The return of Yale students to campus and the beginning of spring semester classes can only mean one thing for Ivy League basketball fans: the return of Ancient Eight play. With a four-team tournament deciding the conference’s automatic bid to the NCAA Tournament for the first time this year, the path from the Ivy League to March Madness is up for grabs. As a project for the Yale Undergraduate Sports Analytics Group, I made a model that predicts the outcome of any NCAA Division I men’s basketball game and applied it to the Ivy League’s upcoming conference slate.
The underlying structure of the model is relatively simple. Using data collected from every college basketball game between Division I teams so far this season, the model can predict the score differential of any future game based on the two teams playing and the location of the game. Simply put, the model assigns a coefficient to each Division I team, which we call the “YUSAG coefficient.”
Taking the difference between any two teams’ coefficients gives the predicted scored differential between those teams if they played on a neutral court. A lot of prior research has examined home-court advantage in college basketball, and it is widely agreed upon that the home team has, on average, a three- to five-point advantage. Factoring this into my model, I spot the home team four points in every game.
While a prediction for score differential is nice, an expected win probability is much easier to understand. Using my model to predict the expected score differential of each game already played this season, I examined the relationship between win percentage and predicted point spread, allowing me to converting those point spreads into win probabilities. A point spread of zero corresponds with a 50 percent win probability, while each additional point by which a team is favored adds roughly 2.1 percentage points to that team’s win probability.
Next, I used the YUSAG coefficients to create a power ranking of all NCAA teams. Among Ivy League teams, Princeton leads our power rankings as the best team in the Ancient Eight, followed closely by Yale, Harvard then Columbia. Examining win probabilities for each upcoming Ivy League game allows me to predict Ivy League standings: Unsurprisingly, the predicted standings include the same top four teams, with Princeton slightly besting Yale for the top spot. On a weekend in which the Bulldogs were road underdogs in games at Penn and Princeton, Yale did well to secure one win. In fact, based on the win probabilities assigned by my model, Yale’s game at Princeton was the toughest the Elis will face in conference play.
Looking at the predicted win probabilities for each of Yale’s remaining games shows that despite last weekend’s setback at Princeton, the Bulldogs will be in good shape to qualify for the Ivy League Tournament when March rolls around. My model favors Yale in all but one of its remaining games, including all games at home in the friendly confines of John J. Lee Amphitheater. The lone contest which the Elis enter as underdogs will be their road contest with Harvard at the end of February.
This season, the Ivy League seems to have three tiers. At the top, Princeton, Yale and Harvard are near locks to make the playoff. In tier two, Columbia, Penn and Brown appear to be in a three-way race for the fourth and final playoff spot. The race seems more likely to come down to Columbia and Penn, although Brown is not going away after upsetting the Quakers on the road this past Saturday, a contest in which the Bears had just a 10 percent win probability according to my model. Penn suffered a massive blow with a home sweep at the hands of upsetters Yale and Brown, dropping the Quakers’ expected wins in the 14-game conference season to just 6.3, and giving Columbia the inside track to the No. 4 seed. Cornell and Dartmouth stand firmly at the bottom of the table, and barring a miracle have no real shot at making the Ivy League Tournament this year.
As lovers of the data side of sports, we in the Yale Undergraduate Sports Analytics Group are looking forward to analyzing this Ivy League season and making weekly predictions. This week, we’ll take Yale over Brown by 7.3 points, Columbia over Cornell by 8.7 points and Harvard over Dartmouth by 18.1 points.