Copyright 2006, Paul Kislanko

About the ratings

Bucklin Maority The Bucklin Majority is not a rating system itself. It's a meta-rating that finds a "consensus" among other ratings by assigning the team the best ranking for which a majority of all ratings agree the team should be ranked that high or higher. For details see this article.
ISOV The Iterative Strength of Victory is a modification of Boyd Nation's Iterative Strength Rating that takes into account the "Strength" of a win compared to a "standard strength."

The ISR (and ISOV) can be defined as a recursive relationship between a team and its opponents, the opponents' relationship to their opponents, etc.

While the ISR is based purely upon wins and losses, the ISOV depends upon the percentage of total points scored by the winner compared to the average of that percentage for all games played.
SOVgame = ( Winner's Score - Loser's Score )

( Winner's Score + Loser's Score )

The ISR uses opponent's ISR ± 25 at each iteration, the ISOV uses

opponent's ISOV ± (TotalPoints_per_game/2 × SOVgame/meanSOVall geams)

The ISOV has many of the characteristics of a predictive system, but unlike most of those it is not true that if ISOV(A) > ISOV(B) then team A would be predicted to win. Rather, the ISOV ratings are useful for normalizing scoring statistics. If SOSISOV is the average of opponents' ISOV values, then ISOV(A)/SOSISOV(B) can be used to determine how many points team B can be expected to score against team A (divide team B's average points-per-game by this factor) and can be expected to allow team A to score (multiply team A's average points per game by this factor).

There's no simple way to order the teams such that the higher rated should be expected to beat a lower rated, unless the home field advantage is zero. The home field advantage is not a function of the rating values, though, so the ISOV alone does not score well on traditional retrodictive violation measurements. When used as input to other ratings that use its SOS data to normalize scoring data, though, the results are reasonably close to actual outcomes.