## The Details of Dominetrics

You don’t need an econ degree to understand the guiding principles of the Dominetrics doctrine. But it might help. Below is a detailed description of how the rankings are compiled and what they say, as of Sunday, about the teams that should be getting the NCAA Selection Committee’s attention.

Visit the Dominetrics website at http://www.beloit.edu/economics/dominetrics/.

1.     RPI:  The Benchmark Barometer against which all alternative rankings metrics must be compared

The NCAA computes a team’s RPI as a weighted average of three components:  (1) a team’s opponents’ winning percentage (this provides a team with the incentive to schedule tough opponents), (2) a team’s opponents’ opponents’ winning percentage (this checks whether a team’s opponents’ winning percentages are in turn achieved against quality foes), and (3) a team’s own adjusted winning percentage.  The weight given to winning percentage (1) is 0.5, and the weights attached to winning percentages (2) and (3) are 0.25 and 0.25.

Who chose these cardinal weights?  It was an unnamed employee or group of employees of the NCAA who came up with the weights of 0.5, 0.25, and 0.25, and it’s interesting to note that no person or persons have stepped forward to take credit.  Why 0.5, 0.25, and 0.25; why not 0.4, 0.3, and 0.3?  Why not any other three fractions that sum to 1?  These are good questions, and they underscore the point that 0.5, 0.25, and 0.25 are subjective reflections of the anonymous inventor(s) of the RPI.

2.     Dominetrics:  Replacing subjective cardinal weights with a more objective ordinal methodology

In their February 2011 Journal of Sports Economics article, Bob Elder and Scott Beaulier adapt to American college basketball a methodology that emerges from recent scholarship on producing rankings when there are multiple dimensions of performance.  In 2006, Laurens Cherchye of the University of Leuven in Belgium and Frederic Vermeulen of Tilburg University in The Netherlands used a “net dominance metric” (which in 2011 Elder and Beaulier contracted into “dominetric”) to rank cyclists who have participated in Tours de France on the basis of their results in six categories of bike-racing achievement.  Earlier, Knut Wittkowski of Rockefeller University used a “u-statistic” in 2003 to rank the performance of countries in the Olympics as a function of their more important gold medal totals, less important silver medal totals, and still lesser important bronze medal totals.  Whether based on three importance-ordered categories of Olympic merit, six importance-ordered categories of Tour de France achievement, or four importance-ordered NCAA basketball winning percentages, the u-statistic, net dominance metric, and dominetric each measure the quantity of rivals that you dominate minus the quantity of rivals that dominate you.

To employ this ordinal methodology, Elder and Beaulier first call attention to the importance-ordering implied by the cardinal weights from the RPI (1st:  opponents’ winning percentage (call this W1); 2nd:  own road and neutral winning percentage (call this W2); 3rd: opponents’ opponents winning percentage (call this W3); 4th:  own home winning percentage (call this W4)).  Given this importance-ordering, Team A dominates Team B if all four of the following criteria are met:

(1)   Team A’s W1 ³ Team B’s W1,

(2)   Team A’s W1 + W2 ³ Team B’s W1 and W2,

(3)   Team A’s W1 + W2 + W3 ³ Team B’s W1 + W2 + W3, and

(4)   Team A’s W1 + W2 + W3 + W4 ³ Team B’s W1 + W2 + W3 + W4.

Only the four raw winning percentages matter in these criteria, and cardinal weights like 0.5, 0.25, 1.4, 1, and 0.6 are no longer part of the calculations.  Thus, a crucial layer of subjectivity is removed.  The importance ordering has been preserved, with the most important winning percentage W1 (opponents’ winning percentage) playing a role in all four criteria for domination, the second most important winning percentage W2 playing a role in three of the four criteria, etc.

Given these criteria for determining who dominates whom, a team’s dominetric equals the quantity of teams that a team dominates minus the quantity of teams that dominate that team.  The ensuing rankings that run from the highest dominetric to the lowest dominetric among all 344 Men’s Division 1 NCAA basketball teams make their case for an objectivity-maximizing approach to selecting the field for the post-season tournament.  To see these rankings, go to http://www.beloit.edu/economics/dominetrics/basketball/.

Note that the un-weighted use of the four raw winning percentages in the ordinal Dominetrics methodology recommends lesser representation from the Big 6 power conferences and greater representation from some of the so-called “mid-major” conferences.  It may not always turn out this way in future years.