# What if the Ivy League had a Conference Tournament?

By Will Ezekowitz and Harrison Chase

Play in the most unique college basketball conference, the Ivy League, is about to start up again this Saturday. The Ivy League is the only conference in the country that doesn’t have a tournament to decide whom to grant its automatic NCAA tournament bid to, but rather relies upon regular season play to determine which team advances. But how would adding a tournament affect teams postseason prospects? As conference play is about to start up, we figured now would be as good a time as any to answer this question.

Last year we ran a Monte Carlo simulation to find not only the distribution of wins for every Ivy team but also each one’s chances of winning the division. We can do the same thing this year, and additionally we can simulate an end of season tournament to explore how Harvard’s chances of making March Madness would change if the Ivy League were to implement a conference tournament at the end of the regular season. This is not a pointless exercise – there have in fact been several talks in the past of changing this. To see how the probability of Harvard making March Madness changed, we ran two simulations. In the first, we simulated just the regular season in a method similar to what we did last year: using Ken Pomeroy’s rankings to get a win probability between each team, both home and away. After simulating every in conference game, the team with the most wins was the champion, and, if there were two or more teams with the same amount of wins, there was then a tiebreaker to decide the winner, who progressed to March Madness. In the second, we simulated the conference games, using those results to seed teams, and then simulated a single elimination tournament at a neutral site (the same set up every other conference has). The winner of that tournament then progressed to March Madness, and no other team did. While it is theoretically possible that an Ivy League team that didn’t win the conference could get an at large bid, it doesn’t seem that realistic.

Below is a plot of all eight Ivy league teams’ chances of making March Madness, with and without a conference tournament (we conducted 10,000 simulations both with and without a tournament).

As you can see, Harvard, being the best team in the conference by a good amount, desperately does not want a tournament, as there is far more variance in a tournament than in fourteen regular season games, and therefor they have a higher chance to lose. Their chance of going to March Madness falls from around 73% to just about 50%. Meanwhile pretty much every other team would benefit from a tournament, including the bottommost teams who see their chances jump from basically nothing up to 2%.

Of course, all of this is assuming that the KenPom rankings are a reflection of a team’s true strength. For example, even though KenPom estimates Harvard to have .7860 Pythagorean ranking they could really be a .85 team, or maybe even a .65 team. Considering this, we can look at how Harvard’s chances of making March Madness would be affected over a spectrum of their possible true team strengths. We can hold every other team’s strength constant but vary the ranking of Harvard from 0.0 to 1.0 and see what their chances then would be with and without a tournament. Doing this allows us to compare their chances of making March Madness across a spectrum of possible strengths. Below is a plot of Harvard’s chances of making March Madness across the spectrum of Harvard’s strengths, with the yellow bar representing what their current strength is.

From this we can see that whenever Harvard has a Pythagorean ranking of below 0.56 they would want a tournament, but when they are above that mark they would prefer it to exist as is, without a tournament. This makes sense – when they are no longer close to being the top team in their division, they would prefer a tournament as it has more variance in its winner. At their current ranking of 0.78 they stand to lose a lot – their chances decrease by nearly twenty five percent. And they would stand to lose the most if their ranking was 0.84, which is very close to what they were ranked during the preseason.

So, in conclusion, Harvard this year should be glad the Ivy League is structured as is. They have a far greater chance of playing in March Madness than other teams in league similar to theirs. For example, Green Bay in the Horizon League and Stephen F. Austin in the Southland Conference are similar to Harvard in terms of both KenPom ratings and conference strength. But due to the conference tournament that will likely determine the sole March Madness participant from the league, both teams have a much smaller chance of making the postseason than Harvard.

Long live the Ivy League.

KenPom ratings used were current as of Jan 2nd, 2015.