Statistically Speaking: The Change-Up’s Ivy League Tournament predictions

Despite strong seasons from several of the Lions’ individual players, the team still has just a 0.2% chance of qualifying for the Ivy League Tournament, according to  The Change-Up’s  model. (Ben Goldsmith)

Despite strong seasons from several of the Lions’ individual players, the team still has just a 0.2% chance of qualifying for the Ivy League Tournament, according to The Change-Up’s model. (Ben Goldsmith)

Statistically Speaking is a weekly update on the men’s Ivy League Basketball standings—rooted in the numbers. This week, we’ve laid out the core concepts behind our model and in the future we’ll examine its changing predictions, accuracy, and hot takes.

If we imagine the rest of the men’s basketball season playing out in one million separate worlds, is there a world where Columbia qualifies for the Ivy League Tournament? That’s the question behind The Change-Up’s statistical strategy of forecasting this year’s Ivy season, and the short answer is: yes, but don’t count on it. Our probabilistic method involves simulating the current season thousands of times to predict which teams will finish where.

At the core of our model live our Elo ratings for Ivy teams. Elo ratings are a simple, informative way of measuring relative team strengths. The basics of an Elo rating system are as follows. We assume every team starts at some average ranking, and every time team A beats team B, team A gains as many points as team B loses. Underdogs gain more points for a win and lose fewer for a loss than favorites.

In sports with scores (unlike chess, where Elo was developed), it’s also typical to have a margin-of-victory multiplier so that bigger wins result in a larger jump in the winner’s ranking, all else equal.

With these Elo ratings, we can come up with win probabilities for individual games using a logistic function. For example, when Columbia—the weakest team in the league right now—heads to Penn—a middle-of-the-table team—on Friday, the Lions are expected to win just 22 percent of the time (accounting for home-court advantage). That’s something, but it hints at the fact that Columbia needs a good deal of luck to climb from eighth place to fourth and qualify before the end of the season.

Although Elo ratings have a few drawbacks (e.g., not adjusting for injuries), they give us a platform to develop season simulations. With Monte Carlo simulations, we can offer precise end-of-season estimates—instead of saying that Princeton has secured a tournament bid, we can say that the Tigers have a 90 percent chance of qualifying.

(Rachel Page)

(Rachel Page)

We’ll talk more about the exact accuracy of these predictions in later pieces, but let’s begin with the basic Monte Carlo simulation process. A single simulated season starts at the current date, accounts for the games already played, and simulates the remaining games.

For each game, a draw from a normal distribution decides the score, gives the appropriate team the win, and adjusts the two teams’ Elo ratings before moving forward.

More technically, the mean and variance for each normal distribution come from a segmented linear regression based on the past five years of Division I game data. By adjusting Elo ratings in the simulations, we can better capture the overall variance of a season by letting teams go on hot and cold streaks throughout the simulated season.

At the end of the simulation, the model looks at the table and settles any ties according to Ivy League Tournament tie-breaking rules. Finally, the model goes back to the start, repeats the process a million times more, and counts the fraction of times each team finished in each place.

After all that, we get our predictions: Penn, Yale, Harvard, and Princeton were most likely to qualify at the start of the season. Brown, Cornell, Dartmouth, and Columbia were the least likely to qualify. So far, the prediction’s been fairly accurate, with Yale, Harvard, and Princeton looking very likely to qualify. Penn and Cornell’s fight for the last spot has been the biggest surprise so far.

(Rachel Page)

(Rachel Page)

Although Penn and Cornell hope to keep their tournament dreams alive (Cornell currently holds two extra wins, but Penn faces an easier upcoming schedule), we still give a roughly 13-percent chance that either Brown or Dartmouth finds its way into the tournament. While that may not seem like much, it could be a final surprise in a season that has gone largely according to plan (or as our model predicted).

If Brown qualifies, it would be the team’s first bid in the tournament’s young history. For Penn, winning next weekend’s matchup against Cornell and securing a win over the visiting Lions are crucial.

The Lions have also yet to qualify for the tournament, but that dream is all but gone for this year. Columbia doesn’t have a zero-percent chance of making the tournament, but rather a 0.2 percent chance (about 2 in 1,000). That slim chance doesn’t rely on one exact outcome for the rest of the season, but it depends on Yale, Harvard, and Princeton continuing to sweep while Penn, Cornell, and Brown mostly tank. And, of course, Columbia would need to pick up wins in most (if not all) of its remaining games.

As the season wraps up over the next few weeks, we’ll keep you updated with individual game predictions before each weekend as well as updated season forecasts. The battle for fourth seed could continue to the very end.And for Lions fans, the hope is to stay alive in that battle for as long as possible.

The Change-Up’s Ivy League Basketball model was built by Leo Goldman and Sagar Lal.

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