Too-early Ratings

February 22, 2014

I have added the link for the Current RPI to the menu, even though it isn't of much use to anyone who isn't just interested in how the formula works. The table is ordered by the "new RPI" but the "Base RPI" values and ranks are also included. The RPI "formula SOS" (not to be confused with schedule strength based upon opponents' RPI) is the same for both ratings.

I do not care much for the new version - it overstates home field advantage considerably. For my interconference comparisons, "gory details" pages and pairwise matrix reporting I will be using the base RPI values. Don't look for that kind of analysis until the field is more nearly connected, about 2500 total games into the season. (See The 2014 Season.)

Of more interest this early is the directed games graph, mainly because watching it change as the field becomes more connected provides some insight into how the ratings systems work. The Second-Order Winning Percentage report isn't a rating itself but if one team has played three opponents and has winning paths to 126 other teams it has more impressive wins than a team with three opponents and winning paths to 85 other teams.

The basic idea is to compare each team that has played to every other team based upon the A→B→… chains connecting them, where → is a series win or tie. For each team pair A & B define WW, LL, TT, and UU as follows:

• IF the A→…→B chain is shorter than the B→…→A chain
          or
  the chains are the same length but there are more A⇒B paths than B⇒A paths
  THEN add 1 to A's WW value and to B's LL value.
• IF the length and number of A⇒B and B⇒A chains are the same
  THEN add 1 to both A's and B's TT values.
• IF there are no such paths in either direction
  THEN add 1 to both A's and B's UU values.

( WW + TT÷2 )

( WW + LL + TT + UU )

You can get a feel for the directed games graph by following the links to team pages that list out the shortest winning chain to each other team for which there's a path in either direction. Last year's report (produced after the CWS) demonstrates what the report is like after a full season.

Neither of these metrics is a good rating on its own, but knowledge of how the directed graph looks at any given time illustrates the kind of detail that advanced rating systems require.