Since I am ranking and writing a bit more, we will try to do the Field of 68 this season. This is more to see blossom over the season as more games get into the model - and more good teams play each other. College basketball teams end up playing somewhere between 50 and 65 percent of their games in conference compared to more like 70% with college football - so there are just more games to use for a pairwise model.
Of course the season is only 2 weeks old - so while there is enough data for a Bradley-Terry sort of model to converge, the error terms are pretty wild. At the same time, who cares? It is interesting to see how the season evolves. The teams that are high now here will drop off pretty quickly (I'm looking at you George Mason) - and losses to good teams are actually helpful.
The Method
Basically this is the same as what I am doing for football. The components.
Bradley-Terry model using a small margin of victory component. This is more or less a logistic regression. A team gets 1 point for having a better rating than a competitor.
Head to Head record. A team gets as many points as net wins over a competitor. (no negative points for a team with a losing record)
Record vs Common Opponents. A pairwin here is worth 1 point.
Regular season leader. During the season we will use the highest rated team with the fewest conference losses. A pairwin here is worth 0.5 points. Based on how the committee seeded teams last year, 0.5 points fit the data better than 0 or 1.
For each component, a team is compared to the other 365 teams (all non D1 are treated as a single opponent) and points are awarded. Whichever head to head has more points counts a pairwin.
For example: Team A has a better rating than Team B, but they had no head to head, Team B did better against common opponents, and Team A was the regular season champ of its conference. In this example Team A has 1.5 points (1 for rating, 0.5 for reg season champ). Team B has 1 point for common record. Team A would get the overall pairwin.
Half pairwins are used for ties. The team with the most pairwins is the #1 overall team. If there is a tie in pairwins, the Bradley-Terry rating is used as a tiebreaker.
The Field of 68
Through the games of 11/14/2024. With so few games, this is genuinely hilarious. The SoS is based on the perspective of a .500 team (using the Bradley-Terry rankings as weights)
The Bubble
The first 4 teams are in the field with byes to the Round of 64. Teams 5-8 are the play-in teams. The others are out in order. As you can see, the model is pretty dumb right now, but it is fun to watch it get smarter.
Comments