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Division III PairWise Rankings explanation

What Are PairWise Rankings?

The D-III East Region and West Region PairWise Rankings (PWR) are a statistical tool designed to approximate the process by which the NCAA selection committee decides which at-large teams are invited to the NCAA men’s and women’s Division III tournaments. While the PWR uses the same criteria as the selection committee, the NCAA does not specify how each is weighted, leaving the committee some leeway in its application of those criteria (see “NCAA Selection Process and PWR Compared” at the bottom of this page.)

The selection process compares the results of teams only within region. However, in addition to the regional PWR comparisons, for both men and women a combined PWR is included to show how the teams would be ranked if there were a combined national ranking.

For men, in the East Region, only games between Division III teams in the ECAC East, ECAC Northeast, ECAC West, NESCAC and SUNYAC are considered. In the West, only games between Division III teams in the MCHA, MIAC and NCHA are considered. Games against the seven Division II teams participating in the eight predominately D-III conferences are not included, nor are any games against Division I teams. Exhibition games against non-NCAA teams, including Canadian colleges and universities, the U.S. National Development Team, and club programs are not included.

For women, in the East Region, only games between Division III teams in the ECAC D-III East, ECAC D-III West, and NESCAC are considered. In the West, only games between Division III teams in the MIAC and NCHA are considered. Games against the Division II teams participating in the predominately D-III conferences are not included, nor are any games against Division I teams. Exhibition games against non-NCAA teams, including Canadian colleges and universities, and club programs are not included.

The PWR method compares every team which owns a .500 or better overall record (a “team under consideration,” or TUC) with every other such team, with the winner of each comparison earning one PWR point. After all possible comparisons are made, the points are totaled up and rankings listed accordingly.

For instance, if there are 20 TUCs, the greatest number of PWR points any one team could earn would be 19, by winning the comparison with each of the other 19 teams. Meanwhile, a team which lost all of its comparisons would have no PWR points.

The PWR compares only those teams at or above .500, judging them by
five primary criteria: winning percentage, Quality of Wins Index, head-to-head record, record against common opponents, and record against teams ranked in the current weekly Division III Men’s and Women’s NCAA Rankings. (In past years, once a team had been ranked by the NCAA, it remained considered ranked for the purpose of calculating the record against ranked teams, even if it dropped from subsequent rankings. Starting with the 2005-2006 season, only ranked teams at the time of ranking are included.)

The Quality of Wins Index (formerly called the Strength of Schedule Index), which is used by the NCAA across the board in Division III, assigns points to a team for wins, losses, and ties, based on the opponent’s record and whether the game is played at home, on the road, or at a neutral site. Here is the table used by the NCAA to assign points:

Win on the road versus a team at or above .66715 points
Win at home versus a team at or above .66714 points
Win on the road versus a team at or above .500, but below .66713 points
Win at home versus a team at or above .500, but below .66712 points
Win on the road versus a team at or above .333, but below .50011 points
Win at home versus a team at or above .333, but below .50010 points
Win on the road versus a team below .3339 points
Win at home versus a team below .3338 points
Loss on the road versus a team at or above .6677 points
Loss at home versus a team at or above .6676 points
Loss on the road versus a team at or above .500, but below .6675 points
Loss at home versus a team at or above .500, but below .6674 points
Loss on the road versus a team at or above .333, but below .5003 points
Loss at home versus a team at or above .333, but below .5002 points
Loss on the road versus a team below .3331 point
Loss at home versus a team below .3330 points

Points for tied contests are calculated by taking the points which would have been awarded with a win, adding the points which would have been awarded with a loss and dividing by two.

The Quality of Wins Index is calculated by adding the total number of points and dividing by the number of games.

A neutral game is defined as being in neither team’s locale and, as such, is awarded as if it were an away game.

The Quality of Wins Index is calculated for ratings at the time of the ranking calls and using final results for selection purposes.

Here’s a hypothetical comparison between two teams which demonstrates how the PWR is applied:

Head to Head Data
WIN -- Winning Percentage
QOW -- Quality of Wins Index
H2H -- Head to Head
COP -- Record vs Common Opponents
RNK -- Record vs Ranked Teams

  Amherst vs Elmira
WIN   0.5000 0      0.5238 1
QOW   7.6000 0      7.6190 1
H2H   1- 0- 0 1     0- 1- 0 0
COP   0- 3- 0 0     0- 1- 2 1
RNK   2- 6- 2 1     0- 5- 0 0
============================================
PTS       2          3
============================================
PWR       0          1

Elmira has the higher winning percentage, and a higher Quality of Wins Index. Amherst won the game the two teams played. Elmira has a better record against common opponents, and Amherst has a better record against NCAA ranked teams. Therefore, Elmira wins this comparison by the score of 3-2, and gets one PWR point. Notice that the final score of the comparison itself doesn’t matter Elmira only gets one PWR point no matter the score of the comparison.

NCAA Selection Process and PWR Compared

The NCAA Division III men’s and women’s ice hockey championship manuals state that at-large teams shall be selected by winning percentage, Quality of Wins Index, head-to-head record, record against common opponents, and record against ranked teams, but not necessarily in that order. While the PWR weighs each of the five selection criteria equally, the NCAA championship manual does not specify any weighting for each of the criteria. Therefore, the selection committee may exercise the authority to weigh each of the selection criteria in as it sees appropriate during any given season’s selection process.

However, the individual comparisons used to calculate the PWR are identical to those used by the selection committee, regardless of how they opt to apply them.

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