Computer Rankings for NCAA D1 Basketball

Consolidating and Comparing Computer Rankings

December 2, 2019

The main purpose of this site is to provide alternative methods of combining multiple ordinal rankings to form a composite. The method is to apply ranked-ballot vote-counting techniques to the computer rankings published by Dr. Massey at https://www.masseyratings.com/cb/compare.htm. I also report rank correlations that measure how alike the ratings are when compared to other ratings.

Team Reports

The rankings used are only the computer-generated ones that rank all teams. Human polls and computer ratings that report fewer rankings are not included. The composites are

Borda
For each rating, consider the number of teams ranked worse than the given team the given team's borda count. Sum the team's borda count for each rating and assign ranks based upon the accumulated points. Borda is equivalent to the ranking by arithmetic mean of the ratings' ranks, and a variation of Borda is commonly used to form human poll composites.
Bucklin (Majority)
The Bucklin rank is the best rank for which more than half of the ratings rank the team better than or equal to the rank. When there is an odd number of ratings, it is the same as the artithmetic median. With an even number of ratings, it is the worst of the two that would be averaged to form the median.
Condorcet (Pairwise)
For each team pair (A,B) count the number of ratings that rank A better than B. If that is a majority of the ratings it is a pairwise win for A and a pairwise loss for B. Pairwise wins, losses and ties are reported.

The team comparison includes the geometric and harmonic means of the rankings. These give more weight to better rankings, with harmonic giving better than geometric giving better than arithmetic. It also lists all of the ranks for each team in best-to-worst order to make visible the best, worst, and median ranks.

Rating Comparisons

To show how similar (really dissimilar) ratings are I use the notion of distance between two rankings. This is the number of discordant pairs. If team A is ranked better than team B in rating X and worse in rating Y the pair is discordant for ratings X and Y. The report is the fraction of non-discordant pairs without the decimal point for brevity. Identical rankings would be reported as 10000.