The 2024-2025 college basketball season ended just over a month ago, but fans are already looking ahead to next year. Currently, most of the focus is on the transfer portal as teams at all levels and in all parts of the country attempt to (re)build their rosters.

But there was another recent announcement that will have an impact of the 2025-2026 Big Ten men's basketball season. The conference provided the first look at the conference schedule for each team on April 29. This includes the seven opponents that Michigan State will face only at home, the seven opponents the Spartans will only face on the road, and the three opponents Michigan State will face twice (both home and away).

The 2025-2026 season will mark just the second year of the 18-team, 20-game Big Ten conference schedule. Based on my research, this is the eighth different scheduling pattern used by Big Ten basketball since 1950.

Over the years, one of my fascinations in the realm of sports is study of strength of schedule. I strive to understand the impact that the schedule has on the results of the season. Can this impact be quantified? If it can, is the new schedule in the super-sized Big Ten more or less fair than past configurations? What can we say at this point about the relative strength of Michigan State's 2025-2026 schedule?

Today we will explore the answers to all of these questions.

There are several ways to potentially quantify the strength of any given sports schedule. The method that I use boils down to estimating the expected number of wins for a hypothetical average team if it were to play the schedule of every team in question.

The results of this calculation are a fractional number of expected wins, which can also be converted into an expected win percentage by just dividing by the total number of games.

In order to make this calculation, it is necessary to have a method to assign a win probability to any arbitrary matchup.

In college football, I have developed my own power ranking system, which can be used for this purpose. For college basketball, I use tempo-adjusted efficiency data such as the adjusted efficiency margins tabulated by Ken Pomeroy.

The goal of this analysis is to understand how different schedule configurations impact variations in strength of schedule. In an ideal world, each team would play an identical schedule and there would be no variation.

In Big Ten basketball, each team could play every other team conference team both at home and away. In the 10-team Big Ten between 1975 and 1989, the 18-game conference achieved exactly this goal of a full round-robin schedule.

But even in this situation the schedules are not perfectly equal because each team cannot play itself. This is an important factor that we will return to later.

As the conference expanded to 11, then 14, and currently to 18 teams, it became impractical to play a full round-robin schedule. The current Big Ten would have to play a 34-game schedule to accomplish this goal. As a result, each conference expansion since 1990 has required a different blend on single-play and double-play (both home and away) opponent.

In order to quantify the effect of conference size and schedule structure on strength of schedule fairness, I conducted a series of simulations. I generated a set of 50,000 random schedules for all possible schedule configurations for a 10-, 11-, 14- and 18-team Big Ten.

I sampled every reasonable number of total games assuming each team would play an equal number of home and away games and that each team would face each other conference foe at least once.

For example, with the current 18-team Big Ten, the smallest number of games with these assumptions is 18. This schedule involves each playing 16 opponents once (either at home or away) and just one team twice (both at home and away).

There are then eight other possible schedule configurations where the number of single-play opponents shrinks and the number of double-play opponents increases up to the full round-robin, 34-game schedule mentioned above.

In total, I simulated 33 different configurations. I used the final Kenpom efficiency margins for the 2024-2025 season for all 18 Big Ten teams to generate the odds for each theoretical matchup.

The key output from the simulation is the variation is schedule strength for each configuration as measured by the standard deviation. If the variance is high, that means that it is more likely for some teams to draw a particularly difficult schedule and for other teams to draw a particularly easy schedule. The smaller the standard deviation, the inherently more fair a given schedule configuration is likely to be.

Several conclusions can be drawn from the large data set resulting from the the strength of schedule simulations. Figure 1 below summarizes the most important result in terms of understanding the inherent fairness and variance of different schedule configurations.

The y-axis in Figure 1 represents the standard deviation of schedule strength (in terms of win percentage) for the 50,000 simulated schedules in this study. The higher the standard deviation, the more likely a team many draw an especially easy or hard schedule.

Each data point represents a different schedule configuration (i.e., total number of conference teams and total number of conference games). The data is organized into series based on the total number of conference.

The x-axis is organized based on the percentage of games on each schedule where the opponent is played only once. Therefore, the far left of the figure represents a schedule where each team plays every conference opponent twice (i.e. a full round-robin). The number of games on the schedule for each series decreases from left to right. The data points on the far right represent schedules where a teams plays each conference opponent only once.

Note that if we constrain the analysis only to schedules where there is an equal number of home and away games, it is only possible to have a 100% single play schedule if there is an odd number of teams in the conference. For this reason, only the 11-team series has data that goes all the way to the right side of the figure.

The larger data points in the figure represent actual schedule configurations that have been used at some point since 1950 as the Big Ten has grown from 10 to 18 teams.

One point to glean from Figure 1 is that adding more teams to a conference generally decreases the variance in strength of schedule. An explanation for this effect is found on the left side of Figure 1 in the set of simulations where x = 0 (the full round-robin schedules).

In these configurations, the only variance in schedule strength is due to the effect of a team not playing itself. These data also quantify the impact of this effect (a standard deviation of 0.009 to 0.016 win percentage). As more teams are added to a conference, this effect is diluted.

The second key point from Figure 2 is the shape of the curves. The primary benefit of plotting the data relative to the fraction of single-play games is that the shape of each series collapses into a single pattern. This reveals an underlying fact that is independent of the size of the conference.

The possible schedule variance is maximized in the configuration where there is an equal number of single-play and double play opponents (i.e. x = 0.5).

It makes sense that the full round-robin configuration (x = 0) would have the lowest variance. Figure 1 confirms that this is true for all conference sizes. It is less intuitive that the variance also approaches a minimum in the configuration where a team only plays each opponent only once. The simulation of a the 11-team conference configurations confirms that this is true.

Most sports fans tend to focus on the details of the home versus the away portions of the schedule when judging relative difficulty. For example, avoiding road game at Purdue and Wisconsin (as Michigan State did in 2024-2025) is viewed as an advantage.

However, if the set of single-play road opponents are slightly easier than average, this also means that the set of single-play home games are slightly harder that average. While there might be a small psychological advantage to playing certain teams at home, this mathematical analysis suggests that the odds all cancel out.

As a practical example, based on the data from last year, the hypothetical reference team had a 31% chance to beat Purdue on the road and a 70% chance to beat Penn State at home. The expected win total for the reference team for this pair of games is 1.01.

If the situation were reversed, the reference team would have a 44% chance to beat Purdue at home, but only a 58% chance to beat Penn State on the road. The expected win total is almost identical at 1.02. The effects cancel.

What is much more important in the current Big Ten schedule (and by extension, any schedule with a combination of double- and single-play opponents) is which teams are on the schedule twice. Playing a weak or strong team twice is much more important that the location of the single-play games.

For Michigan State last year, it was not so important that the Spartans played Wisconsin only in East Lansing. Home-court advantage in college basketball is only worth about 3.0-to-3.5 points. What was important is that Michigan State got to play Minnesota twice instead of a team like Wisconsin or Ohio State. This advantage is worth about seven points with no offsetting factor.

With these facts in mind, Figure 1 reveals which past Big Ten schedule configurations have been more or less fair.

On a win percentage basis, the original 14-game schedule for the traditional 10 Big Ten schools used from 1950 to 1974 was the most prone to schedule imbalance of any configuration in modern conference history. When the conference moved to a full round-robin, 18-game schedule in 1975, the schedule variance decreased significantly to a level lower than at almost any point in history.

When Penn State joined the Big Ten in 1990, the conference kept an 18-game schedule with each team now having a pair of single-play opponents. The schedule variance increase slightly. Oddly, the Big Ten contracted the conference schedule down to 16 games from 1998 to 2007, which further increased the schedule variance. The Big Ten reverted to the 18-game schedule in 2008.

The addition of Nebraska to the conference in 2011 caused a very slight increase in variance, and the further addition of Maryland and Rutgers in 2014 bumped the variance up even further. In 2018, the conference adopted a 20-game conference schedule, which decreased the win percentage variance down a value similar to what it was in the early 1990s.

When the four West Coast teams (Oregon, USC, UCLA and Washington) were added to the Big Ten last year, for the first time in conference history each team had more single-play opponents than double-play opponents. The data point appears on the right side of Figure 1.

But the combination of the large number of team and the proximity of the data point to the right side of the graph results in the fact that the current 18-team and 20-game schedule configuration has the lowest variance relative to win percentage of any Big Ten schedule in modern history. Conference expansion has not resulted a more schedule imbalance.

While looking at the data related to win percentage helps us to understand some of the key mathematical aspects of schedule strength analysis, it's not the best metric to compare the practical variance of different schedule configurations.

Basketball is a sport where (like most) individual games are won or lost. We practically measure a team's performance using games and not percentages. Figure 2 shows the same data displayed in Figure 1, but the y-axis has been converted from win percentage to games.