolis. After that, there is a group of teams in both divisions with about a five to 10 percent chance to win their division: Michigan (8.5 percent) in the East and Minnesota (7.8 percent), Northwestern (7.8 percent), and Nebraska (6.8 percent) in the West.

In addition to the expected win totals shown for each team, the simulation provides a great deal of other information, including the conference win distribution data, which I show below in Table 2.

Table 2: Big Ten Conference win distributions for all 14 Big Ten teams, based on the 100,000 cycle Monte Carlo full-season simulation, including the historical uncertainty in the preseason rankings.

This table is essentially a wall of numbers, but it does give some interesting insights. For Michigan Sate, this data suggests that the Spartans will most likely win between one and three games (about 60 percent odds). But, there is also a 26 percent chance that MSU wins between four and six conference games, and a two percent chance that MSU wins seven or more games (most likely in the scenarios where the Spartans are significantly underrated in the preseason).

On balance, the data predicts a sixth-place finish for Michigan State in the East, just ahead of Rutgers, based on the total number of expected conference wins (2.58). It is also possible to generate odds for MSU to finish anywhere from first to last place in the division (including ties).

That full table can be viewed here for the entire Big Ten. For Michigan State, the data says that the Spartans have a 50-50 chance to finish in either sixth or seventh place in the East. There is a 21 percent chance for MSU to finish in fifth place, a 14 percent chance to finish in fourth, and also a 14 percent shot to finish in the top-three.

It is notable that Table 2 shows that Ohio State’s expected win total is only 7.2 conference wins. Based on this simulation, the Buckeyes have a 50 percent chance to win eight or nine games, and a 50 percent chance to win less. That may seem low, but it bears mentioning that certain teams (like Alabama, Ohio State and Clemson) tend to consistently beat their odds. One could argue that this is why those teams are considered to be the elite teams in college football right now.

The odds are generated based on the average performance of all FBS teams and there is no correction factor for recent success. Over the arc of history, elite teams tend to beat the odds until they don’t. One of these years, a team like Alabama, Clemson or Ohio State is bound to get the injury bug or some bad bounces and regress back to the mean a bit. Will that happen this year? Your guess is as good as mine.

As for our friend in Ann Arbor, four to six conference wins is the most likely results for the Wolverines (54 percent odds). There is only a 17 percent chance of Michigan winning seven or more games, but there is a 29 percent chance that Big Blue wins only three conference games or fewer. These numbers seem about right based on the level of excitement for Michigan basketball in July.

Strength of Schedule

Embedded within Table 1 is also the strength of schedule data for all 14 Big Ten teams. My method to calculate strength of schedule appears to be unique, but it is simple and (in my humble opinion) very powerful. I define strength of schedule as the expected number of wins for a given schedule if the team playing it were an average Power Five team (roughly ranked No. 25 in the country).

Table 1 gives the raw numbers for both the overall and conference only strengths of schedule. However, it is easier to grasp if the data is visualized, which I have done below in Figure 1.

Figure 1: Overall (left) and conference only (right) strength of schedule estimates for the Big Ten. Values represent the number of expected wins an average power five team would have playing each team’s schedule

Overall, there is not a huge disparity in the overall of schedule strength across the Big Ten, but there is some. For context, the team with the toughest schedule in the country is Arkansas (6.85 wins), while the easiest Power Five schedule belongs to Boston College (9.21 wins) which is a difference of about 2.4 wins over a 12-game schedule. In the Big Ten, the range is 1.4 wins overall and just over one win for conference games.

That said, overall, Northwestern has the easiest schedule by half of a game over the second-place team, Wisconsin. Both teams also claim the easiest two Big Ten schedules by about half of a win above the conference average (5.47). Northwestern plays a very soft non-conference schedule this year — Indiana State (FCS), Duke (ranked No. 92) and Ohio (94), and the Wildcats’ Big Ten East crossovers are Michigan State (No. 74), Michigan (30) and Rutgers (76). As for the Badgers, they do face Penn State (12), Norte Dame (11), Iowa (18), and Michigan (30) in 2021, but all four of those games are either in Madison or at a neutral site in Chicago (for the Fighting Irish).

Michigan State’s conference schedule grades out as pretty average (eight-place in the Big Ten), but the presence of the road game at Miami (No. 15) pushes the Spartans’ overall schedule down to the third-most difficult, behind only Nebraska (the Huskers face No. 3 Oklahoma in the non-conference) and Purdue (the Boilermakers travel to No. 10 Notre Dame).

In conference play, Rutgers, Michigan, Minnesota, and Purdue own the four hardest schedules. Also note that in odd-numbered years, the Big Ten East teams play two road games and only one home game against a West Division crossover opponent. Thus, on average, the Big Ten West teams have slightly easier schedules (by about 0.3 wins).


This is all well and good, but there is one potential draw-back to my analysis methodology. One thing that should be clearly noted from Table 1 is that the division odds track exactly with the preseason rankings. While I do inject uncertainty into the simulation, each team has the same amount of positive and negative upside.

In other words, the odds of a team being overrated are the same as the odds that they are underrated. The odds get spread out over more teams (hence MSU’s national title odds are non-zero), but the ranking of the teams are essentially unchanged.

Fortunately, I have one additional tweak to my analysis to look for likely disruptions in the predictable outcome of each division and conference race. For this version of the simulation, I change the parameters to artificially improve the parity of the entire set of FBS teams in order to look for the most likely upsets that could change the outcome of a conference race.

For the Big Ten this year, however, the “disruptive” simulation does not change the prediction. In the base case, Ohio State (No. 4) and Wisconsin (10) are both projected to be favored in all of their games. In the disruptive simulation, Ohio State potentially drops a game at Indiana (23), but as Figure 1 shows, all of the potential Big Ten East challengers have tough schedules on balance. So, even if this were to happen, the Buckeyes are still likely to come out on top.

More specifically, Indiana (23) projects to pick up loses at Penn State (12), at Iowa (18) and at Michigan (30). The Hoosiers will likely need to beat OSU and win two of those three to win the East. As for Penn State, the Lions have to travel to both Madison and Iowa City as well as Columbus. Good luck with that. As for the Wolverines, they have road games at Wisconsin, Penn Sate and Nebraska. In other words, bet on Ohio State in the East.

As for the West, as mentioned above, Wisconsin’s easy schedule sets them up to potentially run the table in the Big Ten, as well as potentially overall. The Badgers project to go 12-0 even in the disruptive simulation, as their toughest true road game is at Minnesota (No. 37). Similar to the discussion of Ohio State above, Wisconsin’s expected win total (based on probabilities) is only 9.25, but Wisconsin will likely be favored in all of their games, making a 12-0 record the most likely single scenario.

That said, Iowa’s schedule is also favorable as they draw Indiana (23), Penn State (12) and Minnesota (37) all in Iowa City. The Hawkeyes’ only projected loss is the Oct. 30 contest against the Badgers in Madison. While Wisconsin still should be favored in this game, an upset could very possibly earn Iowa a return trip to Indianapolis.

Key Big Ten Games

Finally, here is a list of potentially key games involving Big Ten teams that either project to be “disruptive” (i.e. a home underdog stealing a win), are possible division swing contents, or are key non-conference games. The projected spreads are shown in parenthesis.

  • Sept. 4: West Virginia at Maryland (+4.5)
  • Sept. 11: Iowa (+10) at Iowa State
  • Sept. 11: Oregon at Ohio State (-6)
  • Sept. 11: Washington at Michigan (-0.5)
  • Sept. 18: Nebraska (+21) at Oklahoma
  • Sept. 18: Purdue (+19) at Notre Dame
  • Sept. 18: Cincinnati at Indiana (-1)
  • Sept. 18: Michigan State (+18) at Miami
  • Sept. 18: Auburn at Penn State (-9.5)
  • Sept. 25: Wisconsin (-0.5) vs. Notre Dame (in Chicago)
  • Oct. 2: Minnesota at Purdue (+1)
  • Oct. 9: Michigan at Nebraska (even)
  • Oct. 23: Ohio State at Indiana (+6)
  • Oct. 30: Iowa at Wisconsin (-8)
  • Nov. 13: Maryland at Michigan State (even)
  • Nov. 27: Maryland at Rutgers (+0.5)

The month of September features a total of 10 total non-conference games against top-35 Power Five teams, highlighted by the Oregon/Ohio State game in Columbus. Wisconsin, Iowa, Indiana and Penn State all also have notable non-conference games that will certainly impact the overall perception of the Big Ten, which will eventually dictate if the eventual champion makes the College Football Playoff.

Speaking of the Power Five, the next stop on this preseason mathematical journey is a tour of the SEC, ACC, Big 12 and the Pac-12. But, that is all for today. Until next time, enjoy, and Go Green!