Firstly, sorry for the lack of updates. I've had a lot of personal projects in other areas that I've been working on lately. But don't worry, MVP ratings, team ratings, etc, will all be coming back soon.
For now, here's my formula for the 'theoretically correct RPI.' The NCAA uses weights that are somewhat intuitive, but also provably arbitrary/random. So without further ado, let's examine how to get the most accurate "Real Win%" from three values: Win%, Opponents' Win%, and Opponents' Opponents' Win%. This will give us an over and underrated ranking, and tell us which teams, by the NCAA's logic alone, get the short end of the at-large-bid-stick.
Using the same math behind my simple adjusted rebound percent, we will work backwards to accurately represent the three variables involved in the RPI.
first:
B2(Opponents' Real Win%)=A1*B1/(1-A1-B1+2*A1*B1)
where A1=opponents' raw win% and B1=opponents' opponents raw win%
A3(Team's Real Win%) = A2*B2/(1-A2-B2+2*A2*B2)
where A2=raw team win%, and B2=opponents' real win%
I'll do some data mining to get this data officially for all NCAA teams soon, adjusted for home/away...skipping the first step in this equation makes for some strange results. One caveat of this formula is that all 0% and 100% teams remain that way (i.e. Kansas gets the same value as San Diego St.) More soon!
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