2023 Big Ten Basketball Mathematical Preview

The 2023-24 college basketball season kicked off just under a month ago and the action across the country is heating up. Big Ten conference action officially kicked off this weekend and a total of 12 conference games will be played in the month of December.

At the beginning of the season, the various prognosticators and pollsters had an idea of which teams would challenge for the Big Ten title and other post season glory. But we now have a month of actual data about the relative strength of each team. It is time to put that data to work.

Throughout the Michigan State football season, I provided bi-weekly updates on the odds of various season outcomes. I utilized my own power rankings and a set of simulation and other analytical tools to generate these odds. My process for college basketball is very similar.

The major difference is that I prefer to use efficiency metrics, specifically those tabulated by Ken Pomeroy ("Kenpom") to estimate point spreads and odds. These data correlate well to point spreads and point spreads correlate to actual game results. There is no reason for me to recreate the wheel.

I have recently compiled data from the non-conference and performed my first simulation of the 2023-24 Big Ten season. The results of the simulation and other calculations can tell us a lot about how the Big Ten season will progress. Today, I will share what I found.

How Good is the Competition?

It may seem obvious, but the single most important factor in how the Big Ten season will shake out is the relative strength of each team. Good teams tend to win more games than not-so-good teams. The best place to start in this analysis is to review the current Kenpom ranking of all 14 Big Ten teams, which I have summarized below in Figure 1.

Figure 1: Current and preseason Kenpom adjusted efficiency margins for all 14 Big Ten teams. Each bar is labeled with the Kenpom ranking as of Nov. 30.

Figure 1 includes both the current Kenpom efficiencies and rankings as of Nov. 30 as well as the rankings published by Kenpom on Oct. 15, prior to the season. Note that I conducted this analysis prior to the start of the Big Ten season, so it does not reflect Purdue's upset loss at Northwestern or the other games that occurred over the weekend.

Purdue is considered to be head-and-shoulders better than the rest of the Big Ten field, both in the preseason, and even more so on Nov. 30. After the Boilermakers, Michigan State, despite a 4-3 record, grades out as the second-best team with a slightly lower efficiency than expected back in October.

There are currently three other teams in the same general tier as the Spartans. Ohio State, Wisconsin, and Illinois are all ranked in the 20s in Kenpom efficiency margin. Iowa and Nebraska are both ranked around No. 40 nationally and make up the third Big Ten tier, rounding out the top half of the conference.

The fourth Big Ten tier includes Michigan, Rutgers, Northwestern, and Maryland which are all ranked in the 50s nationally. After that there is a steady decline in the quality of the last three teams: No. 72 Indiana, No. 96 Penn State, and No. 119 Minnesota.

Also note that there are a few teams which (so far) are notably better or worse than predicted in the preseason. Ohio State, Iowa, and Nebraska are trending up. In contrast, Northwestern, Rutgers, and Penn State are trending down.

Strength of Schedule

In an ideal world, the Big Ten regular season would be 26 games such that each team could face every other team twice, once on the road and once at home. Instead, there are only 20 conference games meaning each Big Ten team will play seven opponents twice, three opponents at home only, and three opponents on the road only.  

This creates an imbalance in the schedule which does benefit some teams, and which hurts others. But how big is this effect and which teams benefit or suffer?

Table 1 below some a matrix that summarizes the full Big Ten schedule.

Table 1: Big Ten composite schedule showing each team's double-play opponents (in white), home only opponents (green for the team in question's row) and road only (shaded yellow)

The white cells in the matrix indicate teams that play each other twice. The green shaded cells represent the situation where there is only one regular season contest and the team in the row is at home. The yellow shaded cells represent the situation where the team in the row is on the road.

For example, Michigan State will play Ohio State, Rutgers, and Iowa at home only. The Spartans will face Purdue, Nebraska, and Indiana on the road only. All other Big Ten teams will face Michigan State twice.

A glance at Table 1 gives an initial impression of the relative difficulty of each schedule. If a team's row (or column) has a lot of "2s" on the left-hand side (or top) and more "1s" on the right/bottom, this indicates a tougher schedule and vice versa. 

Another slightly more quantitative indication is shown in the bottom row of the table. Here I tabulated the average efficiency margin of the opponents that each team plays only once. The higher this number, in general, the easier the schedule. This implies that the team plays more of the good teams just once and the weaker teams twice.

Fortunately, I have a more mathematically rigorous method to calculate strength of schedule. I use the concept of expected value and run a sort of experiment where a hypothetical top-25-quality reference team plays every Big Ten schedule. The question that I ask is "how many games would this reference team be expected to win?" Mathematically this is equal to the sum of the odds for the reference team to which each game.

Figure 2 below shows the results of this calculation as of Nov. 1.

Figure 2: Big Ten overall strengths of schedule prior to the start of Big Ten play on Nov. 30. The y-axis shows win percentage and the labels show the expected number of wins.

As Figure 2 shows, Michigan State grades out with the second easiest schedule in the Big Ten behind only Ohio State. It is also notable that Illinois and Wisconsin (who are currently ranked similarly to the Spartans by Kenpom) have relatively difficult schedules. The hardest schedule in the conference currently belongs to the Michigan Wolverines.

Figure 2 also shows the raw expected win values for each team's schedule as the label on each bar. This provides a way to quantify the advantage of having an easy or hard schedule. The Spartans' schedule is worth roughly half a game relative to the average Big Ten schedule and over a full game compared to the hardest Big Ten schedule. 

Another way to think about this data is that this year the schedule for Michigan State is basically the equivalent of starting conference play a full game ahead of Michigan in the standings. 

The final point about strength of schedule is that the raw calculation in Figure 2 gives Purdue the third easiest schedule in the conference. However, Purdue has the built-in advantage of not having to play the best team in the conference: themselves.

I have a method that attempt to correct for this factor. Figure 3 below shows the results of this calculation.

Figure 3: Big Ten overall strengths of schedule prior to the start of Big Ten play on Nov. 30 after correcting for a team not playing themselves. The y-axis shows win percentage and the labels show the expected number of wins.

In this case, Michigan State and Ohio State still grade out with easy schedules. Illinois, Wisconsin, and Michigan all have difficult schedules, and Purdue has a remarkably average schedule. That said, it is a fact that Purdue doesn't have to play Purdue. It is a real advantage. For this reason, the values shown in Figure 3 are more useful as a simple reference.

Michigan State Schedule Details

The results of Figure 2 indicate that Michigan State has one of the easiest schedules in the conference. As a next step, Let's take a closer look at the full schedule to get a flavor on the potential ebb and flow of Big Ten conference play.

Figure 4 below visualizes the schedule by showing the projected point spreads and victory odds for all 20 conference games.

Figure 4: Odds for Michigan State to win each Big Ten game, based on Kenpom efficiency margins.

The Spartans are projected to be the favorite in 17 of the 20 total Big Ten games. Furthermore, Michigan State projects to be at least a 5.5-point favorite (70% odds to win or better) in nine of the 20 Big Ten games and at least a 2.5-point favorite (60% odds to win or better) in 15 of the 20 Big Ten games.

The only games where Michigan State is currently projected to be an underdog are the road games at Illinois (-1.2), Wisconsin (-1.8), and Purdue (-9.7). In general, there is also good spacing between the games. There are six total instances of just two days rest between games, but in all cases at least one of the two games is at home. 

The worst travel sequence is playing back-to-back games at Northwestern and at Illinois in early January, but those games are four days apart. I don't see any clear "scheduling loss" on the Big Ten docket.

As for the ebb and flow of the season, the start to Big Ten season is deceptively tricky. The December games against Wisconsin and at Nebraska currently grade out as the sixth and fourth toughest on the 20-game schedule. Soon after New Year's the aforementioned road games at Northwestern and at Illinois are also both in the top eight of difficulty. 

The current odds suggest that Michigan State is expected to win only three of the first five Big Ten games. If the Spartans can get off to a better start than 3-2, it will be a very good sign for the rest of the season. If Michigan State is just 3-2 on January 12, it will not be the end of the world. That is the expectation with the assumption that the Spartans are the second-best team in the conference.

Starting with a home game against Rutgers in mid-January, the middle 11 games on the schedule are not as difficult. The Spartans will face tough road games at Wisconsin and at Michigan in that stretch, but Michigan State should be able to rack up a solid number of wins. The math suggests a 7-4 or 8-3 record in that section of the schedule is expected.

As late February approaches, the Spartans should have 10 or 11 conference wins. In the home stretch, Michigan State will face Ohio State at home followed by a road game at Purdue. The Spartans need to at least get one win in that pair. The final two games of the season against Northwestern and at Indiana are not as challenging.

If the odds for Michigan State to win each conference game are summed, the result is an expected value of 12.97. In other words, the Spartans' most likely final conference record is 13-7.

Overall Big Ten Odds

So far, we have explored the relative strength of each Big Ten team and the strengths of each team's schedule. Now it is time to put the pieces together and forecast how the entire season will play out.

Using Kenpom efficiency margins data, it is possible to estimate the point spread and therefore win probabilities for all 140 Big Ten conference games. With this knowledge, it is possible to run a Monte Carlo simulation on the entire season. This is essentially a gigantic coin flip experiment with a weighted coin representing all 140 games. 

I set the simulation to test out 500,000 full Big Ten seasons to determine the odds for each team to win any number of games and to win the conference. I can also extract odds for eventual Big Ten Tournament seeding and even the outcome of the tournament itself. 

I also take the additional step of modifying the simulation to add a historically accurate amount of variance in the quality of each team. The current Kenpom efficiency margins for each team are not necessarily an accurate measure of each team's true strength. As we get closer to Selection Sunday, the variance decreases. I account for this variance. To my knowledge, this aspect of my simulation makes it state-of-the-art.

Without further ado, Table 2 below shows the initial set of results from this simulation. Specifically, it shows the odds that each Big Ten team will finish with any number of total conference wins, from zero to 20.

Table 2: Updated Big Ten expected wins and win distribution matrix as of Nov. 30, 2023

As expected, the expected win totals largely mirror the current Kenpom efficiency data. Purdue has the highest expected win total at 16.55. Michigan State and Ohio State are neck-and-neck for second place with an expected win total just under 13. 

Wisconsin and Illinois are similarly ranked, but the Badgers and Illinois are about a game behind the Spartans and the Buckeyes due to harder schedules. Iowa and Nebraska are a game further back with expected win totals of 10.6 and 10.2, respectively.

In the bottom half of the conference, Maryland, Northwestern, Michigan, and Rutgers are all expected to win just under nine games. Then comes Indiana (7.5 wins), Penn State (6.5 wins) and Minnesota (5.4 wins).

But as the table indicates, there is a tremendous amount of uncertainty in these numbers. Figure 1 below charts the win distribution for Michigan State using the data from Table 2.

Figure 5: Regular season Big Ten win distribution for Michigan State as of Nov. 30, 2023.

This data reveals that Michigan State has a 29% chance to win at least 15 games, a 39% chance to win between 12 and 14 games, and a 32% chance to win 11 or fewer Big Ten regular season games.

The odds to win or share the Big Ten regular season title are shown below in Table 3.

Table 3: Odds to win or share the Big Ten regular season title and the win distributions for those winning teams as of Nov. 30, 2023.

Here the table shows the odds for each team to win or share the title along with the number of wins needed to finish in first place.

As expected, Purdue leads the way with just under a 70% chance. In the scenarios where Purdue at least shares the Big Ten title, a record of 18-2 is most likely (at least it was before the Boilermakers lost at Northwestern). 

Ohio State and Michigan State both have just under a 12% chance to win or share the title. Wisconsin and Illinois both have odds between 6% and 8%. Iowa and Nebraska's odds are 3-4%. The teams in the bottom half of the conference have championship odds of 1% or less. Poor Minnesota wins the title in about 1-in-3,000 simulations.

Interestingly, the values at the bottom of Table 3 suggest that there is a 46% chance that at least 18 wins will be needed to claim a share of the Big Ten regular season title.  There is a 72% chance that at least 17 wins will be needed and a 90% chance that at least 16 wins will be needed.

Other data that I extract from the simulation tells me that in 84% of all simulations, only one team wins the regular season crown. There is a two-team tie 14% of the time and a three-way tie in only 2% of the simulations.

As for Big Ten Tournament seeding, Table 4 below shows the odds for each team to receive each seed.

Table 4: Big Ten Tournament seeding odds as of Nov. 30, 2023. 

At this point in the season, this data mirrors the expected win data very closely. Michigan State current projects as the No. 2 seed in the Big Ten Tournament.

Table 5 breaks down the seed data based on which day each team will start tournament play.

Table 5: Odds for each Big Ten team to receive a double-bye, a single bye, or no bye in the 2024 Big Ten Tournament

Right now, Michigan State has a 56% chance to receive a double bye and a 40% chance to start the tournament on Thursday with just a single bye.

Finally, Table 6 below shows the current odds for each team to win the Big Ten tournament.

Table 5: Odds for each Big Ten team to advance past each round of the Big Ten Tournament, as of Nov. 30, 2023

In general, the odds to win the Big Ten Tournament will mirror Kenpom efficiency margins. Purdue's odds of repeating as Tournament Champions are at 46%. Michigan State, Ohio State, and Wisconsin have odds between 9% and 10.5%. 

Note that Michigan and Rutgers have slightly higher tournament odds than their projected seeds indicate because the Wolverines and Scarlet Knights have (by far) the two toughest schedules in the conference. This means that there is a chance both teams will be slightly under-seeded in the conference tournament.

Thus ends the lesson for today. Let the Big Ten season begin!