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Wednesday, March 11, 2009

CB: RPI sucks; Enter the cRPI

Since 1981, college basketball fans and selection committees have suffered under the tyranny of the Ratings Percentage Index (RPI), perhaps the worst rating system in all of sports.

And why, you might ask, is the RPI such a waste of intellectual effort? Quite simply, it violates the first law of rating systems: If we are to only consider wins and losses (which is a mistake, but politically correct), we should never penalize a team for winning, regardless of the quality of the competition. Any time a team plays they risk losing-and a meaningful rating system should reflect that. The RPI seems to believe that beating NJIT somehow makes your team less deserving, and that's a load of crap.

So, out of respect for sports of all ball shapes and sizes, I have corrected the RPI. Consistent with the philosophy of the RPI, the cRPI only considers wins and losses, opponent's winning percentage and opponent's opponent's winning percentage-but it is a much more valid reflection of reality.

The cRPI looks a bit more complicated than the RPI, but it really only requires one extra step to calculate. It uses products instead of sums and logs instead of more sums, but its all the same to a computer.

So, how does the cRPI perform. First, I correlated the cRPI, the RPI and a team's winning percentage. A common, and valid complaint, against the RPI is that a team's winning percentage makes up only 25% of the equation. At r=.86, the correlation is actually quite high, but not as high as .96, the correlation between winning percentage and and a team's cRPI.

But the RPI also accounts for strength of schedule. The cRPI and RPI would use the same SOS metric, but use them in different ways. To compare the two, I have compared to two scales to the AP poll as of March 9. The cRPI rank correlates with the AP poll at r=.82 while the RPI rank correlates at only .69. My corrected RPI not only does not undervalue winning, but it is a significantly better reflection of how people judge teams.

the cRPI also has some real nice additional features-it is completely decomposable, it will tend to approximate a normal distribution at both the national level and in the sampling distribution of individual teams, and, relatedly, it can be used for statistical testing and setting rough odds for a game outcome. The link below connects to the complete rating and ranking of the 340 some division I college basketball teams.