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Theoretically Correct RPI, Part I

The Rating Percentage Index, or 'RPI' is College Basketball's tamer BCS computer system (i.e. - it's unfair). By weighting three simple numbers, it assigns each team a score.

RPI = (.25 * Team's Winning %) + (.5 * Opponents' Winning %) + (.25 * Opponents' Opponents' Win%)

However, a better methodology would be to reverse-engineer Bill James' Log5 method and adjust for a teams' schedule.

The simpler (non-adjusted) version looks like this:
WPct = .500 + A - B ( which means: Team's Win% = .5 + Real Win% - Opponents' Real Win%

A little explanation is required here: Bill James' values for A and B are based on how often they beat teams in general. That is to say, if a team has played EVERY team on equal footing (a perfectly adjusted strength of schedule).
the number we want is "Real Win%," so with some algebra, we get: Rwin%=Twin%-.5+O.Rwin% where O.Rwin% roughly equals: O.Rwin%=OTwin%-.5+O.OTwin% (which we get by estimating that the "O.OTwin%" or "Opponents' Opponents' Team Winning%" is roughly equal to their "Real" win %)
Therefore, a team's "real" win% roughly equals:
=Twin%+O.Twin%+O.OTwin%-1  This shows us that a teams' win%, opponents' win%, & opponents' opponents' win% are all roughly EQUALLY weighted in figuring out their 'real' value.
So a better simple RPI would be  RPI= Team's Winning % + Opponents' Winning + Opponents' Opponents' Win% -1

In the next post, we will examine the 'normally-adjusted' version.

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