Thursday, March 26, 2009

Post-Mortem: Pairwise Mathematics

Earlier this week, I took a look at the key differences between the RPI and KRACH. KRACH, I feel, is a far superior methodology for assessing teams and accounting for varying strengths of schedule. Both the RPI and KRACH attempt to do the same thing, but the RPI is only one part (even if it's the most important part) of the PWR. Using the same data from RPI's rankings page, I put together this analysis of the various components and how they relate to one another.

This data again comes from games complete through 3/21, more recent data has altered the rankings slightly, but the relationships between the various systems is more important than the individual ranks of each one.

In this chart, each comparison is relative to the PWR. The three colored columns show the relationship of each ranking to the others.

Like the previous comparison of just KRACH and RPI, the comparison here of KRACH and PWR shows how similar the PWR and the RPI are - often only varying by one or two spots.

The takeaway message is that the PWR, despite all its obvious flaws - the TUC Cliff, the small sampling of COp games - will never be much more than a gussied up version of the RPI.

Wisconsin always seems to be at the forefront of PWR controversies. Back in 2005, Wisconsin was in the news because of the TUC Cliff, where they would have been better off losing their first round series against UAA. In 2008, it was UW sneaking in to the touranment with a sub-.500 record - fueling conspiracy talk due to UW's hosting a regional that season.

How much of that is just luck, and how much of it is the product of a flawed system?