Ranking Ratings

© Copyright 2007,2008 Paul Kislanko

12 December 2007

Summarizing Summaries

The main purpose of this site is to study "the science" of rating sports teams, especially college sports, where the schedules are highly unbalanced. This is the definition of a metric I use to compare rating systems, the Weighted Retrodictive Ranking Violation statistic.

Recall that a retrodictive ranking violation for rating R occurs when after the game has been played the winner has a worse rank than the loser. The Weighted RRV is larger depending upon how highly the rating has ranked the losing team and by how many scores the worse-ranked team won by:
Violation Weightgame(R) = ⌈ (WS - LS)÷3 ⌉ × (WR - LR)
LR
⌈ x ⌉ is the least integer ≥ x
(this is the MOV expressed as # of possessions behind the losing team was)
WS = Winner's Score
LS = Loser's Score
WR = Winner's Rank according to rating R
(note - in these games will be > LR)
LR = Loser's Rank according to rating R
(that of the better-ranked team)

To calculate the Weighted RRRV for a ranking, just sum the violations for all games where the loser has a better rank than the winner and divide by the number of teams ranked by the rating.

Detailing Summaries

We can also summarize WRRVs by team. Here we just sum the game weights for all games where the team lost to a worse-ranked opponent or beat a better-ranked opponent according to any rating, and divide by the number of ratings that ranked the team.