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# Big Ten Basketball Mathematical Analysis, Part Three: The Big Ten Tournament

In the third and final installment of this mathematical preview of the Big Ten basketball season let’s dive into the seeding for the Big Ten Tournament and clarify just how important it is to secure a top-four seed.

In the first two installments of this Big Ten basketball preview, we have taken a close look at the Big Ten conference schedule and the results of a simulation of the Big Ten regular season. The results show that Michigan State has a schedule of average difficulty and about an 18 percent chance to win the Big Ten regular season title. Furthermore, Wisconsin seems to have the edge in the Big Ten regular season race, due to a combination of the fact that the Badgers are supposed to be pretty good and the fact that they have the easiest schedule in the entire conference.

However, the Big Ten also hands out banners and trophies to the team that wins the Big Ten postseason tournament. Do the Spartans have better odds to add this specific addition to the rafters of Breslin Center? Once again, it is possible to use the magic of mathematics to find out.

I reviewed the basic methodology in my previous installments. Very briefly, I use adjusted efficiency margin data from Kenpom.com, convert the projected point spreads for all Big Ten regular season games into win probabilities, and then perform a full season Monte Carlo simulation to generate odds.

In addition to tracking which team(s) finish in a at least a tie for first place in the regular season, I have also added the tiebreaker rules for seeding such that I can generate a complete set of odds for the Big Ten Tournament. As with the previous analyses in this study, this analysis is heavily reliant on the idea that Kenpom’s estimation of each teams strength is accurate in the preseason.

Table 1 below summarizes the results of this part of the simulation and shows the odds for each Big Ten team to earn each seed from No. 1 to No. 14 in the Big Ten Tournament.

As Table 1 shows, the most likely seed for each team generally parallels the preseason Kenpom rankings and it exactly matches the order of teams based on the regular season title odds presented in Part Two of this series. MSU is in second place on this list, behind Wisconsin, but the single outcome with the highest probability for the Spartans (shown in green) is actually for the MSU to claim the No. 1 seed.

A critical feature of the Big Ten Tournament is the number of byes that a team gets, which has a significant impact on a team’s odds to advance. In the current structure of the tournament, the top four seeds all receive a double bye and are immediately placed in the quarter finals. The teams seeded No. 5 through No. 10 receive a single bye and begin play on Thursday in the second round. The teams who finish the season as one of the bottom four seeds start in the first round on Wednesday. Table 2 below summarizes the odds for each team to finish in each of those three tiers.

Once again, Wisconsin has a clear advantage and has by far the best odds (72 percent) to receive one of the coveted double byes. The Spartans’ odds are essentially 50-50 to receive a single or double bye. Ohio State, Michigan, and Iowa all have very similar odds as MSU.

While seeding is important, the most important answer that we seek is which team will actually wind up cutting down the nets on Selection Sunday? Before this question can be answered, however, some assumptions need to be made regarding the actual seeds for each team.

One approach is to use the seed list shown above in Table 2. Once the seeds are set, it is straightforward to run a new simulation on the results of the Big Ten Tournament to generate the odds for each team to advance and eventually win the tournament. The results of this simulation are shown below in Table 3.

As expected the odds also mirror the odds for each team to win the regular season title. Wisconsin still has the best odds, at 21 percent, which is a significant drop from the Badgers’ odds to win the regular season title (38 percent). As for the Spartans, the odds to win the Big Ten Tournament (16 percent) are just slightly lower than the odds to win the regular season title (18 percent). It should be noted that a big reason for the drop in odds for the Badgers is related to the fact that more than one team can share the regular season title, while the Big Ten Tournament title is all or nothing.

However, the tournament seed order shown in Tables 1 through 3 is essentially an average and does not necessarily represent any single outcome. It is also instructive to look at a more specific scenario. There are a total of 140 games on the Big Ten schedule, each of which has two possible outcomes. Therefore, there are a total of 1.4 x 10^42 (two to the power of 140) different possible season outcomes.

Of all of those outcomes, there is a single one that has the highest overall probability. This scenario is the one where the projected favorite wins all 140 conference games. The odds of this specific scenario is also ridiculously small, but it remains the most likely single outcome. In this case, the seeds and odds for the Big Ten Tournament are summarized below in Table 4.

In this scenario, Michigan and Wisconsin tie for first place in Big Ten play with a record of 14-6 and the Wolverines win the tie-breaker to claim the top seed. MSU finishes with a final record of 13-7 and in a tie with Ohio State, Rutgers, and Illinois. MSU wins the tiebreaker and claims the No. 3 seed.

However, a comparison of Table 4 and Table 3 show that the odds to actually win the Big Ten Tournament do not change much for the contenders. Wisconsin, Michigan State, and Michigan essentially all have the same odds in both scenarios. But, the odds do change significantly for Rutgers (3.7 percent to 9.3 percent), Ohio State (16.4 percent to 11.6 percent), and Iowa (9.2 percent to 7.7 percent).

But, these difference can be understood by comparing the seeds that each teams were assigned in each scenario. In the scenario of Table 3, Ohio State was the No. 3 seed while Iowa was the No. 5 seed, and Rutgers was the No. 8 seed. Clearly the Buckeyes’ odds are boosted by the double bye, while Rutgers’ odds suffer by drawing No. 1 seed Wisconsin in the quarterfinals.

But, in the scenario of Table 4, the specific tiebreakers in play push Rutgers up to the No. 4 seed which more than doubles the Scarlet Knights’ odds to win the tournament. Meanwhile, Ohio State falls to No. 5 and their odds drop by five percentage points. As for Iowa, a change from the No. 5 seed to the No. 8 seed costs the Hawkeyes 1.5 percentage points.

This particular thought experiment inspired another. In order to better understand the role of seed in the Big Ten Tournament, it is possible to simulate the odds for a team of fixed quality to win the Big Ten Tournament by arbitrarily assigning that team to all possible seeds from No. 1 to No. 14 and rerunning the simulation keeping the seed order of the other 13 teams fixed. I performed this simulation for MSU using the scenario shown in Table 3 as a base case. The results of this experiment are shown in Figure 1.

This figure highlights the importance of securing a top four seed in the Big Ten Tournament. MSU’s odds to the win the tournament are virtually identical for No. 1 to No. 3 seed and only drop slightly for the No. 4 seed.

However, the odds drop by at least five percentage points (from roughly 16 percent to 10 percent) once MSU falls to the No. 5 seed. The odds for the No. 6 seed are similar, but there is yet another drop of two percentage points for seeds No. 7 to No. 10, which makes sense as these seeds would line up against against the No. 1 or No. 2 seeds in the quarterfinals. This is also consistent with the changes observed for Ohio State, Rutgers, and Iowa in the two scenarios discussed above.

The odds for MSU as an No. 11 seed do not change much, as MSU would still be heavily favored to beat No. 14 seed Nebraska in the first round, but as the No. 12 to No. 14 seed, the odds to win the whole tournament fall by another two percentage point to roughly six percent.

Recall that in this contrived scenario, MSU is still the 11th best team in the country so the odds in Figure 1 reflect only the effect of seed position. Clearly, there is a major advantage to getting a top six and especially a top four seed in the Big Ten Tournament.

This concludes this particular study of Big Ten basketball prior to tip-off on Wednesday night. Fortunately the tools that I displayed in this series are not static. I can and will continue to simulate the results of the Big Ten season as more game are played and more data is accumulated. As always I will be here to do the math so you don’t have to. Until next time, enjoy, and Go Green.