Choosing
We will look at determining who should receive at-large bids for the NCAA mens tournament, and the seeding for the tournament. Whilst currently determined by a committee, opinions are informed by various statistics of a team's performance (e.g. record against top-50/top-100 teams) -- though it is unclear how informative or interpretable such statistics are.
Statistical models for ranking basketball teams have been introduced previously. A standard approach to ranking basketball teams (Harville 2003) uses information on winning margins in games, which has the disadvantage of basing rankings on net point difference rather than matches won/loss. Analysis of win/loss records (e.g. using logistic regression) results in highly variable estimates of the relative strengths of different teams.
We propose a hybrid method for ranking teams; together with how to produce more informative measures of a team's performance that can be used to inform decisions on who should receive at-large bids for the competition. Analysis of this year's data suggest that one team in particular is unfortunate not to have been selected. The analysis also gives insight into how close other teams (e.g. South Carolina) were to making the field.