RPI
This RPI uses only a team's winning percentage, its opponents' combined
winning percentage, and its opponents' opponents' combined winning
percentage to determine a numerical score (the formula the NCAA started
using for 2004-05 also takes road wins and home losses into account).
The weights given to each
component of the score are 25%, 50%, and 25% respectively. Various
published RPIs may differ from the NCAA's (and each other) because of
differences in computing opponents' and opponents' opponents' winning
percentage. For example, if team X beat team Y, does team Y's loss to
X count against X in X's opponents' winning percentage? The NCAA's
answer (and mine) is supposedly "no."
Dr. Glenn's Power Index
Dr. Glenn's Power Index uses an iterated method to determine each
team's power index. Before each iteration, each team is assigned the
same power index (perhaps 60.0). During each iteration, each team is
given a grade for each game based on the opponent's power index and
the margin of victory (with some consideration given to not having
blowouts affect the final power index). So a team may be graded
higher for beating a good team by just 1 point than it would be for
beating a bad team by 20. Once the grade for each game is determined,
the average grade is determined for each team, and that value is used
to recompute grades on the next iteration. All teams start with the
same power index, and as we progress through the iterations, good
teams will have their power indices rise while bad teams will have
theirs decline. After enough iterations, things generally settle down
and the final numbers are output. (One problem with my current method
is that the numbers do not always converge -- some teams' power
indices may rise and fall a significant fraction of a point over a
period of ten or so iterations. In these cases, we have to stop after
a large number of iterations and take average power indices over the
last several iterations.)
The above is the basic idea for many other computer rankings; these will differ primarily in how the grade for each game is computed.
All in one(Power, RPI, Strength of Schedule)