Percentage Index 2
The Percentage Index 2 is the result of analysis motivated by Boyd Nation's observation that the RPI did not characterize division one baseball teams as well as it apparently does division one basketball. The hypothesis was that baseball was more "regional", but measurement showed that baseball was the least "regional" of division one college sports. The "problem" with the RPI turned out to be fundamentally systemic - the way it is defined there is a lot of duplication of WP in OOWP and OWP in OOWP, and that is magnified in sports like baseball where the most common relationship between opponents is a 3-game series.
The theoretical justification for the RPI is sound - winning percentage against teams with a winning percentage against other teams ought to be able to be combined with the other teams' winning percentage against the rest of the field to relate a team to the field. But the method used includes the team's own WP in the "rest of the field" category, and its opponents' WP in the "rest of the field" for opponents who have played the same team(s) as the team for which the RPI is being calculated.
The duplication of WP in OOWP and OWP in OOWP is not as big a problem in basketball, because it is rare for teams from different conferences to play more than one game, but it is standard in baseball for a team-pair to play a two or three -game series. The RPI definition counts the duplicated OWP and OOWP values for each game played.
Another systemic problem is that the RPI's combination of WP and SOS is additive. A winless team could theoretically have the best RPI just by losing to only undefeated teams, and then when other teams also beat the 0-fer team, they get higher RPI ratings because the team they beat lost to better teams than them. The PI2 combines WP and its version of SOS by multiplying the components, so an oh-fer winds up as zero, not "how good the teams are you lost to" and the teams that beat an oh-fer don't get credit for its opponents losing to a better team than them.
SOS2
The SOS component of the PI2 calculation includes OWP and OOWP, but defines those to be consistent with the WP definition and precludes duplication. A game can contribute to WP, OWP, OOWP, or none of the above, but cannot contribute to more than one bucket. OWP is just the sum of opponents' wins against other teams divided by that sum plus the sum of opponents losses against other teams.
The OOWP is similarly defined, but unlike the RPI it excludes games involving the team in question and games involving other opponents. A game can contribute to only one of WP, OWP, or OOWP. The definition of SOS2 is
| ( #OO × OWP + #O × OOWP ) |
|
| ( #O + #OO ) |
OWP is weighted by the number of teams against which the record was achieved, and OOWP the number of teams required to connect the team in question to the Opponents' opponents. On the report CI is the sum of the number of opponents and unique opponents' opponents, and GI the number of games that contribute to either WP, OWP or OOWP.
PI2
Since the SOS is in the same units as WP and there is no duplication in the different WPs, we can combine the SOS and WP by multiplying instead of adding as in the RPI. This avoids the problem noted above where a winless team can have too high a rating just by losing to strong teams. The actual formula is the geometric mean of WP and SOS2: