My Lazy Lazy Lazy Lazy RPI

EDIT/UPDATE: I'm not very happy with the math here.

I have constructed a very lazy RPI, that is more theoretically sound than the RPI.


Considering the linear version of the Log5 win-percentage formula, we could (lazily) assume the following:


Season Win%= 0.5 + Real Win% - Opponent's Real Win%


Therefore:
1) Real Win% = Season Win% + Opponent's Real Win% - 0.5


and


2) Opponent's Real Win% = Opponent's Season Win% + Opponent's Opponent's Real Win% - 0.5


If we assume (lazily) that "opponent's opponents" play average (.500) teams, we can then also assume that their Season Win% equals their Season Win%, like so:


3) OOSeasonWin% = 0.5 + OORealWin% - .5
4) OOSeasonWin%=OORealWin%
So we can replace "Opponent's Opponent's Real Win%" in #2 with "Opponent's Opponent's Season Win%"

When we replace Opponent's Real Win% with #2, we get


5) Real Win% = Season Win% + (Opponent's Season Win% + Opponent's Opponent's Season Win% - 0.5 )-0.5
6) Real Win% = Season Win% + Opponent's Season Win% + Opponent's Opponent's Season Win% - 1


or as the RPI would have it,
RPI = WP + OWP + OOWP - 1




So in theory, Win%, Opponent Win%, and Opponent's Opponent Win% should all be weighted 'equally.'